Free vibrations of laminated beams using mixed theory

Abstract

An analytical method for evaluating the natural frequencies of laminated composite and sandwich beams has been developed in this paper using higher-order mixed theory. The stiffness and mass matrices for the laminate are computed by evaluating the integrands explicitly. Each lamina of the laminate is assumed to be orthotropic and in a two-dimensional state of plane stress. Hamilton's principle has been employed to derive the equilibrium equations. Numerical experiments on laminated composite and sandwich beams of thin and thick sections are performed. The results obtained are compared with those of the first-order shear deformation theory and are validated by comparing them with the published results of analytical methods incorporating displacement-based higher order theories.