Dynamic analysis of partial-interaction composite beams

The state-space method is used to investigate the dynamic behavior of partial-interaction composite beams. The state-space formula is properly established via selecting the appropriate state variables. The characteristic equations of frequency and the corresponding modal shapes of free vibration under generalized boundary conditions are then obtained. Based on the state-space formula and the concept of symplectic inner product, a new route is proposed to prove the orthogonality of vibration modes of composite beams under generalized boundary conditions. By virtue of mode superposition method, we obtain the solution of the inhomogeneous equation for forced vibration and the dynamic response of the partial-interaction composite beams subjected to a uniformly distributed pulse load, a uniformly distributed step load or a moving constant force. Finally, some numerical examples are presented and compared with those available in the literature to validate the present method. The effect of the rigidity of shear connector on dynamic responses of a composite beam under moving constant force is discussed.