Vibrations of Timoshenko Double-Beam Systems with Arbitrary Intermediate Supports and Axial Loads

Although the double-beam systems are widely utilized, few investigations have been conducted on the general form of the double-beam system, considering shear deformation and rotary inertia. The present paper tackles the free and forced vibrations of the Timoshenko double-beam system with arbitrary intermediate supports and axial loads (TDBS-IS-AL) subjected to arbitrary exciting forces under the general boundary conditions by two methods, i.e., shape function method (SFM) and uncoupled mode shape (UMS) method. The generalized mode shape solutions obtained by the SFM are exact and explicit, based on which the characteristic frequency equations are constructed. Implementing Lagrange's equation and the modal expansion technique, the dynamic responses (displacement, velocity, and acceleration) of the TDBS-IS-AL are obtained. The natural frequencies and dynamic responses calculated by the UMS are utilized to benchmark the results of SFM. In addition to the theory, illustrating examples are demonstrated to justify the validity of the solutions. It is shown that the results of specific configurations of the double-beam system comply well with the literature. Besides, the frequency and dynamic responses of the SFM are consistent with those of the UMS. The effects of the intermediate support on the vibration characteristics and dynamic responses are also studied.