Journal of Low Frequency Noise,Vibration and Active Control

The phase sensitivity of the condenser type acoustic transducers at low frequencies is crucial for locating large-scale natural and manmade activities, but is now commonly calibrated based on comparison methods. Although the primary method, which traces its sensitivity back to the international standard unit is few studied. Recently, the explicit sensitivity models of the condenser type acoustic transducers based on the laser-pistonphone technique are built, and can be used to study the phase responses of acoustic transducers at infrasonic frequencies. So that, in this paper, the phase sensitivities of acoustic transducers when its rear vent connected to the calibrating sound field or outside atmosphere are studied in detail. Secondly, time domain analysis of generated sound pressures by displacement excitation are derived to reveal the mechanism of phase variation. Calculations show two distinct sensitivities with 90° phase lead and −10° phase lag limits for vent in field and vent out field calibrations, which are dominated by the pressure leakage and heat conduction effects at infrasonic frequencies.

Based on the impact damper, a dynamic model of a non-fixed constrained collision system was established. The coefficient of restitution is used as the main control parameter to analyze the system’s periodic movement and its bifurcation region. The chattering movement characteristics of the system were revealed. The interval of restitution coefficient for the chattering of collision system under various mass ratio and frequency ratio was obtained. The results show that the chattering phenomenon occurs in the collision system when the coefficient of restitution is greater than 0.5; as the mass ratio decreases, the interval of restitution coefficient for chattering continues to expand; as the frequency increases, the interval of restitution coefficient for chattering narrows.

Dynamic characteristics of the asymmetric rotor system supported in axial-grooved gas-lubricated bearings are studied. In order to solve nonlinear dynamic response of rotor system effectively, a hybrid numerical model is established by coupling the motion equation of rotor with the rational function model of the gas film forces. The rational function model of the gas film forces of gas-lubricated bearing is established based on vector fitting theory. By using the hybrid numerical model, the repeated calculations of the unsteady Reynolds equation and gas film forces are avoided; the continuous rotor trajectory and the dynamic gas film forces can be calculated simultaneously; and for the rotor system supported in the same bearings, the computing cost can be saved effectively. The nonlinear dynamic responses of asymmetric rotor system supported in axial-grooved gas-lubricated bearings are investigated by trajectory diagrams, frequency spectrum, Poincaré maps, and time series. The bifurcations are analyzed by the bifurcation diagrams with different rotating speeds and mass eccentricities. The dynamic behaviors of the asymmetric rotor system appear complex nonlinear dynamic phenomenon and specific bifurcation characteristics.

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

In this paper, the Khater II analytical technique is used to examine novel soliton structures for the fractional nonlinear third-order Schrödinger (3-FNLS) problem. The 3-FNLS equation explains the dynamical behavior of a system’s quantum aspects and ultra-short optical fiber pulses. Additionally, it determines the wave function of a quantum mechanical system in which atomic particles behave similarly to waves. For example, electrons, like light waves, exhibit diffraction patterns when passing through a double slit. As a result, it was fair to suppose that a wave equation could adequately describe atomic particle behavior. The correctness of the solutions is determined by comparing the analytical answers obtained with the numerical solutions and determining the absolute error. The trigonometric Quintic B-spline numerical (TQBS) technique is used based on the computed required criteria. Analytical and numerical solutions are represented in a variety of graphs. The strength and efficacy of the approaches used are evaluated.

This paper investigates the efficiency of three surrogate model-based dynamic finite element model updating methods, the response surface, the support vector regression, and the radial basis function neural network, using the engineering background of the Tsing Ma Bridge tower. The influences of two different sampling methods (central composite design sampling and Box–Behnken design sampling) on the model updating results are also assessed. It was deduced that the impact of the surrogate model type on the updating results is not significant. More precisely, the models updated using the response surface method and the support vector regression method are similar in terms of reproducing the dynamic characteristics of the physical truth. However, the effects of the employed sampling method on the model updating results are significant as the model updating quality using the central composite design sampling method is higher than that using the Box–Behnken design sampling method in some considered cases.

The double-helical gear system was widely used in ship transmission. In order to study the influence of backlash on the nonlinear frequency response characteristics of marine double-helical gear system, according to the structural characteristics of double-helical gear transmission, considering the time-varying meshing stiffness, backlash, damping, comprehensive transmission error, external load excitation, and other factors, a three-dimensional bending-torsional-axial-pendular coupling nonlinear dynamic modeling and dynamic differential equation of 24-DOF double-helical gear transmission system were established. The Runge–Kutta numerical method was used to analyze the influence of backlash, time-varying meshing stiffness, damping, error and external load excitation on the amplitude frequency characteristics. The results show that the backlash can cause the runout of the double-helical gear system, and the system has first harmonic and second harmonic response. With the increase of backlash, the amplitude of the system increases and the jumping phenomenon remains unchanged. The amplitude frequency response of the system is stimulated by time-varying meshing stiffness and comprehensive transmission error, and restrained by damping and external load excitation. The vibration displacement amplitude of the system increases with the increase of vibration displacement and has little effect on the state change of the system. The vibration test of double-helical gear is carried out. The frequency response components obtained by numerical simulation are basically consistent with the experimental results, which proves the correctness of the theoretical calculation. It provides a technical basis for the study of vibration and noise reduction performance of double-helical gear.

A locally resonant metastructure is a promising approach for low-frequency vibration attenuation, whereas the attachment of many resonators results in unnecessary and multiple resonance outside the bandgap. To address this issue, we propose a damping metastructure combining local resonators and an autonomous synchronized switch damping circuit. On the basis of modal analysis, we derive an electromechanically coupled equation of the proposed metastructure. The piezo ceramics, which are attached on a small portion of the metastructure and connected to the circuit, remarkably decrease the magnitude of the resonant vibration with no extra sensors, signal processors, or power sources. The displacement at unnecessary resonance was decreased by approximately 75%. The results of the coupled analysis were similar to the experimentally observed results in terms of the location and width of the bandgap on the frequency axis and the decreased displacement for the circuit. The proposed technique can overcome the disadvantage of the metastructure.

This study proposes an algorithm for autonomous modal estimation to automatically eliminate false modes and quantify the uncertainty caused by the clustering algorithm and ambient factors. This algorithm belongs to the stochastic subspace identification (SSI) techniques and is based on the Block-Bootstrap and multi-stage clustering analysis. First, the Block-Bootstrap is introduced to decompose the response signal of the structure into M blocks of data. The covariance-driven stochastic subspace identification (SSI-Cov) method is used to process a random sample of data and obtain the corresponding M stabilization diagrams. In addition, the hierarchical clustering method is adopted to carry out the secondary clustering of the picked stable axis according to the defined distance threshold. Then, false modes are eliminated according to the proposed true and false modal discrimination index (MDI). Finally, the above steps are repeated B times, and MDI is used to modify the initial modal parameters of group B. The mean value of elements in the cluster is taken as the recognition result of modal parameters, and the standard deviation is used to measure the accuracy of the recognition result. The numerical simulation results and the modal parameter identification of the Jing-yuan Yellow River Bridge show that, for identifying true and false modals, the proposed modal discrimination index is more effective than the threshold value of the traditional index. Also, it was found that the proposed method can eliminate the uncertainty introduced in the clustering process. In addition, this method can remove the influence of ambient noises, and it can improve the identification accuracy. It will be shown that this method has better anti-noise performance.

The pull-in voltage is crucial in designing an optimal nano/micro-electromechanical system (N/MEMS). It is vital to have a simple formulation to calculate the pull-in voltage with relatively high accuracy. Two simple and effective methods are suggested for this purpose; one is an ancient Chinese algorithm and the other is an extension of He’s frequency formulation.

The homotopy perturbation method (HPM) was proposed by Ji-Huan. He was a rising star in analytical methods, and all traditional analytical methods had abdicated their crowns. It is straightforward and effective for many nonlinear problems; it deforms a complex problem into a linear system; however, it is still developing quickly. The method is difficult to deal with non-conservative oscillators, though many modifications have appeared. This review article features its last achievement in the nonlinear vibration theory with an emphasis on coupled damping nonlinear oscillators and includes the following categories: (1) Some fallacies in the study of non-conservative issues; (2) non-conservative Duffing oscillator with three expansions; (3)the non-conservative oscillators through the modified homotopy expansion; (4) the HPM for fractional non-conservative oscillators; (5) the homotopy perturbation method for delay non-conservative oscillators; and (6) quasi-exact solution based on He’s frequency formula. Each category is heuristically explained by examples, which can be used as paradigms for other applications. The emphasis of this article is put mainly on Ji-Huan He’s ideas and the present authors’ previous work on the HPM, so the citation might not be exhaustive.

Nonlinear vibration arises everywhere in a bistable system. The bistable system has been widely applied in physics, biology, and chemistry. In this article, in order to numerically simulate a class of space fractional-order bistable system, we introduce a numerical approach based on the modified Fourier spectral method and fourth-order Runge-Kutta method. The fourth-order Runge-Kutta method is used in time, and the Fourier spectrum is used in space to approximate the solution of the space fractional-order bistable system. Numerical experiments are given to illustrate the effectiveness of this method.

To solve the problem of large operating noise of existing pyrotechnic separation devices, a new low-noise pyrotechnic separation device is designed by changing the utilisation mode of pyrotechnic separation, using micro gas pyrotechnic as heat sources, and shape memory alloy material to convert heat energy into mechanical energy. The results showed that the separation time was 1.526 s when the preload was 20 kN, and the maximum shock response was 319 G (2268 Hz) for 100 Hz–100 kHz. When used underwater, the maximum sound pressure level is 106.9 dB at 12,698 Hz and 98.5 dB from 10 Hz–5 kHz. Compared with a conventional separation nut, the frequency band sound pressure level can be reduced by more than 70 dB, realising underwater low-noise separation.

In this paper, in order to reduce the influence of vibration and noise generated by the motor in rock cotton centrifuges on the quality of the output fiber and the damage to the operator’s hearing, it is meaningful to analyze and optimize the vibration and noise. A high-speed magnetic suspension motor is proposed for the rock cotton centrifuge in the paper. First, the motor model is established in Maxwell, the radial force density wave distributed in the air gap is calculated by the field solver, the main harmonic source is analyzed according to its FFT decomposition graph, and then the optimization scheme of short-range double-layer winding is determined. Second, the optimization scheme is analyzed in modal mode and harmonious response, and the vibration response spectrum of the motor stator is obtained. Finally, the electromagnetic noise characteristics of the motor are obtained through ANSYS acoustics simulation. The results show that the optimized motor noise has a reasonable level under the premise of ensuring electromagnetic performance.

Noise cancellation is one of the most successful applications of the wavelet transform. Its basic idea is to compare wavelet decomposition coefficients with the given thresholds and only keep those bigger ones and set those smaller ones to zero and then do wavelet reconstruction with those new coefficients. It is most likely for this method to treat some useful weak components as noise and eliminate them. Based on the cyclostationary property of vibration signals of rotating machines, a novel wavelet noise cancellation method is proposed. A numerical signal and an experimental signal of rubbing fault are used to test and compare the performances of the new method and the conventional wavelet based denoising method provided by MATLAB. The results show that the new noise cancellation method can efficaciously suppress the noise component at all frequency bands and has better denoising performance than the conventional one.

Generally, the synchronization studies on two or multiple exciters are preconditioned by being a single frequency, while the multiple-frequency synchronization problems in a vibrating system, including double-frequency and triple-frequency, are less considered, which are also very significant in engineering. This paper attempts to solve this issue by considering a dynamical model with an isolation frame, driven by the four exciters. The synchronization for the four exciters and its stability under the double-frequency and triple-frequency conditions are studied in detail. Firstly, the mathematical modeling of the system is established, and the corresponding motion differential equations are derived. Using the asymptotic method and the average method, yields the theoretical condition of implementing multiple-frequency synchronization, and the theoretical condition for stability of the system complies with the Routh–Hurwitz criterion. The dynamic characteristics of the system, including stable phase differences, stability abilities, responses of the system, and relative motion relationship, are qualitatively discussed by numeric. Finally, simulations are performed by applying a Runge–Kutta program to validate the theoretical and numerical qualitative results. It is shown that, by reasonably matching the key parameters of the system, the stronger, stable, and valuable motion states of vibrating machines, including vibration amplitudes, frequencies, and motion trajectory, can be realized, which are exactly the desires in engineering.

This paper describes the design, simulation, and performance evaluation of hybrid MR damper on quarter bus semi-active seat suspension coupled with human biodynamic model. Also, the whole body vibration (WBV) exposures were evaluated based on the international standard ISO 2631 (1997), and its parameters were used to measure the level of discomfort for bus drivers. The hybrid MR damper was proposed to enhance the damping force within low current supplied and achieve a fail-soft capability in case of electrical failure. The characteristics of the proposed hybrid MR damper were compared to the conventional MR damper by considering the same size, materials, and current input. The designed damper was incorporated to seat suspension system coupled with biodynamic lumped model, and the governing equations of motion of the full model were derived. Skyhook controller was used to control the amount of current to be supplied to hybrid MR damper. The controlled semi-active hybrid MR and conventional MR seat suspension are compared to uncontrolled system for two types of road excitation. The simulated results show that the driver seat comfort was improved by the skyhook controller than the uncontrolled case. The evaluated WBV showed that the hybrid MR damper can improve the driver life from fairly uncomfortable to little discomfort.

Smart materials properties are altered using external stimuli such as temperature, pressure and magnetic field. Magnetorheological Elastomer (MRE) is a type of smart composite material consisting of a polymer matrix embedded with ferromagnetic particles. In the presence of an external magnetic field, its mechanical properties, such as stiffness, change due to the interaction between the magnetic particles, which have applications in vibration isolation. Unwanted vibration in machines can cause severe damage and machine breakdown. In this work, a semi-active vibration isolator using MRE is proposed for a potential application in a drilling system to isolate the torsional vibration. The MRE was fabricated with a 35% mass fraction (MF) consisted of silicon rubber and iron particles. It was fitted with aluminium couplers and attached to the shaft (drill string) to study its efficiency in vibration isolation under a magnetic field. Two tests were conducted on the drilling prototype setup used in this work; the first test was a hammer impact test. The torsional transfer function TTF analysis showed that the system’s natural frequency has shifted from 13.9 Hz to 17.5 Hz by the influence of increasing magnetic field around the MRE. The results showed that the continuous rotational vibration amplitude of the prototype is attenuated by more than 40%.

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

To improve the ride comfort of wheeled armored vehicles, air springs are used. To describe the vehicle motion more accurately, a nine-degree-of-freedom air suspension system for the whole vehicle was established, and its equations of motion were derived. Through theoretical analysis of the stiffness characteristics and forces on the air springs, the nonlinear restoring force was obtained as a cubic polynomial of the air spring displacement. The simulation results obtained by fitting the polynomial and radial basis function curves with MATLAB/Simulink software are consistent with the actual test results, thus verifying the correctness of the nonlinear air spring polynomial model. Finally, a fuzzy fractional order PI^λD^μ controller is designed and simulated for the vehicle-seat-body model in terms of wheel dynamic load, suspension dynamic deflection, body acceleration, and other indicators. The simulation results show that the fuzzy fractional order PI^λD^μ Proportion Integral Differential (PID) control strategy has better overall performance than the PID control strategy, fuzzy control strategy, and fuzzy PID control strategy.

Time-delay feedback control can effectively broaden the damping frequency band and improve the damping efficiency. However, the existing time-delay feedback control strategy has no obvious effect on multi-frequency random excitation vibration reduction control. That is, when the frequency of external excitation is more complicated, there is no better way to obtain the best time-delay feedback control parameters. To overcome this issue, this paper is the first work of proposing an optimal calculation method that introduces stochastic excitation into the process of solving the delay feedback control parameters. It is a time-delay control parameter with a better damping effect for random excitation. In this paper, a 2 DOF one-quarter vehicle suspension model with time-delay is studied. First, the stability interval of time-delay feedback control parameters is solved by using the Lyapunov stability theory. Second, the optimal control parameters of the time-delay feedback control under random excitation are solved by particle swarm optimization (PSO). Finally, the simulation models of a one-quarter vehicle suspension simulation model are established. Random excitation and harmonic excitation are used as inputs. The response of the vehicle body under the frequency domain damping control method and the proposed control method is compared and simulated. To make the control precision higher and the solution speed faster, this paper simulates the model by using the precise integration method of transient history. The simulation results show that the acceleration of the vehicle body in the proposed control method is 13.05% less than the passive vibration absorber under random excitation. Compared with the time-delay feedback control optimized by frequency response function, the damping effect is 12.99%. The results show that the vibration displacement, vibration velocity, and vibration acceleration of the vehicle body are better than the frequency domain function optimization method, whether it is harmonic excitation or random excitation. The ride comfort of the vehicle is improved obviously. It provides a valuable tool for time-delay vibration reduction control under random excitation.

This study is concerned with the development of multi-input multi-output control algorithms for the active vibration suppression of structures using accelerometer signals and force-type actuators. The concept of the single-input single-output virtual tuned mass damper control algorithm developed in the previous study was extended to cope with multiple natural modes of structure equipped with a limited number of sensors and actuators. Two control algorithms were developed based on the assumption of collocated control. One is the decentralized virtual tuned mass damper control that produces the actuator signal using only the accelerometer signal of that actuator position. The other is the centralized virtual tuned mass damper control that is designed in modal-space, and produces the modal control force using the modal coordinate. Both the theoretical and experimental results show that the proposed control algorithms are effective in suppressing multiple natural modes with a lesser number of sensors and actuators. However, the decentralized virtual tuned mass damper control can be designed and implemented more easily than the centralized virtual tuned mass damper control.

In this study, the design of adaptive backstepping sliding mode control (ABSMC) has been developed for vibration suppression of earth-quaked building supported by magneto-rheological (MR) damper. The control and adaptive laws developed based on ABSMC methodology has been established according to stability analysis based on Lyupunov theorem. A Single degree of freedom (SDOF) building system has been considered and the earthquake acceleration data used in performance analysis of the proposed controller is based on El Centro Imperial Valley Earthquake. The ABSMC has been compared to classical sliding mode control in terms of vibration suppression in the controlled system subjected to earthquake. The performance of proposed controller has been assessed via computer simulation, which showed its effectiveness to stabilize the building against earthquake vibration and the boundness of estimated stiffness and viscosity coefficients.

Mechanical vibration is mostly harmful, and it may not only generate noise but also affect the working life of the equipment. Lever, inerter, and grounded stiffness have good performance in the field of vibration control, but the dynamic vibration absorber simultaneously containing lever, inerter, and grounded stiffness is rarely studied. Based on the grounded dampertype dynamic vibration absorber, a dynamic vibration absorber with lever, inerter, and grounded stiffness is presented. And the optimal system parameters are analytically researched in detail. Firstly, the differential equation of motion is established according to Newton’s second law, and the analytical solution of the system is obtained. According to the amplitudefrequency curve of the system, it is obvious that there are two fixed points unrelated to the damping ratio. Meanwhile, the optimal frequency ratio of the dynamic vibration absorber is obtained based on the fixed-point theory. Under the premise of ensuring the system stability, the optimal grounded stiffness ratio is screened out, and the working range of inerter is further calculated. It is found that the inerter ratio has two working ranges when the coupling term values of magnification ratio and mass ratio are different. Furthermore, the approximate optimal damping ratio is derived by minimizing the maximum value of the amplitudefrequency curve. Using MATLAB, the numerical result is analyzed, and the correctness of analytical results is verified. Compared with other dynamic vibration absorbers under harmonic and random excitations, it is known that the model in this paper can evidently reduce the resonance amplitude and broaden the vibration band of the primary system. These results may provide a theoretical basis for the optimal design of similar dynamic vibration absorbers.

To effectively and efficiently control vibrations in steel bridge decks, the flexural wave band gap and vibration attenuation mechanism are studied. The band structures and displacement fields of the eigenmodes at the band gap edges of infinite periodic U-rib stiffened plates are calculated. The calculation method is combining the finite element method with Bloch periodic boundary conditions. A scaled specimen test of a finite periodic U-rib stiffened plate is used to validate the numerical results. A comparison of results confirms that introducing the U-rib allows the periodic U-rib stiffened plates to yield several flexural wave band gaps. In the band gaps, flexural wave propagation is stopped and clear flexural vibration suppression is achieved. Furthermore, the effects of geometric parameters and structural schemes on the flexural wave band gaps are analyzed in detail. Finally, by analyzing a specific case, it is demonstrated that the flexural wave band gaps and vibration attenuation properties can be controlled. This provides a new approach to vibration and noise control in steel bridges.

The level of annoyance is an important basis to determine the acceptable degree of noise and develop noise standards. Psychoacoustic annoyance (PA) calculated by Zwicker’s model and perceived annoyance (such as mean annoyance, MA and the percentage of highly annoyed population, %HA) obtained through individual self-reports are widely used. PA and MA (or %HA) cannot be directly compared because the ranges of their values are different. Thus, the conversion relationship of PA and MA (or %HA) needs to be developed. As a case study, the model between PA and MA (or %HA) of substations noise was established and the rationality of model was verified. Results showed that the maximum value of the difference of MA (or %HA) between the calculation result of model and experimental result was less than 0.89 (or 15%). In this way, the perceived annoyance of substation noise samples can be determined by calculation without experiments.