Free and forced vibration analyses of simply supported Z-reinforced sandwich structures with cavities through a theoretical approach

Abstract This paper develops a theoretical approach to study free and forced vibrations of simply supported Z-reinforced sandwich structures with cavities in vacuum and water. A multi-level homogenization model is firstly proposed to transform the core layer of the sandwich structure to an orthotropic material. Then the first-order shear deformation theory (FSDT) is adopted to describe displacement fields and Hamilton’s principle is used to derive motion equations of the sandwich structure. In water domain, the acoustic pressure and the continuity on the fluid-structure coupling face are governed by Helmholtz equation and Euler’s equation respectively. By the aid of Green’s function, the transverse vibration formula is rebuilt through regarding the submerged sandwich structure as a thin plate. New motion equations are thus achieved. Under simply supported boundaries, natural frequencies and forced vibration responses are obtained via the Navier method. By comparing theoretical results with those from finite element (FE) and boundary element (BE) analyses, the high accuracy of the present approach is verified and a clear application frequency range is found. Besides, effects of diameters of reinforcements and cavities on free vibration are discussed. Influences of the external force location and fluid loading on forced vibration are also studied.