Development of Algorithm for Vibration Analysis with High Speed and with High Accuracy

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In this investigation, the flexural lateral linear free vibrations of straight line structure, multiple layered structure, two and three dimensional tree structure and systems with variable parameters mechanical characteristics of which change continuously were treated regarded as the lumped mass system and the distributed mass system, using the transfer influence coefficient method. The algorithm of the transfer influence coefficient method is based on the concept of the successive transmission of the dynamic influence coefficients.The present method has the following advantages : (1) The unification of the boundary conditions by virtue of the linear and rotational spring constants, (2) simplification of the programming and absence of the need for special treatment for a structure with intermediate stiff supports, and (3) a simple approach to eliminate the false roots based on the occurrence mechanism of the poles generated in the frequency equation relative to the use of the bisection method.Furthermore, the present method was applied to the analysis of the linear flexural forced vibration for a straight line structure and the nonlinear vibration for a in-line structure. To analyze the nonlinear vibration systems, incremental transfer influence coefficient method was anew presented as a analytical method which combined the concept of the method of harmonic balance with the one of the transfer influence coefficient method by using the incremental method.The results of the comparatively simple computational examples on a personal computer demonstrate the validity of the present algorithm, that is, the high numerical accuracy and the high speed of the present method, as compared with the transfer matrix method by which the vibration analysis is often carried out.