The symplectic method for free vibration, buckling and dynamics analysis of partial-interaction composite beams based on Timoshenko theory

This paper presents a symplectic state-space formulation based on Timoshenko beam theory for analyzing the free vibration, buckling, and dynamic responses of composite beams with partial shear interaction. By introducing dual state variables, the governing equations are transformed into a first-order Hamiltonian system, enabling analytical solutions under general boundary conditions. A symplectic inner product is used to rigorously establish the orthogonality of vibration modes, providing a robust foundation for modal superposition. The proposed method is further extended to multi-span beams with nonuniform shear connection stiffness. Numerical examples validate the model’s accuracy and demonstrate its capability to capture complex behaviors under distributed and moving loads. Compared to conventional methods, the symplectic formulation offers a unified and computationally efficient approach for analyzing partially interactive composite structures subjected to static and dynamic excitation.