Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.

https://web.iitd.ac.in/~maloy/papers/rupesh1.pdf

Nonlinear vibration of symmetrically laminated composite skew plates by finite element method

Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT

Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented The governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions To cause the impact due to nonlinear terms more significant, in-plane immovable simply supported, clamped and different combinations of them are considered The effects of different parameters on the convergence and accuracy of the method are studied The resulted solutions are compared to those from other numerical methods to show the accuracy of the method Some new results for laminated composite skew plates with different mixed boundary conditions are presented and are compared with those obtained using the first order shear deformation theory based DQ (FSDT-DQ) method Excellent agreements exist between the solutions of the two approaches but with much lower computational efforts of the present DQ methodology with respect to FSDT-DQ method

A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates

Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.

Large amplitude free flexural vibrations of laminated composite skew plates

Differential quadrature nonlinear analysis of skew composite plates based on FSDT

Large amplitude free vibrations of skew plates including transverse shear deformation and rotatory inertia—a new approach

Non-linear static behaviour of rhombic plates has been analysed following Banerjee's hypothesis (B. Banerjee, Large deflections of polygonal plates under non-stationary temperature. J. Thermal Stresses 7 , 285–292 (1984)). Calculations have been carried out for different skew angles. To test the accuracy of the theoretical results so obtained, experiments were carried out on copper and steel rhombic plates. The theoretical results were found to be in excellent agreement with those obtained from an analysis of the experimental data.

Large deflections of rhombic plates―a new approach

Nonlinear static and dynamic behaviours of freely supported Rhombic sandwich plates have been studied following Banerjee's hypothesis Numerical results for 0° skew angle are compared with other known results Results for other skew angles are believed to be new

Biswanath Bhattacharjee

Papers

Large amplitude free vibrations of skew plates including transverse shear deformation and rotatory inertia—a new approach

Large deflections of rhombic plates―a new approach

Nonlinear analysis of skewed sandwich plates

Non-linear analysis of heated rhombic plates