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In this paper, an analytical technique, the so-called Fourier Spectral method (FSM), is extended to the vibration analysis of a rotating Rayleigh beam considering the gyroscopic effect. The model presented can have arbitrary boundary conditions specified in terms of elastic constraints in the translations and rotations or even in terms of attached lumped masses and inertias. Each displacement function is universally expressed as a linear combination of a standard Fourier cosine series and several supplementary functions introduced to ensure and accelerate the convergence of the series expansion. Lagrange's equation is established for all the unknown Fourier coefficients viewed as a set of independent generalized coordinates. A numerical model is constructed for the rotating beam. First, a numerical example considering simply supported boundary conditions at both ends is calculated and the results are compared with those of a published paper to show the accuracy and convergence of the proposed model. Then, the method is applied to one real work piece structure with elastically supported boundary conditions updated from the modal experiment results including both the frequencies and mode shapes using the method of least squares. Several numerical examples of the updated model are studied to show the effects of some parameters on the dynamic characteristics of the work piece subjected to moving loads at different constant velocities. [ABSTRACT FROM AUTHOR]

This paper deals with reconstruction of excitation forces and analyses of the root causes of vibro-acoustic responses of an elastic structure by using nearfield acoustical holography and modal expansion theory. Derivations of formulations for reconstructing excitation forces, including distributed, line, and point forces, acting on the back side of a rectangular thin plate simply supported on an infinite, rigid baffle, are presented. The reason for choosing a baffled plate is that analytic solutions to vibro-acoustic responses are readily available, so the accuracy in reconstruction can be examined rigorously. For simplicity, the effect of fluid loading is neglected, and input data are assumed error-free. Numerical examples of reconstructing excitation forces are presented, and results agree very well with benchmark values. The impacts of various parameters, such as the ratio of measurement aperture versus plate size, microphone spacing, standoff distance, the number of natural modes, etc., on reconstruction accuracy are investigated. Needless to say, in practice such idealized scenario is nonexistent and the accuracy in reconstruction of excitation forces are severely compromised by measurement errors and interfering signals. Nevertheless, the concept as presented is sound, except that more effective regularizations must be employed to enhance signal to noise ratio, and reconstruction results. [ABSTRACT FROM AUTHOR]