A derivation and solution of dynamic equilibrium equations of shear undeformable composite anisotropic beams using the DQEM

In this paper, Hamilton's principle is used to derive the dynamic equilibrium equations of composite nonprismatic beams made of anisotropic materials. The effects of transverse shear deformations are neglected. The displacements are defined on an arbitrarily selected coordinate system. For Hamilton's principle, the dynamic behavior of nonprismatic beams is characterized by two energy functions: a kinetic energy and a potential energy. The formulation uses the procedure of variational operations. The obtained dynamic equilibrium equations and natural boundary conditions are strongly coupled. They can be solved by the differential quadrature element method (DQEM).