Vibration analysis and design optimization of sandwich beams with constrained viscoelastic core layer

Abstract

Dynamic properties of sandwich beam-type structure are analyzed using finite element method based on a nonlinear model for displacement field in the viscoelastic core layer of the beam structure. Results obtained for the nonlinear and linear models are compared to the test data available in literature. It is revealed that the nonlinear model provides more accurate results than the linear one. Parametric studies are carried out on the nonlinear model to illustrate the effect of viscoelastic core thickness on the loss factor and natural frequencies of structure. These results are also compared with those obtained for the linear model. Parametric studies on the nonlinear model revealing the sensitivity of the location of untreated and treated patch and the length of treated patch are presented. Finally, an optimization problem is formulated for the nonlinear model to locate the optimal distribution and numbers of partial treatments in order to attain the maximum damping in the sandwich beam for various boundary conditions.

Keywords

Sandwich beam structure finite element analysis nonlinear model optimization partial treatment

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References

Kerwin

. Damping of flexural waves by a constrained viscoelastic layer. J Acoust Soc Am 1959; 31: 952–962.

Di Taranto

. Theory of vibratory bending for elastic and viscoelasic layered finite-length beams. ASME J Appl Mech 1965; 32: 881–886.

Mead

Markus

. The forced vibration of a three-layer damped sandwich beam with arbitarary boundary conditions. J Sound Vib 1969; 10: 163–175.

Kung

Singh

. Development of approximate methods for the analysis of patch damping design concepts. J Sound Vib 1999; 219: 785–812.

Yan

Dowell

. Governing equations for the measurement of damping sandwich plates and beams. ASME J Appl Mech 1972; 94: 1041–1047.

Bai

Sun

. The effect of viscoelastic adhesive layers on structural damping of sandwich beams. Mech Struct Mach 1995; 23: 1–16.

Douglas

. On the forced vibrations of three layer damped sandwich beams. J Sound Vib 1974; 32: 513–516.

Johnson

Kienholz

Rogers

. Finite element prediction of damping in beams with constrained viscoelastic layers. Shock Vib Bull 1981; 51: 71–81.

Soni

. Finite element analysis of viscoelastically damped sandwich structures. Shock Vib Bull 1981; 51: 97–109.

10.

Mace

. Damping of beam vibrations by means of a thin constrained viscoelastic layer: evaluation of new theory. J Sound Vib 1994; 172: 577–591.

11.

Thamburaj

Sun

. Effect of material anisotropy on the sound and vibration transmission loss of sandwich aircraft structures. J Sandwich Struct Mater 1998; 1: 76–92.

12.

Baber

Maddox

Orozco

. A finite element model for harmonically excited viscoelastic sandwich beams. Comput Struct 1998; 66: 105–113.

13.

Maddox RA. A finite element model for harmonic response of a viscoelastic sandwich beam. MSc Thesis, Department of Civil Engineerimg, The University of Virginia, May 1996.

14.

Chen

Chan

. Integral finite element method for dynamical analysis of elastic and viscoelastic composite structures. Comput Struct 2000; 74: 51–64.

15.

Leibowitz

Lifshitz

. Experimental verification of modal parameters for 3-layered sandwich beams. Int J Solid Strucut 1990; 26: 175–184.

16.

Lifshitz

Leibowitz

. Optimal sandwich beam design for maximum viscoelastic damping. Int J Solid Strucut 1987; 23: 1027–1034.

17.

Muc

Gurba

. Genetic algorithms and finite element analysis in optimization of composite structures. Compos Struct 2001; 54: 275–281.