Nonlinear vibration analysis of initially stressed thin laminated rectangular plates on elastic foundations

Muthurajan, K.G.; Sankaranarayanasamy, K.; Tiwari, Shashi Bhushan; Rao, B. Nageswara

doi:10.1016/j.jsv.2004.03.047

Cited by 14 publications

(5 citation statements)

References 20 publications

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“…By contrast with analytical methods known to be limited to only a few cases, numerical methods are more effective in a wide range of cases involving various physical properties, arbitrary boundary conditions, and sophisticated loading configurations. Various numerical procedures are available for flexural vibrations of multi-layered composite plates [2][3][4][5][6][7][8][9][10][11][12], among which the most representative and widely used one is the finite element method (FEM) that has already been successfully incorporated into commercial software. However, FEM generally uses low-order approximating functions; consequently, a higher accuracy can only be achieved by mesh refinement, resulting in a higher computation cost.…”

Section: Introductionmentioning

confidence: 99%

Application of a Modified Differential Quadrature Finite Element Method to Flexural Vibrations of Composite Laminates with Arbitrary Elastic Boundaries

Xiang

Lin

2022

Buildings

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This paper formulates a modified differential quadrature finite element method (DQFEM) by a combination of the standard DQFEM and the virtual boundary spring technique, which makes it easy to implement arbitrary elastic restraints by assigning reasonable values to the boundary spring stiffnesses. This new formulated method can offer a unified solution for flexural vibrations of composite laminates subjected to general elastic boundary combinations including all the classical cases. The influences of the number of Gauss–Lobatto nodes and the boundary spring stiffnesses on the convergence characteristics of natural frequencies are investigated, and some conclusions are drawn in terms of the minimum number of unilateral nodes required to generate convergent solutions and the optimal values of the boundary spring stiffnesses to simulate classical boundaries. Numerical examples are performed for composite laminates under various classical boundary conditions. Excellent accuracy, numerical stability, and reliability of the present method are demonstrated by comparisons with available exact and numerical solutions in open literatures. Additionally, for elastically constrained composite laminates, which are beyond the scope of most existing approaches, numerous new results obtained by the present method may serve as reference values for other research.

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Section: Introductionmentioning

confidence: 99%

Application of a Modified Differential Quadrature Finite Element Method to Flexural Vibrations of Composite Laminates with Arbitrary Elastic Boundaries

Xiang

Lin

2022

Buildings

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“…Geometrically nonlinear behaviour of laminated plates including residual stresses, is a rich literature; the reader can find a sample of it in Reddy (2004), Dash and Singh (2010), Reddy and Chandrashekhara (1985), Chang and Huang (1991) and Muthurajan et al (2005). We hereby provide a semi-analytical solution instead of FEM calcuations.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical modelling of piezoelectrically actuated MEMS tunable lenses with geometric nonlinearity

Farghaly

Карташов

Akram

et al. 2021

Journal of Intelligent Material Systems and Structures

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This article presents a variational model for the geometrically nonlinear behaviour of the piezoelectrically actuated MEMS tunable lenses. Residual stresses during fabrication and larger actuation voltages cause large deflections such that a linear model would provide less accurate approximation. This presses the need for a nonlinear model that can explain the softening and hardening effects exhibited by the lens during its operation and affect its optical performance. Thus, in the view of von Kármán’s plate theory, the presented nonlinear model predicts the lens displacement after solving a cubic nonlinear system of equations. The chosen displacement ansatz fits the problem under study by satisfying the mechanical boundary conditions, and simplifying calculation of the variational integrals and optical representation of the lens’ sag. The model also shows good agreement with FEM simulations over various combinations of tensile and compressive residual stresses. Moreover, it succeeds in fitting measurements when used in a constrained optimization scheme in which the layers’ residual stresses and the e-form piezoelectric coupling coefficient are the fitting parameters.

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“…The nonlinear forced vibrations of the plate have also been studied by many researchers over the past decades. Muthurajan et al (2005) studied the nonlinear vibration of an initially stressed thin laminated rectangular plate and pointed out that the amplitude for the applied lateral and compressive in-plane forces had significant effects on the nonlinear resonance frequency of the plate. Xue et al (2011) investigated the nonlinear primary resonance of an orthotropic and magnetoelastic rectangular plate by using the multi-scale method.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow

Yao

2013

Journal of Vibration and Control

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The nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow with simply supported boundary conditions is investigated. Based on the von Karman’s plate theory, the equation of motion of the plate is established using Hamilton’s principle. The aerodynamic pressure induced by the coupled vibration of the plate and subsonic airflow is derived from the linear potential flow theory and compared with the existing model. The variable separation method is used to transform the equation of motion of the plate into nonlinear ordinary differential equations. The influences of the flow velocity, the length-to-thickness ratio and the ply angle of the plate on the nonlinear vibration behaviors of the plate are discussed. From the analytical and numerical results it can be seen that the critical instability velocity obtained from the present aerodynamic model is the same as the existing result. The first-order expansion of the transverse displacement can reflect the dynamic characteristics of the plate. With the increase of the flow velocity and the length-to-thickness ratio, the instability interval of the nonlinear vibration can be prolonged and the nonlinear resonance frequency can be increased. The composite laminated plate with smaller ply angle exhibits more stable dynamic properties than that with larger ply angles.

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Nonlinear vibration analysis of initially stressed thin laminated rectangular plates on elastic foundations

Cited by 14 publications

References 20 publications

Application of a Modified Differential Quadrature Finite Element Method to Flexural Vibrations of Composite Laminates with Arbitrary Elastic Boundaries

Application of a Modified Differential Quadrature Finite Element Method to Flexural Vibrations of Composite Laminates with Arbitrary Elastic Boundaries

Electromechanical modelling of piezoelectrically actuated MEMS tunable lenses with geometric nonlinearity

Nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow

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