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An improved Fourier expansion-based differential quadrature (DQ) algorithm is proposed to study the free vibration behavior of truncated conical shells with different boundary conditions. The original function is expressed as the Fourier cosine series combined with close-form auxiliary functions. Those auxiliary functions are introduced to ensure and accelerate the convergence of series expansion. The grid points are uniformly distributed along the space. The weighting coefficients in the DQ method are easily obtained by the inverse of the coefficient matrix. The derivatives in both the governing equations and the boundaries are discretized by the DQ method. Natural frequencies and modal shapes can be easily obtained by solving the numerical eigenvalue equations. The accuracy and stability of this proposed method are validated against the results in the literature and a very good agreement is observed. The centrosymmetric properties of these newly proposed weighting coefficients are also validated. Studies on the effects of semivertex angle and the ratio of length to radius are reported. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the free vibrations of cylindrical shells with elastic boundary conditions. Based on the Flügge classical thin shell theory, the equations of motion for the cylindrical shells are solved by the method of wave propagations. The wave numbers are obtained by directly solving an eighth order equation. The elastic-support boundary conditions can be arbitrarily specified in terms of 8 independent sets of distributed springs. All the classical homogeneous boundary conditions can be considered as the special cases when the stiffness for each set of springs is equal to either infinity or zero. The present solutions are validated by the results previously given by other researchers and/or obtained using finite element models. The effects on the frequency parameters of elastic restraints are investigated for shells of different geometrical characteristics. [Copyright &y& Elsevier]

In this paper, an exact analytical solution is proposed to investigate the free in-plane vibration of sector plates. The highly complex and coupled differential equations of in-plane vibration motion are decoupled by invoking Helmholtz decomposition. The method of separation of variables is used to solve the resulting uncoupled Helmholtz equations. Applying the boundary conditions at both radial edges, the compatible eigenvalue problems for sector plates are obtained. Then, applying the boundary conditions at inner and outer circumferential edges, the corresponding characteristic equations can be solved to obtain the natural frequencies and the associated mode shapes. The results from the proposed method agree very well with the results from the available literature and the FEM. Significant influence of the boundary conditions and the geometric parameters on the free in-plane vibration characteristics of sector plates is investigated and addressed. The superficial frequency veering "aberration" between neighboring modes is discussed and found in fact to be an eigenvalue crossing phenomenon. It is proved that for a sector plate, only with simply supported radial edges, there exists an exact analytical solution. The proposed exact analytical solution can provide not only the detailed characteristics of the free in-plane vibration of sector plates but also the benchmark for further study. [ABSTRACT FROM AUTHOR]