Finite element formulation for free vibration of composite beams

Abstract

Investigations concerning the dynamic response of composite beams with partial interaction are scarce. Derivation of the differential equations describing the interaction between composite elements normally involves with the solution of high order system of equations, which closed form solutions are difficult. This study concerns with the finite element formulation of composite beams for free vibration. The formulation involves with the establishment of the stiffness matrix and the mass matrix of the beam. The former was obtained through extremization of the total potential energy (or Hamilton principle for dynamic) whilst the latter was obtained by lumping the elements mass at nodes. Natural frequencies of the beam were obtained as eigenvalues. These were then verified by existing analytical solution.