Stability of parametric vibrations of laminated composite plates
The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotin's method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.
Non-linear parametric vibration responses of composite plates on Pasternak foundations using extended dynamic stiffness method
ABSTRACT In this work, the non-linear parametric vibration responses of rectangular laminated composite plates subjected on Pasternak foundation, under in-plane periodic compressive load applied along two opposite edges, are theoretically studied using the extended dynamic stiffness method. The authors present the new method to establish the exact dynamic stiffness matrices of rectangular laminated composite plates subjected to in-plane periodic forces based on general Von-Kármán large deflection plate theory. A set of second-order ordinary differential non-linear equations of extended Mathieu–Hill type with periodic coefficients is formed to determine the regions of dynamic instability and non-linear parametric vibration responses based on Bolotin method. The effects of various parameters such as static load, dynamic load, aspect ratio, boundary conditions, orthotropy and foundation stiffness factor on the dynamic instability regions and non-linear parametric vibration characteristics are investigated and discussed. For linear theory, the present results are found to be in agreement with available conclusions in the literature which was obtained based on the linear analysis.
Non-linear vibrations of simply supported rectangular cross-ply plates
A method of direct numerical integration of the frequency-ratio expression is proposed to study the non-linear free vibration behaviour of rectangular cross-ply laminates. The proposed method, even with single-term approximations for the admissible functions, yields results that agree very well with the existing perturbation solutions. Non-linear behaviour of the cross-ply laminates is also studied with the harmonic oscillations assumption, by using the conservation of energy and the modal equation. The results are found to be lower and upper bounds to those obtained from the direct numerical integration method. It is also observed that the arithmetic mean of the two solutions with the harmonic oscillations assumption matches very well with that of the direct numerical integration method. Non-linear vibration characteristics are obtained for several configurations of cross-ply plates. Results for orthotropic and isotropic plates are also obtained as special cases.