Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

Éshmatov, B. Kh.

doi:10.1016/j.jsv.2006.08.024

Cited by 43 publications

(11 citation statements)

References 24 publications

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“…The numerical results of Refs. [28][29][30][31][32][33][34][35][36] obtained by this method agree well with experimental data [3].…”

supporting

confidence: 73%

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Éshmatov

2007

Nonlinear Dyn

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The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov-Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov-Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.

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“…The numerical results of Refs. [28][29][30][31][32][33][34][35][36] obtained by this method agree well with experimental data [3].…”

supporting

confidence: 73%

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Éshmatov

2007

Nonlinear Dyn

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“…al, 2012), variation principle (Eshmatov, 2007), Rayleigh-Ritz (Belytschko and Lu, 1994), and perturbation method have been applied to investigate the problem of dynamic response of membrane structure under impact load (Liu et. al, 2010).…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of Orthotropic Membrane Structure under Impact Load based on Multiple Scale Perturbation Method

Zheng

Liu

et al. 2017

Lat. Am. j. solids struct.

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This paper investigates the dynamic response of rectangular prestressed membrane subjected to concentrated impact load based on multiple scale perturbation method. The governing equations of motion of nonlinear vibration are derived based on the Föppl large deflection theory and Galerkin method. By introducing different time scales to consider the process of vibration, the results of dynamic response are obtained by applying the multiple scale perturbation method. Furthermore, the effects of pretension force, velocity of load and dimension of membrane on the dynamic response of membrane are discussed. The present work studies the problem of the dynamic response of prestressed membrane subjected to concentrated impact load in different time scales, and provides a more accurate theoretical model for design of membrane structure.

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“…Chien and Chen [5] studied the effects of initial stresses on the nonlinear vibrations of laminated plates resting on elastic foundations. Eshmatov [6] used the Kirchhoff-Love hypothesis and ReissnerMindlin generalized theory to study the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. Singha and Daripa [7] investigated the large amplitude free flexural vibration behaviour of symmetrically laminated composite *Corresponding author: Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of annular sector plates using differential quadrature method

Hejripour

Saidi

2011

Proceedings of the Institution of Mechanical Engineers, Part C:

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The nonlinear free vibration of isotropic annular sector plates is studied using differential quadrature method. The geometric nonlinearity is used into the strains and based on the first-order shear deformation plate theory, the nonlinear governing equations of motion are obtained. According to differential quadrature analogue, the equations of motion and boundary conditions are discretized. The harmonic balance method is used to obtain the eigenvalue system. The eigenvalue system is solved using an iterative solution. The obtained results are verified for fully clamped annular sector plates and the convergence of results is investigated for some boundary conditions. The effects of some parameters, such as thickness to outer radius ratio, inner to outer radius ratio and sector angle on the nonlinear to linear natural frequency ratio, are also studied. It is shown that the simply supported plate is more sensitive to the geometrical parameters than the fully clamped plate.

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Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

Cited by 43 publications

References 24 publications

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

Dynamic Response of Orthotropic Membrane Structure under Impact Load based on Multiple Scale Perturbation Method

Nonlinear free vibration analysis of annular sector plates using differential quadrature method

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