Nonlinear Vibrations of Viscoelastic Composite Cylindrical Panels

2006 ◽  
Vol 129 (3) ◽  
pp. 285-296 ◽  
Author(s):  
Bakhtiyor Eshmatov ◽  
Subrata Mukherjee
Keyword(s):  
Numerical Method ◽  
Nonlinear Vibrations ◽  
Rheological Parameters ◽  
Quadrature Formulas ◽  
Relaxation Kernel ◽  
Viscoelastic Composite ◽  
Nonlinear Statement ◽  
Cylindrical Panels ◽  
Singular Kernels ◽  
Waves Propagation

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.

scholarly journals Vibration analysis of airfoil on hereditary deformable suspensions

2019 ◽  
Vol 97 ◽  
pp. 06006
Author(s):  
Botir Usmonov ◽  
Quvvatali Rakhimov
Keyword(s):  
Dynamic Stability ◽  
Nonlinear Vibrations ◽  
Degree Of Freedom ◽  
Rheological Parameters ◽  
Viscoelastic System ◽  
Weakly Singular ◽  
Singular Kernels ◽  
Comparison Of The Results ◽  
The Galerkin Method ◽  
Two Degree Of Freedom

This paper describes the analyses of the nonlinear vibrations and dynamic stability of an airfoil on hereditary-deformable suspensions. The model is based on two-degree-of-freedom structure in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Abelian type kernel, with rheological parameters. To solve problems of viscoelastic system with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic two-degree-of-freedom structure have been solved. A comparison of the results obtained via this method is also presented. In all problems, the convergence of the Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

scholarly journals Numerical Research Of Nonlinear Vibrations Of Isotropic Viscoelastic Plates With Variable Rigidity By The Method Of Computer Simulation

2011 ◽  
Vol 3 ◽  
Author(s):  
Rustam Abdikarimov
Keyword(s):  
Nonlinear Vibrations ◽  
Physical Dependence ◽  
Viscoelastic Plate ◽  
Quadrature Formulas ◽  
Geometrically Nonlinear ◽  
Variable Rigidity ◽  
Weakly Singular Kernel ◽  
Nonlinear Statement ◽  
Numerical Research ◽  
The Given

In the given work the problem about vibrations of a isotropic viscoelastic plate with  variable rigidity in  geometrically nonlinear statement is considered. With the help of Bubnov-about nonlinear vibrations of viscoelastic isotropic plate in geometrically  nonlinear  statement  on  Kirchhoff-Love’s kinematic  hypothesis,  physical  dependence  between. Galerkin method the problem is reduced to the decision of system of nonlinear ordinary integro-differential equations of Volterra’s type. The numerical method based on the use of quadrature formulas is applied for the decision of the received system at weakly singular kernel of Koltunov- Rzhanitsin’s. Influences of  viscoelastic properties of  a material, geometrical characteristics, and also dependences. 

scholarly journals Vibrations of dam–plate of a hydro-technical structure under seismic load

2021 ◽  
Vol 264 ◽  
pp. 05057
Author(s):  
A Tukhtaboev ◽  
Sergey Leonov ◽  
Fozil Turaev ◽  
Kudrat Ruzmetov
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Numerical Method ◽  
Quadrature Formulas ◽  
Seismic Load ◽  
Geometrically Nonlinear ◽  
Material Parameters ◽  
Weakly Singular ◽  
Technical Structure ◽  
Nonlinear Statement

In present paper, the problem of the vibration of a viscoelastic dam-plate of a hydro-technical structure is investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement. This problem is reduced to a system of nonlinear ordinary integro-differential equations by using the Bubnov-Galerkin method. The resulting system with a weakly-singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature formulas. The behavior of the viscoelastic dam-plate of hydro-technical structure is studied for the wide ranges of physical, mechanical, and geometrical material parameters.

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

1984 ◽  
Vol 51 (2) ◽  
pp. 383-390 ◽  
Author(s):  
David Hui
Keyword(s):  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Vibration Mode ◽  
Vibration Frequencies ◽  
Linear Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Cylindrical Panels ◽  
Initial Geometric Imperfections ◽  
Large Amplitude Vibrations

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

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