A closed-form solution of forced vibration of a double-curved-beam system by means of the Green's function method

Double-curved-beam systems (DCBSs) are usually seen in many engineering fields. Compared to straight double-beam systems, DCBSs are more efficient in noise and vibration control. This paper aims to obtain a closed-form solution of steady-state forced vibration of a DCBS. The classical Euler-Bernoulli beam model is employed in this work to model vibration equations of the DCBS. Green's function and Laplace transform methods are successively used to obtain the fundamental solution of vibration equations of the DCBS. The fundamental solution is the general solution and can be used for any boundary conditions. In the numerical result section, the present solution is verified by comparing its results with some results in references. Effects of some important geometric and physical parameters on vibration responses and interaction between the stiffness of the elastic layer and the DCBS are discussed. Results show that the DCBS can be degenerated to a straight double-beam system by setting two radii of curvature of the beams to infinity, and the DCBS can also be reduced to a double-beam system whose one upper or lower beam is a straight beam and the other is a curved beam.

Automated summary

This paper aims to derive a closed-form solution for steady-state forced vibration of a double-curved-beam system (DCBS). The classical Euler-Bernoulli beam model is used to establish the vibration equations of the DCBS. The fundamental solution of the vibration equations is obtained using Green's function and Laplace transform methods, which can be applied to any boundary conditions. The numerical results validate the proposed solution by comparing with previous studies and investigate the effects of geometric and physical parameters on vibration responses and the interaction between the elastic layer stiffness and the DCBS.