Development of a system of vibration analysis for large scale nonlinear structures by using the incremental transfer stiffness coefficient method

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In this research, a numerical computational method of high performance was developed to compute the very accurate solution for large scale nonlinear structures and to analyze the stability of the solution obtained. In addition, the useful computation system of nonlinear vibration analysis suited for the practical works of mechanical design was constructed. The following results were obtained.1. The incremental transfer stiffness coefficient method was applied to the forced vibration analysis of the straight-line beam structure supported by the nonlinear elements, and the effectiveness and possibility of the present method were discussed in detail. The incremental transfer stiffness coefficient method was formulated by combining the concepts of both the method of harmonic balance and the transfer stiffness coefficient method through the incremental method. In the application, the beam element was regarded as the linear beam and was modeled as the lumped mass system. Both the continuous nonlinear support element and the piecewise linear support element were considered. The present method was applied also to the two and three dimensional tree structures having some crooked parts and subsystems, and the nonlinear coupled vibration generated in such structures was analyzed.2. The effectiveness of the present method was confirmed by evaluating the performance in detail from the viewpoints of computation speed, computational accuracy and memory size to be required.3. An very efficient method for stability analysis was newly formulated. In this method, the stability of the approximate solution obtained by the incremental transfer stiffness coefficient method was determined from the dimension reduced model in which the few modes dominating the stability of the solution were extracted by applying the concept of the modal analysis. It was confirmed that the computation speed was reduced remarkably without the decrease in computational accuracy by applying the present method.