In-Plane Free Vibration and Wave Propagation of Composite Curved Beam Using Spectral Element Method

Abstract

Laminated anisotropic composite materials are used in various fields like civil engineering structures, aerospace, marine, auto mobile industries etc. due to its superior qualities over isotropic material. Qualities like High strength-to-weight ratio, stiffness-to-weight ratio, and their ability to be tailored for specific applications are putting composite materials forward as a better alternative for the isotropic materials. Thus more and more accurate dynamic study of such composite members are desired as we come across new and better implementation of composite material.
For vibration problems with higher modes of vibrations, the dynamic stiffness matrices for elements can be formed by using the frequency dependent shape functions. The shape functions in the frequency domain can be derived using frequency dependent solutions for the exact governing differential equations. These dynamic stiffness matrices for the elements are assembled like FEM to form the global Dynamic Stiffness Matrix. The great advantage of such a method is that even higher frequencies of a structure can be obtained by considering only a few elements thus minimising the computational cost.