Abstract
A method is introduced for vibration analysis of a wide class of beam, plate and shell problems including the effects of variable geometry and material properties. The method is based on the discrete technique of component mode analysis. For each of these components the mode shapes are written in terms of Rayleigh-Ritz expansions involving simple Fourier sine or cosine series. Due to the nature of these series, special attention must be given to end point behavior in the modal expansions and in the derivatives of these modal expansions. This is done via the mechanisms of Stokes' transformation. Continuity between components is enforced with Lagrange multipliers. The resulting frequency equation is exact and the associated eigenvector contains a combination of force and displacement types terms. Numerical solutions are found by truncating the series and monitoring the frequency determinant on a computer.
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