IN-PLANE DYNAMIC ANALYSIS OF CIRCULARLY CURVED BEAMS BASED ON THE STATE SPACE METHOD

The state space method is adopted to study the in-plane dynamic behavior of circularly curved beams. By selecting appropriate state variables, the state space formula is properly set up. The frequencies and corresponding modal shapes of circularly curved beams are then obtained on the basis of state-space formulae. By utilizing the conception of symplectic inner product, the mode orthogonality with respect to the mass and rotary inertia properties for curved beams under three common boundary conditions in engineering (simply-supported, clamped and free) is established. Based on the orthogonality relation, the mode superposition method is utilized to obtain the solution of the inhomogeneous equation for forced vibration and dynamic response of curved beams subjected to a vertical moving constant force. The numerical results show that the proposed method is very accurate and reliable.