Substructure elimination method for evaluating bending vibration of beams

IF 0.4 Q4 ENGINEERING, MECHANICAL
Keisuke YAMADA, Jinchen JI
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Abstract

In this study, a vibration analysis method is presented based on the substructure elimination method for a Bernoulli-Euler beam. Vibration analysis using modal analysis is effective for reducing the degrees of freedom and enables the analysis of a beam on which actuators and sensors are installed. When mechanical impedances are installed at the boundaries or the beam is coupled to other structures, a free-free beam is employed for conventional modal analysis using continuous functions. However, conventional modal analysis provides inaccurate simulation results when the coupled mechanical impedances considering the characteristic impedances of the beam are large. To address this issue, the modal analysis of a beam using the substructure elimination method was proposed in this study. Because the substructure elimination method for beams was only briefly reported on by the first author, several problems currently exist. To solve these problems, a substructure elimination method is proposed using a simply supported beam in addition to a guided-guided beam. Additionally, a new formulation method based on constraint conditions was proposed as a versatile method for setting arbitrary boundary conditions. The appropriate length, line density, and bending stiffness of the elimination regions, and the highest order of the eigenmode, were determined through simulations. The effectiveness of the proposed method was then verified by comparing the simulation results of the proposed method and exact solutions obtained using the boundary conditions. Based on a comparison with the simulation results of conventional modal analysis using a free-free beam, the precision of the proposed method is significantly higher than that of conventional modal analysis.
评估梁弯曲振动的子结构消去法
本文提出了一种基于子结构消去法的伯努利-欧拉梁振动分析方法。使用模态分析进行振动分析对于降低自由度是有效的,并且能够对安装了致动器和传感器的梁进行分析。当在边界处设置机械阻抗或梁与其他结构耦合时,使用连续函数进行常规模态分析时采用自由-自由梁。然而,考虑到梁的特性阻抗,当耦合机械阻抗较大时,传统的模态分析结果不准确。为了解决这一问题,本研究提出了采用子结构消去法对梁进行模态分析。由于第一作者对梁的子结构消除方法的研究比较简单,目前还存在一些问题。为了解决这些问题,提出了一种除导导梁外再加简支梁的子结构消除方法。此外,提出了一种新的基于约束条件的表述方法,作为设置任意边界条件的通用方法。通过仿真确定了消除区的合适长度、线密度、弯曲刚度以及特征模态的最高阶。通过将所提方法的仿真结果与利用边界条件得到的精确解进行比较,验证了所提方法的有效性。通过与传统自由-自由梁模态分析仿真结果的比较,表明该方法的精度明显高于传统模态分析的精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mechanical Engineering Journal
Mechanical Engineering Journal ENGINEERING, MECHANICAL-
自引率
20.00%
发文量
42
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