Abstract

A hitherto unavailable analytical solution to the free vibration problem of general cross-ply laminated rigidly clamped rectangular plates, incorporating first-order shear deformation, and rotatory and in-plane inertias into the formulation, is presented. A recently developed boundary continuous displacement-based generalized Navier solution technique is used to solve the five highly coupled linear second-order partial differential equations with constant coefficients, and the associated geometric boundary conditions. The assumed solution functions are in the form of double Fourier series, which satisfy the rigidly clamped boundary conditions a priori in a manner similar to the conventional Navier method. Convergence characteristics of the natural frequencies of both symmetric and antisymmetric cross-ply plates are numerically established. Other numerical results presented herein include (i) comparison with the corresponding available first-order shear deformation theory-based Galerkin and classical lamination theory-based boundary-discontinuous analytical solutions, and (ii) study of the effects of thickness and aspect ratio on the natural frequencies.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.