Shuangxia Shi

An analytical method for vibration analysis of cylindrical shells coupled with annular plate under general elastic boundary and coupling conditions

A unified solution for coupled cylindrical shell and annular plate systems with general boundary and coupling conditions is presented in the study by using a modified Fourier-Ritz method. Under the framework, regardless of the boundary and continuity conditions, each displacement for the cylindrical shell and the annular plate is invariantly expressed as the modified Fourier series composed of the standard Fourier series and auxiliary functions. The introduction of the auxiliary functions can not only remove the potential discontinuities at the junction and the extremes of the combination but also accelerate the convergence of the series expansion. All the expansion coefficients are determined by the Rayleigh-Ritz method as the generalized coordinates. The arbitrary axial position of the annular plate coupling with the cylindrical shell considered in the theoretical formulation makes the present method more general. The theoretical model established by present method can be conveniently applied to cylindrical shell-circular plate combinations just by varying the inner radius of the annular plate. The convergence and accuracy of present method are tested and validated by a number of numerical examples for coupled annular plate-cylindrical shell structures with various boundary restraints and general elastic coupling conditions. The effects of the axial position of the annular plate and elastic coupling conditions on the vibration behavior of the coupled system are also investigated. The power of present method compared to conventional finite element method is demonstrated with less computation cost. Some new results are presented to provide useful information for future researchers.

A General Analytical Method for Vibroacoustic Analysis of an Arbitrarily Restrained Rectangular Plate Backed by a Cavity With General Wall Impedance

A general modeling method is developed for the vibroacoustic analysis of an arbitrarily restrained rectangular plate backed by a cavity with general wall impedance. The present method provides a uniform way to obtain the solution of the coupled structure-cavity system, making changes of both boundary conditions of the plate and impedance of the cavity walls as simple as the modifications of geometrical or material parameters without requiring any altering of the whole solution procedure. With the displacement of the plate and acoustic pressure in the cavity expanded as double and triple Chebyshev polynomial series, respectively, a simple yet efficient solution to the problem of the modal and vibroacoustic behavior of the coupled system is obtained under the Rayleigh–Ritz frame. The current method can be applied to handle strong structural-acoustic coupling cases and this is illustrated explicitly by considering one case with a shallow cavity and very thin plate while the other with a water-filled cavity. The spatial matching of velocity at the interface is checked by numerical examples. The excellent orthogonal and complete properties of the Chebyshev series representations enable excellent accuracy and numerical stability. An experiment is conducted to validate the present method. In addition, the accuracy and reliability of the current method are also extensively validated by numerical examples and comparisons with theoretical solutions, finite element results, and results available in the literature. The effects of several key parameters are analyzed, including structural boundary conditions, plate thickness, cavity depth, and wall impedance.

Three-Dimensional Vibration Analysis of Isotropic and Orthotropic Open Shells and Plates with Arbitrary Boundary Conditions

This paper presents elasticity solutions for the vibration analysis of isotropic and orthotropic open shells and plates with arbitrary boundary conditions, including spherical and cylindrical shells and rectangular plates. Vibration characteristics of the shells and plates have been obtained via a unified three-dimensional displacement-based energy formulation represented in the general shell coordinates, in which the displacement in each direction is expanded as a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to eliminate any possible jumps with the original displacement function and its relevant derivatives at the boundaries. All the expansion coefficients are then treated equally as independent generalized coordinates and determined by the Rayleigh-Ritz procedure. To validate the accuracy of the present method and the corresponding theoretical formulations, numerical cases have been compared against the results in the literature and those of 3D FE analysis, with excellent agreements obtained. The effects of boundary conditions, material parameters, and geometric dimensions on the frequencies are discussed as well. Finally, several 3D vibration results of isotropic and orthotropic open spherical and cylindrical shells and plates with different geometry dimensions are presented for various boundary conditions, which may be served as benchmark solutions for future researchers as well as structure designers in this field.