The article is devoted to research of fluctuations (vibration) of complex real shells. An example of such shell can be the ship hull. Part of the ship hull interacts with adjoining fluid. The forced harmonic fluctuations are considered. The purpose of this study is derivation of mathematical model for fluctuations of a shell using the module-element method (MEM). The module-element method is the modification of the finite element method. The important feature of the proposed mathematical model is the consideration of the fluctuation of the shell together with an adjoining fluid. The coupled system "structure- liquid" is considered. The problem is solved using theory of hydroelasticity. The theoretical problem is solved using combination of two numerical methods: a module-element method and a boundary element method. The mathematical model also accounts for the effect of damping on fluctuations of coupled system "structure- liquid".
The theoretical solution of the problem of vibration of the complex real shells is challenging due to following reasons:
the complex geometry of real shell;
the internal damping or damping of shell material. This damping can be related to the properties of the material, the energy loss in welds and other energy loss;
the damping of the external environment, for example, damping due to viscousity of the adjacent liquid;
inertial interaction of the fluctuating shell with the liquid involved in the joint movement;
complicated external impacts on a real shell.
The vibrations of complex real shells can lead to unexpected events of resonant oscillations which reduces reliability and operability of complex real shells.
We will consider a case of the forced fluctuations of complex system taking into account external and internal damping using theory of hydroelasticity. Only small fluctuations (vibrations) are considered. The problem will be solved using Module Element Method or MEM (Postnov and Taranukha, 1990; Taranukha and Leizerovich, 2005).
