The free vibration of skew plates using the hierarchical finite element method

Abstract The hierarchical finite element method is used to determine the natural frequencies and modes of flat, isotropic skew plates. A number of such plates with different boundary conditions—including free edges and point supports—are considered in this paper. The dependence of frequency on skew angle, aspect ratio and Poisson's ratio is investigated, though succinctness prohibits a complete study exploring the full interrelation of these parameters. Extensive results are presented in diagrammatic, graphical, and tabular format; these are shown to be in very good agreement with the work of other investigators, and should prove a valuable source of data for use by engineers and scientists.

[1]  L. Morley.  Skew plates and structures , 1963 .

[2]  Tomisaku Mizusawa,et al.  Vibration of skew plates by using B-spline functions , 1979 .

[3]  V. Sigillito,et al.  Upper and lower bounds for frequencies of clamped rhombical plates , 1980 .

[4]  S. Durvasula.  Free vibration of simply supported parallelogrammic plates. , 1969 .

[5]  N. S. Bardell,et al.  Free vibration analysis of a flat plate using the hierarchical finite element method , 1991 .

[6]  Leonard Meirovitch,et al.  Elements Of Vibration Analysis , 1986 .

[7]  S. Durvasula,et al.  Natural frequencies and modes of clamped skew plates. , 1969 .

[8]  T. Kajita,et al.  Vibration of skew plates resting on point supports , 1987 .

[9]  Leonard Meirovitch,et al.  On the inclusion principle for the hierarchical finite element method , 1983 .

[10]  K. M. Liew,et al.  Application of two-dimensional orthogonal plate function to flexural vibration of skew plates , 1990 .

[11]  S. Durvasula,et al.  Vibration of skew plates , 1973 .

[12]  I. Katz,et al.  Nodal variables for complete conforming finite elements of arbitrary polynomial order , 1978 .

[13]  Rama B. Bhat,et al.  Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables , 1987 .

[14]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[15]  Alberto Peano,et al.  Hierarchies of conforming finite elements for plane elasticity and plate bending , 1976 .

[16]  M. Waller.  Vibrations of free plates: line symmetry; corresponding modes , 1952, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  J. Z. Zhu,et al.  The finite element method , 1977 .

[18]  Arthur W. Leissa,et al.  Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[19]  N. Bardell.  The application of symbolic computing to the hierarchical finite element method , 1989 .