基于人工弹簧模型的周期结构带隙计算方法研究

冯青松; 杨舟; 郭文杰; 陆建飞; 梁玉雄

doi:10.6052/0459-1879-21-007

基于人工弹簧模型的周期结构带隙计算方法研究

doi: 10.6052/0459-1879-21-007

冯青松^*,
杨舟^*,
郭文杰^*,2), ,,
陆建飞^†,
梁玉雄^*

^*华东交通大学铁路环境振动与噪声教育部工程研究中心, 南昌330013
^†江苏大学土木工程与力学学院, 江苏镇江 212013

基金项目: 1)国家自然科学基金(51878277);国家自然科学基金(52068029);江西省主要学科学术和技术带头人培养计划(20194BCJ22008);江西省重点研发计划(20192BBE50008);江西省青年科学基金(20202BABL214049)

详细信息

作者简介:
2)郭文杰, 博士, 主要研究方向: 结构振动与噪声控制. E-mail: guowenjie@ecjtu.edu.cn.

通讯作者:
郭文杰

中图分类号: O327,O328
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出版历程
- 收稿日期: 2020-01-06
- 刊出日期: 2021-06-01

RESEARCH ON BAND GAP CALCULATION METHOD OF PERIODIC STRUCTURE BASED ON ARTIFICIAL SPRING MODEL

^*Engineering Research Center of Railway Environment Vibration and Noise, Ministry of Education, East China Jiaotong University, Nanchang 330013, China
^†Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, Jiangsu, China

摘要

摘要: 能量法具有将求解微分方程边值问题转化为泛函极值问题的优点,故而在结构动力学分析中被广泛使用, 近年来也被引入到周期结构带隙计算中. 然而,由于周期结构边界条件相对复杂,采用传统能量法(如Rayleigh-Ritz法)分析时位移函数构造难度大;且由于位移函数中包含波数项,扫描波数计算带隙的过程中质量、刚度矩阵需不断重算, 导致计算量较大. 鉴于此,本文对传统能量法进行改进,通过引入人工弹簧来模拟包含周期边界在内的各类边界条件,可将边界约束转化为人工弹簧的弹性势能,故而各能量分部中仅有周期边界弹性势能包含波数项,扫描波数时仅需重新计算与其对应的刚度矩阵,其余的质量、刚度矩阵只需要计算一次, 继而显著降低了计算量. 研究结果表明,本文方法准确、可靠, 且相较于传统能量法, 本文方法的计算效率更高,随着结构质量、刚度矩阵的维度增大, 或者扫描波数点数的增多,本文方法计算效率优势更加明显. 此外, 人工弹簧模型使用灵活、便捷,可进一步地拓展到更为复杂的周期性组合结构带隙分析中.
- 人工弹簧 /
- 计算效率 /
- 周期结构 /
- 带隙 /
- 能量法
Abstract: The energy method is widely used in structural dynamicsanalysis with its advantage of converting the boundary value problems fordifferential equation into the functional extreme value problem, and hasalso been introduced into periodic structure band gap computation in recentyears. However, it is difficult to construct the displacement function whenusing traditional energy methods (such as the Rayleigh-Ritz method) foranalysis because of the certain complexity in boundary conditions of theperiodic structure. Additionally, the wave number term is contained in thedisplacement function so that the mass and stiffness matrix need to berecomputed continuously in the process of calculating the band gap ofscanning wave number, which leads to a large amount of calculation. For thatreason, this paper improved the traditional energy method by introducingartificial spring model to simulate various boundary conditions includingperiodic boundaries so that boundary constraints could be transformed intothe elastic potential energy of artificial springs and only the periodicboundary elastic potential energy in energy distributions contains the wavenumber term, by which the corresponding stiffness matrix only needed to berecomputed in the scanning process of wave number and other mass andstiffness matrices need to be calculated only once and then significantlyreduced the computational burden. The research results show that the methodin this paper is accurate and reliable. The calculation efficiency of thismethod is advantageous compared with the traditional energy method. Theadvantage of calculation efficiency of this method is more obvious comparedwith the traditional energy method in the situation that the mass andstiffness matrix promote in dimension, or the scanning points of wave numberincrease. In addition, the artificial spring model is more flexible andconvenient to use, and can be further adopted to band gap analysis of morecomplex periodic composite structures.
- artificial spring /
- computational efficiency /
- periodic structure /
- band gaps /
- energy method

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