An exact model for free vibration of structures coupled by arbitrarily shaped plates

In this paper, an exact model for free vibration of structures coupled by arbitrarily shaped thin plates is developed. In order to obtain the energy expressions of flexural and in-plane vibration of arbitrarily shaped sub-plates, a domain segmentation integral method is proposed. The arbitrarily shaped integration domain is divided into several trapezoid domains with curved sides. Accordingly, the penalty method and Gram-Schmidt orthogonalization process are combined to calculate the energy integrals. Four types of virtual coupling springs are set along the coupling edge of the sub-plates to simulate the coupling interactions, so that the flexural and in-plane vibrations of the sub-plates are taken into account in the model. Then the vibration characteristics are obtained by using the Rayleigh-Ritz program. When the contour curve equations of sub-plates enable the energy integrals to be analytically calculated, the model can obtain the exact solutions of free vibration of structures coupled by arbitrarily shaped plates under general elastic boundary conditions; otherwise, the semi-analytic results can be obtained by combining Gauss-Legendre method. The accuracy of the proposed model is verified through the convergence study and comparison with the results of literatures and finite element software. Furthermore, the proposed model is applied to determine the natural frequencies of structures coupled by arbitrarily shaped plates. Taking the structure coupled by a rectangular plate and a semicircular plate as examples, the effect of the coupling angle on the vibration characteristics of the structures is studied.