Nonlinear Vibrations of Viscoelastic Composite Cylindrical Panels

[+] Author and Article Information
Bakhtiyor Eshmatov

 Institute of Mechanics and Seismic Stability of Structures, Akademgorodok, Tashkent, 700143, Uzbekistanebkh@mail.ru

Subrata Mukherjee

Department of Theoretical and Applied Mechanics, Kimball Hall, Cornell University, Ithaca, NY 14853sm85@cornell.edu

J. Vib. Acoust 129(3), 285-296 (Nov 04, 2006) (12 pages) doi:10.1115/1.2730532 History: Received March 02, 2006; Revised November 04, 2006

This paper is devoted to mathematical models of problems of nonlinear vibrations of viscoelastic, orthotropic, and isotropic cylindrical panels. The models are based on Kirchhoff-Love hypothesis and Timoshenko generalized theory (including shear deformation and rotatory inertia) in a geometrically nonlinear statement. A choice of the relaxation kernel with three rheological parameters is justified. A numerical method based on the use of quadrature formulas for solving problems in viscoelastic systems with weakly singular kernels of relaxation is proposed. With the help of the Bubnov-Galerkin method in combination with a numerical method, the problems in nonlinear vibrations of viscoelastic orthotropic and isotropic cylindrical panels are solved using the Kirchhoff-Love and Timoshenko hypothesis. Comparisons of the results obtained by these theories, with and without taking elastic waves propagation into account, are presented. In all problems, the convergence of Bubnov-Galerkin’s method has been investigated. The influences of the viscoelastic and anisotropic properties of a material, on the process of vibration, are discussed in this work.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Vibration
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 2

The numerical convergence of the Bubnov-Galerkin method: 1—N=1; 2—N=3; 3—N=7; 4—N=11

Grahic Jump Location
Figure 3

Dependence of the deflection on time for various values of A: 1—A=0.0; 2—A=0.05; 3—A=0.1

Grahic Jump Location
Figure 4

Dependence of the deflection on time for various values of α: 1—α=0.15; 2—α=0.25; 3—α=0.75

Grahic Jump Location
Figure 5

The influence of the material orthotropicity (qkl=1): 1—Δ=1; 2—Δ=2; 3—Δ=3

Grahic Jump Location
Figure 6

Dependence of the deflection on time for various kernels of relaxation: 1—exponential kernel; 2—weakly-singular kernel of Koltunov-Rzhanitsyn

Grahic Jump Location
Figure 7

Dependence of the deflection on time for various values of geometrical parameter θ: 1—θ=6; 2—θ=12; 3—θ=18

Grahic Jump Location
Figure 8

Dependence of the deflection on time for various theories: 1—q=3, λ=1; 2—q=1, λ=1.5, with account 3—q=3, λ=1; 4—q=1, λ=1.5, without account of elastic waves propagation

Grahic Jump Location
Figure 9

The influence of the initial imperfections: 1—w0=10−4; 2—w0=0.6∙10−4; 3—w0=0.2∙10−4

Grahic Jump Location
Figure 10

Dependence of the deflection on time for various values of λ: 1—λ=1; 2—λ=2; 3—λ=3

Grahic Jump Location
Figure 11

The influence of the static shearing edge load q: 1—q=0; 2—q=0.001; 3—q=0.002

Grahic Jump Location
Figure 12

The influence of the nonlinear properties of the plate material: 1—λ=1; q=1; w0=10−1; 2—λ=1; q=3; w0=10−4; 3—λ=3; q=1; w0=10−4, linear case; 4—λ=1; q=1; w0=10−1; 5—λ=1; q=3; w0=10−4; 6—λ=3; q=1; w0=10−4, nonlinear case

Grahic Jump Location
Figure 13

The influence different viscoelastic properties of the material (qkl=1): 1—A=A13=A23=0.05, Aij=0, i,j=1,2; 2—A=Aij=0.05, i=1,2, j=1,2,3; 3—A=0.05, A11=0.06, A12=0.07, A21=0.08, A22=0.09, A13=0.1, A23=0.11

Grahic Jump Location
Figure 14

Dependence of the deflection on time for various theories: 1—Timoshenko; 2—Kirchhoff-Love

Grahic Jump Location
Figure 15

Dependence of the deflection on time for various values of geometrical parameter δ: 1—δ=15; 2—δ=20; 3—δ=25



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In