On the transverse vibration of Timoshenko double-beam systems coupled with various discontinuities

An efficient analytic framework is developed in this paper to study transverse vibrations of double-beam systems used in numerous engineering applications, in which two parallel Timoshenko beams are connected by discrete springs and coupled with various discontinuities. By dividing the entire structure into a series of distinct components, and then systematically organizing compatibility and boundary conditions with matrix formulations, closed-form expressions for the exact natural frequencies, mode shapes and frequency response functions (FRFs) can be determined. In particular, the proposed model enables one to simultaneously consider (1) both the free and forced vibrations, (2) translational and rotational effects of the connection springs, (3) any boundary conditions, and (4) various combinations of discontinuities. Furthermore, regardless of the number of discontinuities and connections, the sizes of all associated matrices are never larger than 8×8. This results in a significant computational advantage, especially for the derivation of the FRFs. Some results are compared with previous publications and also with the finite element method to demonstrate the accuracy and versatility of the proposed method. Finally, parametric studies are performed for a practical example to illustrate the influences of parametric variabilities on the dynamic behaviors.