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

高速高精度振动分析算法的开发

• 批准号: 63550190
• 负责人: SUEOKA Atsuo
• 金额: $ 1.28万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63550190/
• 关键词: Method of Vibration Analysis; Transfer Influence Coefficient Method; Modified Transfer Influence Coefficient Method; Generalized Release; Natural Frequency; Forced Vibration; Nonlinear Vibration; Stability; 伝達マトリックス法; 増分調和バランス法; 強制振動; 動的影響係数マトリ

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.

本文采用传递影响系数法，将直线结构、多层结构、二维和三维树形结构以及力学特性连续变化的变参数体系的弯曲横向线性自由振动视为集中质量系统和分布质量系统。传递影响系数法的算法是基于动力影响系数逐次传递的概念。该方法具有以下优点：(1)通过线性和转动弹簧常数统一边界条件；(2)简化了程序设计，不需要对中间刚性支承结构进行特殊处理；(3)相对于二分法，根据频率方程中产生的极点的产生机理，提出了一种简单的消除伪根的方法。此外，该方法还具有很好的通用性应用该方法分析了直线结构的线性弯曲强迫振动和直列结构的非线性振动。为了分析非线性振动系统，将谐和平衡法的概念与增量法的传递影响系数法相结合，提出了一种新的分析方法--增量传递影响系数法。在PC机上进行了较为简单的算例计算，结果表明，与通常用来进行振动分析的传递矩阵法相比，该方法具有计算精度高、速度快等优点。

项目成果

末岡 淳男: "伝達影係数法による多層構造物の自由振動解析(第1報,集中系に対する定式化)" 日本機械学会論文集. 54. 1724-1731 (1988)

Atsuo Sueoka：“使用传递阴影系数法进行多层结构的自由振动分析（第一份报告，集总系统的公式）”日本机械工程师学会会刊 54。1724-1731（1988）。

Atsuo SUEOKA et. al: "Free Vibration Analysis of Systems with Variable Parameters by the Modified Transfer Influence Coefficient Method (Formulation for a Disk with Variable Thickness)" Trans. of JSME. vol. 57, No. 535 C. (1991)

末冈敦夫等。

近藤 孝広: "Free Vibration Analysis of a Multiple StraightーLine Structure Regarded as a Distributed Mass System by the Transfer Influence Coefficient Method" JSME International Journal. 34. (1991)

Takahiro Kondo：“通过传递影响系数法对多直线结构进行自由振动分析”JSME 国际期刊 34（1991）。

Atsuo SUEOKA et. al: "Free Vibration Analysis of a Multiple Layered Structure by the Transfer Influence Coefficient Method (2nd Report, Computational Results of a Structure with Two Layers Regarded as a Discrete System)" Trans. JSME. Vol. 54, No. 504 C. 1

末冈敦夫等。

Takahiro KONDOU et. al: "Free Vibration Analysis of a Two-Layered Structure by the Transfer Influence Coefficient Method" Technical Report of Electronics Institute of Fukuoka Institute of Technology. vol. 5. 45-53 (1988)

近藤贵宏 等