Estimation of acoustic parameters for metallic and composite configurations with experimental validation

Abstract

Acoustic energy is the primary source of vibration input to a Space Launch Vehicle. The Sound Pressure Level produced by high velocity gases can have adverse effect on subsystem reliability if not subsided to an allowable limit. In this research, the theory underlying the transfer matrix approach is described first followed by a description of the experimental setup using Impedance tube. Various results, including the absorption coefficient and normal incidence Transmission Loss are presented for an acoustic insulation of variable Melamine Foam thickness from 25 mm to 70 mm; different Honeycomb / Carbon sandwich; and metallic structures. The results are first estimated numerically using COMSOL and later validated experimentally. The working frequency range is described with the placement of small and large diameter tubes from 31.5 Hz to 8000 Hz. The resonance features are obtained due to sample constraint around its edges. The acoustic characteristics of Melamine Foam with different thicknesses are presented to optimize acoustic insulation blanket within Payload Fairing to protect satellite and other avionics from harmful Sound Pressure Level. Since the primary vibroacoustic environment occurs at the very beginning of a mission, such failures are likely to have a greater mission impact than failures induced by other space environments over time. Consequently, an optimized acoustic insulation is mandatory for Payload Fairing to attenuate acoustic loads up to a desired level. This approach of sound attenuation is equally applicable for other applications which are vulnerable against acoustic loads.

Keywords

Transmission loss honeycomb/carbon face sheet sandwich panel melamine foam sound pressure level impedance tube

Introduction

An acoustic noise requirement on spacecraft is defined to ensure the structural integrity of the vehicle and its components in the vibroacoustic launch environment. It can induce dynamic loads comparable or even greater than other excitation sources such as structural resonance or coupled structure-fluid interaction. Flowing are some reason which explains that Acoustic noise is important compared to other phenomena:-

⁃ Due to very high magnitude compared to other excitation sources. Rocket launch can produce acoustic load around 180 dB, particularly near the launch pad. These high intensity pressure waves cause vibrations that can damage structural components.

⁃ Acoustic loads are of broadband nature, and can excite multiple modes, making it more dangerous than a single – mode resonance.

⁃ Acoustic loading can dominate the coupled effect (aero-elastic environment) because it occurs in the immediate proximity of the noise source (the engines).

Some notable failure of launch mission due to excessive Vibro-acoustic loads are Apstar 2 Launch (1995), Mercury – Atlas 1 (1960), Glory Satellite Launch (2011), Arian 5 Flight 501 (1996), Space shuttle Columbia (1981), Titan III (1970), and Proton Rocket. Acoustic noise are generated from the propagation of sound pressure waves through air or other media. During the launch of a rocket, such noise is generated by the release of high velocity engine exhaust gases by the resonant motion of internal engine components and aerodynamic flow field associated with high speed vehicle movement through the atmosphere. This environment places severe stress on flight hardware and has adverse impact on subsystem reliability. The amplitudes of acoustic loadings are generally very high and required to be diminished to save electronic components. In space missions, satellite launch system encounters a wide range of broadband noise loads. Therefore, acoustic emission and Transmission Loss (TL) must be studied during critical instants of a launch system including maximum dynamic pressure condition, transonic flight condition and lift off. For the determination of Sound Pressure Level (SPL) inside the Fairing, a vibro-acoustic environmental analysis must be carried out. Numerical prediction of vibro-acoustic response of satellite launch vehicle is a pre-requisite so that the noise control engineer could effectively optimize the vehicle system.^1–4

While designing for acoustic noise attenuation, the upper parts of the launchers such as Payload Fairing and bays have the prime importance. Glaese and Anderson⁵ used two passive techniques to reduce SPL in Fairing. The first is by increasing the TL along the Fairing’s wall, this approach will increase the design cost and reduce mass ratio of optimized design. The other approach involves the application of acoustic blanket which is more commonly used to absorb acoustic loads. Among commonly used porous materials, Melamine Foam (MF) is characterized by its light weight, high flexibility and high sound absorption coefficient within a mid-high frequency noise range.^6,7 Moreover, MF is experimentally demonstrated by National Aeronautics and Space Administration (NASA) to have superior noise attenuation performance as traditional acoustic blankets.^8–10 Many researchers demonstrated that MF lining and different porous material could achieve noise reduction up to 4–8 dB within the low and medium-frequency range.^11–18 Typically, one of the most common manufacturing material for Payload Fairing is honeycomb/carbon face sheet sandwich panel with MF lining as acoustic insulation.¹⁹ There are many researchers who estimated/measured TL for honey comb sandwich panel using different analytical and numerical techniques supported by experimental results.^20–29 The acoustic properties of a porous material are first estimated analytically. Therefore, Finite Element Techniques are extensively useful in resolving problems arising in different industrial sector. COMSOL is a commercially available finite element software package which can be used for modelling acoustic propagation and transmission problems.^30–32

For experimental validation of results obtained using FEA, the impedance tube method is commonly used to measure TL for different materials.³³ Bolton et al.³⁴ described a method for measuring the normal incidence TL and related acoustical properties of a sample placed in a four-microphone standing wave tube. The use of the impedance tube is not only limited to measure the acoustic parameter of porous material but also used in variety of applications such as fluid and soil TL measurements.^35–38

The fluctuating pressures associated with acoustic energy during launch can cause structural vibration over a broad frequency band, ranging from 20 Hz to 10,000 Hz. Such high frequency vibration can lead to rapid structural fatigue. The acoustic noise requirement assures that flight hardware particularly structures with a high ratio of surface area to mass, are designed with sufficient margin to withstand the launch environment.

In this research, the theory underlying the transfer matrix approach is described first, then followed by a description of the experimental setup using impedance tube. Various results, including the normal incidence TL are presented for an acoustic insulation of variable MF thickness with comb/carbon sandwich and metallic structure numerically and experimentally. The working frequency range is described with the placement of small and large diameter tubes. The resonance features are obtained due to sample constraint around its edges. The acoustic characteristics at different thicknesses of MF are presented for estimation of required insulation blanket within Payload Fairing to protect satellite and other avionics from harmful SPL. This technique is equally applicable for other applications which are vulnerable against acoustic loads.

Acoustic parameters and testing methodology

Acoustic parameters

The Absorption Coefficient (AC) shows the capability of insulating material to absorb sound energy as shown in Figure 1. The value of AC is measured by the ratio of absorbed sound intensity and is incident sound intensity with range of 0 ∼ 1. The value of 1 shows the total absorption whereas the value of 0 suggest no absorption.

Figure 1.

Different components of sound energy passing through an acoustic insulation.

The Transmission Loss (TL) is the accumulated decrease in sound energy by a particular medium which is propagating from a source. As the acoustic wave propagates outwards from the source, the intensity of the signal is reduced with increasing range due to spreading and attenuation. The Sound Pressure Level (SPL) is a logarithmic measure (expressed in decibels) of the effective pressure (in RMS) of a sound wave relative to a reference value. It can be used to quantify actual acoustic loads generated from the engine ignition or during flight. It can be defined as:-

dB = 20 Log (\frac{P}{Pref})

These are acoustic loads over the spectrum of frequencies at which the pressure can fluctuate. The internal sound pressure can be evaluated by subtracting the TL from external SPL. Where p is measured in Pascals (Pa) and Pref is ostensibly the audible limit of the human ear, with a reference value defined as 2 × 10⁻⁵ Pa.

When pressure levels are defined with these methods, it is convenient to provide a measure of the overall acoustic noise intensity. The overall sound pressure level (OASPL) can be calculated as the decibel equivalent of the mean square (MS) pressure. It should be noted that this value is greater than any individual SPL in the specification, because it represents an intensity of the spectrum as a whole. To quantify the acoustic environment, launch vehicles are often instrumented with internal microphones to measure noise levels within Fairing. This data is telemetered to the ground for processing and ultimately plotted in the form of a SPL versus frequency spectrum. Since the acoustic forcing function is stochastic, depending on many atmospheric and other variables, data from a number of such flights are generally gathered and developed to encompass the historical record of microphone data. The OASPL can be calculated as:-

P_{i} = {Log}^{- 1} (\frac{SPL (dB) x P ref}{20})

O A S P L = 20 Log \frac{\sum_{i = 1}^{n} P_{i}}{P ref}

where P_i is the pressure at respective frequency point for entire frequency range, i and n are the first and last frequency point of 31.5 Hz and 8000 Hz respectively.

Testing methodology

An acoustic testing facility comprised of Reverberation chamber which is used by the space agencies in order to qualify both Acoustic blanket and Payload. For the qualification of acoustic blanket, the external acoustic profile of SPL is given as input whereas for the qualification of Payload internal SPL are applied as input. The testing facility is huge, requiring massive foreign exchange, time, technical expertise and cost. Small Payload are not flexible, thus only random vibration test is recommended. Payload Acoustic qualification is not required due to structure having low surface area to mass ratio. Forging in view, existing testing setup of Impedance Tube is utilized in combination with estimated external SPL as shown in Figure 2. The experimental results are supported by numerical simulations. This research serves the preliminary objective of acoustic qualification performed by an alternate approach instead of huge reverberation chamber. The desired SPL inside Payload Fairing can be achieved by optimized acoustic insulation of structure configuration.

Figure 2.

Testing methodology using impedance tube.

Selection of configurations

The spacecraft is protected by Payload Fairing that shields it from various environmental effect including high-speed air-stream, acoustic noises, aerodynamic loads and heating etc. The Fairing provides the favorable internal environment for spacecraft. The Payload Fairing consists of dome, power series, cylindrical and reverse cone section (boat tail) as shown in Figure 3. All of these sections must provide enough capability to mitigate harmful sound effect up to desired level. Therefore, the Fairing skin is manufactured with specific material and configuration to provide required internal SPL. For this research, following three configurations are considered:-

1. Configuration 1
a. Material	Composite
b. Carbon prepreg (T700S-12K) thickness	1.30 mm
c. Honeycomb (AL 5056) thickness	16 mm.
d. Melamine Foam thickness	30∼70 mm
2. Configuration 2
a. Material	Composite
b. Carbon prepreg (T700S-12K) thickness	1.30 mm
c. Honeycomb (AL 5056) thickness	16 mm
d. Melamine foam thickness	30∼70 mm
3. Configuration 3
a. Material	Aluminum 2024
b. Aluminum thickness	3.00 mm
c. Melamine foam thickness	30∼70 mm

Figure 3.

Three selected configurations of Payload Fairing.

As per international practice, the thickness of acoustic foam can reach up to 3 inch depending upon the base composite configuration and diameter of Payload Fairing.^39–41 Therefore, for this research, the MF thickness is selected from 30 mm to 70 mm. The total thickness of sample cannot exceed 100 mm as experimental constraint to avoid interaction of the sample with microphone.

Analytical relation

Absorption coefficient

The material absorption coefficient (AC) is an important parameter that is characterized by its normal or random incidence characteristics. The ISO standard 10534-2-(1998) illustrates the well-known process to determine the absorption and impedance characteristics of noise-insulating materials through the “two microphones” or “transfer-function” method as shown in Figure 4.

Figure 4.

Two microphone impedance tube for AC measurement.

The transfer function method depends on the ratio of the SPL of the reflected and the incident wave at termination (at x = 0), given by equation (1).⁴² The AC for materials is given in equations (1)–(4).

P (x) = P_{i} (x) + P_{r} (x) = A e^{- j k x} + B e^{j k x}

(1)

R = [(H_{12} - e^{- j k s}) / (e^{j k s} - H_{12})] (e^{j k (s + x_{2})})

(2)

H_{12} = \frac{P (x_{2})}{P (x_{1})} = \frac{S_{12}}{S_{11}}

(3)

α = 1 - | R^{2} |

(4)

The AC for random incidence can also be measured in a reverberant room, where the diffuse acoustic fields can be simulated with approximation. Internationally, the impedance tube method is widely adopted for determining the sound absorption coefficient.^43–46

Transmission loss

The Transmission Loss (TL) computation of noise absorbent materials is essential in building acoustic and environmental noise reduction studies. Internationally, impedance tube method is widely adopted for determining TL. Generally, sound TL measurement tubes comprise three parts: the upstream tube, the sample holder, and the downstream tube (Figure 5). The TL can be measure with enclosed and open boundary conditions in the downstream tube with a semi-anechoic termination. Bolton et al.⁴⁴ modified a sound absorption measurement impedance tube so that it could be used in measuring the TL of automotive sealant materials. Ho et al.⁴⁵ measured the TL of perforated panels with an impedance tube somewhat similar to Bolton’s measurement system, the differences between two is the type of sample holder and a monotonic wave. More recently, a commercial TL measuring system, proposed by Ryu,⁴⁶ has become available i.e., the B&K 4206T tube kit for TL measurement.

Figure 5.

Four microphone impedance tube for TL measurement.

The impedance tube used for computation of TL is shown in Figure 7. A set of two microphones (1 & 2) are mounted in the up-stream tube, similarly two microphones (3 & 4) are mounted in the downstream tube to measure both incident and reflected waves. The reference position (x = 0) is given as the front surface of a sample, $x_{1}, x_{2}, x_{3}, x_{4}$ denote each microphone’s position. If a one-dimensional plane wave in the tube is assumed to be $p e^{j (w t - k x)}$ then the Fourier components of the sound pressure at micro-phone placed at positions 1, 2, 3 and 4, after eliminating the time-dependent term, can be expressed by the following equations.^47–49

p_{1} = A e^{- j k x_{1}} + B e^{j k x_{1}}

(5)

p_{2} = A e^{- j k x_{2}} + B e^{j k x_{2}}

(6)

p_{3} = C e^{- j k x_{3}} + D e^{j k x_{3}}

(7)

p_{4} = C e^{- j k x_{4}} + D e^{j k x_{4}}

(8)

where,

k

is the wave number,

A

and

B

are the incident and reflected components of upstream tube respectively.

C

and

D

are the transmitted and reflected components of downstream tube respectively. Equations (5)–(8) can be rearranged to solve for the coefficients

A

D

as shown in equations (9)–(12). In order to simplify the equation, two microphones are placed at an equal distance. TL is defined by the ratio C/A and the TL equals

- 20 \log | H_{t} |

: as shown in equation (13).

A = [j (p_{1} e^{j k x_{2}} - p_{2} e^{- j k x_{2}}) / 2 \sin k (x_{1} - x_{2})]

(9)

B = [j (p_{1} e^{j k x_{2}} - p_{2} e^{- j k x_{2}}) / 2 \sin k (x_{1} - x_{2})]

(10)

C = [j (p_{1} e^{j k x_{2}} - p_{2} e^{- j k x_{2}}) / 2 \sin k (x_{1} - x_{2})]

(11)

D = [j (p_{1} e^{j k x_{2}} - p_{2} e^{- j k x_{2}}) / 2 \sin k (x_{1} - x_{2})]

(12)

T L = 20 \log | (e^{j k s} - H_{12}) / (e^{j k s} - H_{34}) | - 20 \log | H_{t} |

(13)

where,

s = | x_{1} - x_{2} | = | x_{3} - x_{4} |

H_{12} = p_{2} / p_{1}

is the transfer function, which is the ratio of the Fourier-transform component between the sound pressures at positions 1 and 2 and

H_{34} = p_{4} / p_{3}

is the transfer function, which is the ratio of the Fourier-transform component between the sound pressures at positions 3 and 4

H_{t} = \sqrt{| S_{d} / S_{u} |}

. White noise was generated by the spectrum analyzer and the noise signal was simultaneously measured using all four microphones.

Analytical relation

Absorption coefficient

Pressure acoustic model of FEA software is utilized to compute the absorption properties of open cell, acoustic proofing foam. In porous materials, acoustic wave travels through a complex arrangement of small interconnected pores. Since the pores are small, losses usually arise due to heat conduction and friction. Porous foams are not only used in the sound proofing of rooms and ducts but also to mitigate reverberation problems in closed spaces. The aim of this model is to distinguish the absorption properties more specifically, the surface impedance and the AC of acoustic foam in terms of frequency. A 2D model is employed to simulate the absorption behavior of the porous material over a wide range of frequency band.

Melamine foam is modeled using the Pressure Acoustics interface’s rigid Biot equivalent fluid condition. Figure 6 depicts the geometry of the modeled system, in which an incident sound field hits the porous melamine foam layer at angle θ. The incident wave has wave vector k . The dotted lined indicates the model domain’s boundaries. A portion of width W is modelled and periodic Floquet boundary conditions on the left and right boundaries are applied to extend the domain to infinity. At the top, a plane wave radiation condition with an incident wave is used. The thickness of the porous melamine layer is Hp and the height of the modeled air region is H.

Figure 6.

Geometry of the modeled system.

To get information about the scattered, incident, and total fields, an incident pressure field at the top are used where the plane-wave radiation condition are applied. The incident pressure is given as:-

P_{i n c} = e^{- i (k . x)} k = k_{o} (\sin θ, \cos θ)

(14)

where θ is the incidence angle and

k_{o}

is the wave number in the free field (air domain). The pressure p is the total field and the scattered field

P_{s c a t}

is given as

P_{s c a t}

= p −

P_{i n c}

. Note that this expression for the scattered filed is only valid for the air domain as the incident field is not know a priori in the porous material. The absorption coefficient, which represents the ratio of the absorbed and incident energy, is defined as:-

α = 1 - | R^{2} | R = \frac{P_{s c a t}}{P_{i n c}}

(15)

where R is the pressure reflection coefficient that gives the ratio of the scattered to the incident pressure.

Figure 7 shows the schematic of the absorption model in which an incident sound wave strikes the surface of the porous MF. Only a small portion of width of the domain is modeled and the periodic Floquet conditions are applied on the left and right boundary to extend the domain to infinity. A plane wave radiation condition is applied at the top of the domain. MF is modeled as a porous elastic material and the material parameters used in the simulation model are listed in Table 1. A rigid surface is used at the bottom surface to eliminate the further transmission of the incident wave. The surrounding fluid domain is comprising of air. The acoustic pressure level computed from simulation is shown in Figure 7. Sound wave travelling from left to right and subsequent acoustic energy suppression is encountered in MF.

Figure 7.

Schematics and numerical simulation results of AC.

Table 1.

Melamine material parameters for AC computation.

Parameter	Value
Porosity	0.995
Flow resistivity	10,500 Pa·s/m²
Viscous characteristic length parameter	0.49
Thermal characteristic length	470 μm
Viscous characteristic length	240 μm
Tortuosity factor	1.0059

Transmission loss

The Poro-elastic waves interface method is utilized to compute TL. The Poro-elastic wave model describes as the small deformation elastic waves propagating in a porous material coupled in a fluid. The model accounts for the coupled displacement of the fluid and the structure which makes it a fluid-structure interaction problem. The 2D axisymmetric geometry is shown in Figure 8. The central portion contains Honeycomb/Carbon face sheet sandwich with MF lining and air in the rest of the system. The porous material is assumed to be isotropic with material properties listed in Table 2. Figure shows the acoustic pressure level throughout the domain where sound waves are travelling from left to right and subsequent acoustic energy suppression is encountered in all layers of materials. Honey comb/ Carbon sandwich structure is modeled as a rigid structure and MF as a porous elastic material.

Figure 8.

Schematics and numerical simulation results of TL for Configuration 1 & 2 (Left), Configuration 3 (Right).

Table 2.

Material properties for acoustic analysis.

Description	Unit	Material
Description	Unit	Melamine	Honeycomb	Carbon	Aluminum
Density	kg/m³	8	72.08	1583	2700
Young’s modulus	kpa	180	1.28e6	8.6e6	73e6
Poisson’s ratio	-	0.46	0.001	0.3	0.33
Biot-Willis coefficient	-	1	1	0.02	0.01
Porosity	-	0.995	1	0.02	0.01
Permeability of porous matrix	m²	1.5e-9	1	0.71e-10	0.05e-10
Tortuosity factor	-	1.0059	0.10	0.70	1

In this model, the acoustic properties of a simplified 2D axisymmetric particulate-filter like geometry are analyzed using the Poroelastic Waves Interface. The poroelastic wave model describes the small-deformation elastic waves propagating in a porous material coupled to waves in a fluid. The model accounts for the coupled displacement and is thus a fluid-structure interaction problem. The Biot-Willis coefficient is equal to the porosity for rigid porous materials and is equal to 1 for a soft porous material (or a suspension of solid in liquid). The fluid parameters are that of air including the compressibility which for an ideal gas is equal to (P₀)⁻¹, where P₀ is the absolute pressure (here 1 atm). The filter is characterized acoustically by the transmission loss T_loss (given in dB) as function of frequency f.

T_{l o s s} = 20 \log (| \frac{P_{i n}}{P_{o u t}} |)

(16)

where Pin is the inlet pressure and pout is the outlet pressure. When setting up the porous material model, you also need to specify whether to use the low-frequency (default) or high-frequency range approximation for the fluid viscosity. The transition between the two ranges is defined by the reference frequency fc given by the expression

f_{c} = \frac{ε_{p} μ}{2 π k p ρ_{f}}

(17)

where

ρ_{f}

is the fluid (air) density 1.2 kg/m3 and μ is the dynamic viscosity of the fluid (for air 1.810⁻⁵ Pa⋅s).

ε_{p}

is the porosity,

k p

is the permeability of porous matrix, and

μ

is dynamic viscosity.

Sample prepration

Melamine foam

MF is selected as porous material for sound attenuation which is available in block as shown in Figure 8(a). It is an open cell foam made from melamine thermoset polymer resin. The material properties are shown in Table 3. This foam comprises of three-dimensional network structures consisting of slender and easily shaped filaments. Key characteristics of this foam are:

• Low density and high acoustic absorption capacity

• Good heat insulation properties

• Can withstand temperature up to 240°C

Table 3.

Material properties of MF.

Parameter	Unit	Value
Density	kg/m³	8
Young’s modulus	kpa	180
Poisson’s ratio	-	0.46
Tensile strength	kpa	>120

Initially, MF block is cut in five selected thicknesses (30 mm, 40 mm, 50 mm, 60 mm, and 70 mm) using bend saw machine. Later, Foam samples of two different diameters (100 mm and 30 mm) are obtained to measure TLs using two different sizes of impedance tube to get required frequency range as shown in Figure 9(b) and (c).

Figure 9.

Manufacturing of MF samples, (a) Melamine Block, (b) Samples of required Sizes.

Composite configuration

For composite configurations 1 & 2, initially, carbon face-sheet is prepared as per required sheet thickness (1.3 mm & 2.0 mm) using placement of carbon prepreg layers (Plan weave). Subsequently, rectangular samples of Honey comb/Carbon sandwich are prepared using honey comb core and carbon face sheets Figure 10(a) and (b). The final rectangular samples are then cut to get the samples of 100 mm and 30 mm diameter based on impedance tube diameter as shown in Figure 10(c). Finally, MF of different thicknesses (30 mm, 40 mm, 50 mm, 60 mm, and 70 mm) is applied with circular sandwich panel as shown in Figure 10(d).

Figure 10.

Manufacturing of MF samples, (a) Carbon & Honeycomb sheets, (b) Sandwich structure, (c) Samples of required diameter, (d) Sandwich sample with Melamine Foam.

The sample is comprised of three materials, a honey comb core, carbon face sheets and MF lining at the inner most position. For configuration 3, aluminum 2024 is used as base material with two diameters of 100 mm & 30 mm and MF lining is applied in similar manner. The material/geometrical properties of each material is shown in Tables 4–6. All the constituents of sandwich structure possess individual distinct set of properties but the overall TL will depend on the properties of finished sample.

Table 4.

Material/geometrical properties of honeycomb core (AL 5056).

Parameter	Unit	Value
Cell size	mm	3.2
Density	kg/m³	72
Compressive strength	MPa	4.3
Compressive modulus	Mpa	1275

Table 5.

Material/geometrical properties of carbon preg (T700S-12K).

Parameter	Unit	Value
Tensile modulus	Gpa	55
Tensile strength	Mpa	912
Fiber arial weight	g/m²	190
Thickness (config. 1)	mm	1.3
Thickness (config. 2)	mm	2.0

Table 6.

Material/geometrical properties of aluminum (2024).

Parameter	Unit	Value
Young’s modulus	GPa	73
Tensile strength	MPa	75
Thickness	mm	3.0
Density	kg/m³	2780
Poisson’s ratio	-	0.33

Experimental setup

Introduction

The hardware comprises of impedance tube and data acquisition system with software code of VA-Lab2 IMP. The Transfer function method uses a set of two microphones to acquire specific pressure level by a sound generating source near the sample. VA-Lab IMP can accurately separate the incident wave from reflecting wave to measure TL. An extended frequency range can be obtained from the combination of measurement results gained from the tubes of different diameters. VA-Lab4 IMP supports four microphones transfer function method to measure TL [User’s Manual “Impedance Tube Test System”]. For both AC and TL, the working frequency range is defined Tube diameter, distance between two microphones and the distance from the sample to the nearest microphone. The experimental frequency range is 64 Hz to 6300 Hz and the data out of this pre-defined range will be inaccurate. The accuracy of the measured results depends on many other environmental parameters including, Atmospheric pressure, Temperature, Humidity, Velocity and Characteristic impedance

Testing setup

Absorption coefficient

The setup of the absorption coefficient testing system is shown in Figure 11. The Source tube and Sample holder are necessary to measure the AC of the material. The sound will be generated via a loudspeaker located at the extreme left side, and the sample holder is located at the extreme right of the tube. Two microphones are used to measure the amplitude and phase of both waves. The specifications of microphone and loud speaker are mentioned in Table 7. Data acquisition board & a Lab. VIEW system are used to gather and process the data. Microphones are positioned to capture all frequency ranges from 64 Hz to 6300 Hz.

Figure 11.

Complete experimental setup for the measurement of AC.

Table 7.

Specification of microphone and loud speaker.

Tube type	Microphone	Loud speaker
Large tube (SW 422)	Size: 1/4 inch diameter	Size: 4 inch diameter
	Sensitivity (±2 dB): 50 mV/Pa (−26 dB re 1 V/Pa)	Power: 20 Watts
	Output impedance: < 110 Ohm	Rated impedance: 8 Ohm
	Dynamic range: 29dBA ∼ 127 dB	Working freq: 20 Hz ∼ 8000 Hz
Small tube (SW 477)		Size: 2 inch diameter
		Power: 3 Watts
		Rated impedance: 8 Ohm
		Working freq: 200 Hz ∼ 8000 Hz

Transmission loss

Setup for measurement of TL is shown in Figure 12. Sample holder is replaced by extension tube. The sound is generated via loud speaker placed at extreme left position; extension tube is attached with the source tube at extreme right, and sample is placed between source tube and extension tube. Two microphones are positioned on the upstream and two are placed on the downstream region. Four microphones are used to measure the sound energy level before and after transmission. Data acquisition system processes these energy levels and computes TL. Microphones are positioned to capture desired range of frequencies from 64 Hz to 6300 Hz.

Figure 12.

Complete experimental setup for the measurement of TL.

As per testing standard, the loudspeaker should work at least 10 minutes before testing. The different positions of microphones work in different effectual frequency range and curves out of the range will be random. The test sample should fit snugly with optimized compression to prevent it from bulging. It is recommended to fill in the interspaces by using Vaseline or Plasticine between the sample and the tube. The test sample can be held firmly, if necessary, by adhesive tape or grease. Most of the specimen, even the uniform one, should be tested repeatedly. TL of the same sample in different diameter tubes will be dissimilar mostly because of the dimension of the specimens and the condition of specimens’ edge. Uncertainties to the determined acoustic material properties can be caused by samples material/placement, bias errors and reference plane definition.

Result and discussion

In this section, the AC and TL of MF only is measured and compared with results obtained via numerical simulation. Furthermore, the TL of all three selected configurations is measured, subsequently, internal SPLs of three composite configurations are estimated based on external SPLs and TLs for all selected MF thicknesses.

Absorption coefficient

The ACs of five samples (30 mm, 40 mm, 50 mm, 60 mm and 70 mm) are measured using both small and large tubes as shown in Figure 13 for working frequency range of 64 Hz to 6300 Hz. This range is achieved with three arrangements for both ACs and TLs. The first range from 63 Hz to 500 Hz is achieved with wide spacing of microphones. The second range from 400 Hz to 1600 Hz is achieved with normal spacing. The third arrangement is for 1600 Hz to 6300 Hz with small diameter tube and normal spacing of microphones. The flow resistance of the material under test is relatively low, and because the sample is effectively anechoically-terminated, most of the incident energy is either transmitted through the sample or is dissipated within it. As a result, the reflection’s magnitude is relatively low, consequently having a higher AC except at the lower frequencies where the edge constraint’s effect stiffens the sample. It may be seen, as expected, that the ACs are nearly unity, except at the lower frequencies.

Figure 13.

AC for 30 mm, 40 mm, 50 mm, 60 mm MF and 70 mm of MF.

Note also that there are resonance features at two different locations. This behavior is due to sample edge constraint on the normal incidence absorption loss of an elastic porous material. The two features represent the effects of the first two diaphragm-like modes of the samples in which the sample experiences a pure shearing motion. The frequencies at which these features occur are inversely proportional to the sample diameter and are directly proportional to the square root of the ratio of the shear modulus and density of the sample. Thus, the first resonance in the large tube case occurs at approximately one-quarter of the small tube’s resonance frequency. A similar relation exists in the difference of the impedance tube’s diameter (100 mm & 30 mm). These features are not visible in FEA results because the acoustic analysis is performed on an infinite plate sheet where the sample edge constraint effect does not exist. Furthermore, the difference of diameter does not exist in FEA simulation.

Figure 13 shows that the numerical and experimental results are in good agreement. The saturation in AC is achieved at lower frequencies with increased sample thickness. The saturation frequency and saturation value of each thickness is achieved comparatively at lower frequency for higher thickness samples. The magnitude of saturation value is also increasing with the increase of MF thickness. The value of 1.00 is achieved with MF thickness of 70 mm. It suggests that no further advantage can be extracted in terms absorption property with the increase of MF thickness (Table 8).

Table 8.

Saturation frequency and saturation value of AC.

MF thickness (mm)	Saturation Frequency (Hz)	Saturation Value
30	3150	0.89
40	2500	0.93
50	2000	0.98
60	1600	0.99
70	1250	1.00

Transmission loss

The TL of all five MF samples (30 mm, 40 mm, 50 mm, 60 mm and 70 mm) is estimated first through FEA and later validated with both large and small diameter impedance tubes as shown in Figure 14. It is shown that the TL increases monotonically with increasing frequency as expected for a porous layer. The working frequency range is from 64 Hz to 6300 Hz. The resonance features are at approximately 500 Hz and 2000 Hz in the large and small tube respectively. This behavior is typical of the effect of sample edge constraint on the normal incidence TL of an elastic porous material. Similar features are observed in the measurement of AC. Thus, the first resonance in the large tube case occurs at approximately one-quarter of the small tube’s resonance frequency. A similar relation exists in the difference of impedance tube diameters (100 mm and 30 mm). These features are not visible in FEA results because the acoustic analysis is performed on an infinite plate sheet where the sample edge constraint effect does not exist.

Figure 14.

TL for 30 mm, 40 mm, 50 mm, 60 mm MF and 70 mm of MF.

Nonetheless, a close examination of the data shows that the TL does increase with decreasing frequency below the first resonance in both the large and small tube results. Consequently, at low frequencies, the sample edge constraint causes the normal incidence TL of a porous sample measured in a tube to differ from that of a laterally infinite plane sheet of the same material as depicts in FEA results. This effect becomes more significant as the flow resistivity of the samples increases (therein increasing the strength of the coupling between the solid and fluid phases of the material), and the shear stiffness of the sample increases in proportion to its bulk density (increasing the frequency of the diaphragm-like resonances).

Figure 14 show that the numerical results obtained via commercial FEA software and experimental results are in good agreement for all five MF samples. It is observed that the trend of both approaches is same. However, variation in magnitude around resonance is observed due to variation in boundary condition. Experimental results for all five MF samples show that the magnitude of TL is continuously increasing with the increase in the MF thickness. The TL produced by the MF is extremely useful at low frequency to safeguard the avionics from low frequency SPL.

Initially, the TL of individual layer like carbon face sheet, honey comb core and aluminum sheet is measured to estimate the individual layer TL and to find few unknown material properties for numerical simulations. Later, the complete sandwich composite configuration with different MF thicknesses is considered to measure TL as shown in Figures 15–17. For configuration 1 & 2, the contribution of HC is negligible in overall TL. Whereas, the magnitude is increasing substantially with the addition of solid material like carbon face sheets which further increases with the addition of MF lining.

Figure 15.

TL of individual layer for configuration 1 with Carbon 1.3 mm and HC 16 mm.

Figure 16.

TL of individual layer for configuration 2 with Carbon 2.0 mm and HC 25 mm.

Figure 17.

TL of individual layer for configuration 2 with Aluminum 3.0 mm.

For configuration 3, the aluminum sheet has solid thickness of 3.0 mm causing the increase of TL with base material only. However, the magnitude of TL still increases with addition of MF lining. The MF lining gives the advantage of increasing the TL to more than 40 dB. Thus, the desired sound mitigation is achieved with combined structure. Eventually, these results are compared with numerical estimation to assess the accuracy and consistency. The results are found in good agreement as shown in Figures 18–20. The results are comparatively more consistent at higher MF thicknesses. Furthermore, the magnitude of average and maximum TL for each configuration is shown in Table 9. The highest values of these parameters is observed with configuration 2 and lowest for configuration 3. TL profile at different frequencies for all three configurations is plotted in Figure 21. The metallic structure has less TL because the sound can travel much faster in solids compared to carbon composite. Thus, the configuration 3 being metallic Fairing offers less resistance to sound energy.

Figure 18.

TL for 30 mm, 40 mm, 50 mm, 60 mm and 70 mm of MF for Configuration 1.

Figure 19.

TL for 30 mm, 40 mm, 50 mm, 60 mm and 70 mm of MF for Configuration 2.

Figure 20.

TL for 30 mm, 40 mm, 50 mm, 60 mm and 70 mm of MF for Configuration 3.

Table 9.

Comparison of TL for all three configurations.

MF thickness (mm)	Configuration 1		Configuration 2		Configuration 3
MF thickness (mm)	Max. TL (dB)	Avg. TL (dB)	Max. TL (dB)	Avg. TL (dB)	Max. TL (dB)	Avg. TL (dB)
30	41.73	16.70	43.38	20.10	16.38	14.39
40	42.44	18.13	49.46	22.13	19.56	15.38
50	46.32	20.12	50.63	23.46	21.12	16.88
60	47.23	20.99	52.55	24.81	20.99	17.90
70	49.55	22.46	57.91	26.17	23.20	19.09

Figure 21.

TL for all three configurations with 30 mm, 40 mm, 50 mm, 60 mm and 70 mm of MF.

Conclusion

The acoustic parameter of TL is investigated both numerically and experimentally with working frequency range of 64 Hz to 6.2 kHz for honey comb / carbon sandwich panel and MF lining. Three different configurations of aerospace structure with MF are employed to have better correlation of the acoustic parameters with respect to frequency and thickness. The resonance features are identified in TL measurements. Numerically computed parameters are validated using impedance tube setup and are found in good agreement. The configuration can be selected based on the internal sound pressure requirement which depends on the average TL at respective frequency. The absorption coefficient can help in evaluating the initial parameter for the utilization of acoustic attenuation performance of MF lining with different thickness. These results are very useful to estimate the acoustic characteristics of insulation blanket for different structure which are vulnerable against acoustic loading.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Behzad Ahmed Zai

Najam Us Saqib

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