Vibration of unconstrained layered circular plates

: Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.

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Vibration of plates

The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.

Application of the simultaneous iteration method to undamped vibration problems

The finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness An annular element is derived which incorporates the number of diametral modes in the deflection function This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti-node of the particular vibration mode Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness



The method is checked with several numerical examples Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions

Vibration of unconstrained layered circular plates

References

Vibration of plates

Application of the simultaneous iteration method to undamped vibration problems

Vibration of circular and annular plates using finite elements

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