A SPECTRAL-DIFFERENTIAL QUADRATURE METHOD FOR 3-D VIBRATION ANALYSIS OF MULTILAYERED SHELLS

The equivalent single layer (ESL) theories can be grossly in error for predicting vibration characteristics of thick multilayered shells because the vibration displacement and stress field of such shells under vibration are in full 3-D coupling condition. It is necessary to develop more accurate and efficient methods which are capable of dealing with multilayered structures with different boundary conditions, general laminations as well as arbitrary thickness universally. In order to overcome the drawback of the existing three-dimensional methods that are only confined for very limited cases such as cross-ply laminated rectangular plates under simply-supported boundary conditions, a general spectral-differential quadrature method is proposed. This method is undertaken by the exact 3-D elasticity theory so that it’s able to study very well the dynamic behavior of thick multilayered structures which cannot be provided by the 2-D ESL theories. In each individual layer, the transverse domain is discretized by the differential quadrature technique. The displacement fields of the discretized surfaces are selected as fundamental unknowns. Then, each fundamental unknown is invariantly expanded by the general spectral method as a series of complete, orthogonal polynomials. The problems are stated in a variational form by the aid of penalty parameters which provides complete flexibilities to describe any prescribed boundary conditions. The current method can successfully avoid solving a highly nonlinear transcendental equation that is rely on roots-locating numerical method and all the modal information can be obtained just by solving linear algebraic equation systems. Numerical verification shows that the proposed method has high calculation precision. The method can be directly extend to the static and dynamic analysis of multilayered shells as well.