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

本研究开发了一种高性能的数值计算方法，用于计算大型非线性结构的非常精确的解，并分析解的稳定性。建立了适用于机械设计实际工作的非线性振动分析计算系统。得到了以下结果：将增量传递刚度系数法应用于非线性单元支撑的直线梁结构的强迫振动分析，详细讨论了该方法的有效性和可行性。通过增量法，将谐波平衡法和传递刚度系数法的概念相结合，形成了增量传递刚度系数法。在应用中，将梁单元视为线性梁，并将其建模为集总质量系统。考虑了连续非线性支撑单元和分段线性支撑单元。将该方法应用于具有弯曲部件和子系统的二、三维树形结构，并对其产生的非线性耦合振动进行了分析。从计算速度、计算精度和所需内存大小三个方面对该方法进行了详细的性能评价，验证了该方法的有效性。提出了一种非常有效的稳定性分析方法。该方法从降维模型出发，利用模态分析的概念提取出控制解稳定性的少数模态，确定增量传递刚度系数法得到的近似解的稳定性。结果表明，该方法在不降低计算精度的前提下，显著降低了计算速度。

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.