Higher‐order perturbation solution of a free vibration problem of coupled piezoelectricity by Kato's theory

The present study considers the free vibration analysis of moderately thick conical shells based on the Novozhilov theory. The higher order governing equations of motion and the associate boundary conditions are obtained for the first time. Using the Frobenius method, exact base solutions are obtained in the form of power series via general recursive relations which can be applied for any arbitrary boundary conditions. The obtained results are compared with the literature and very good agreement (up to 4%) is achieved. A comprehensive parametric study is performed to provide an insight into the variation of the natural frequencies with respect to thickness, semivertex angle, circumferential wave numbers for clamped (C), and simply supported (SS) boundary conditions.

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Free vibration of laminated composite plates—a simple finite element based on higher order theory

Computers & Structures ◽

10.1016/0045-7949(94)90225-9 ◽

1994 ◽

Vol 52 (3) ◽

pp. 397-404 ◽

Cited By ~ 23

Author(s):

A.K. Ghosh ◽

S.S. Dey

Keyword(s):

Finite Element ◽

Free Vibration ◽

Laminated Composite ◽

Composite Plates ◽

Order Theory ◽

Higher Order ◽

Laminated Composite Plates ◽

Higher Order Theory

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An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

Engineering Computations ◽

10.1108/ec-07-2021-0430 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Yongliang Wang ◽

Jianhui Wang

Keyword(s):

Finite Element ◽

Free Vibration ◽

Cylindrical Shells ◽

Higher Order ◽

Wave Number ◽

Adaptive Finite Element ◽

Content Type ◽

Circular Cylindrical Shells ◽

Geometrical Factors ◽

Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

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