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分级周期梁结构的振动带隙特性优化研究 被引量:2

Optimization of Band-gap Characteristics of Hierarchical Periodic Beam
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摘要 针对分级周期梁结构,进行了振动带隙特性优化研究,以期提高结构的减振性能.采用谱元法计算分级周期梁的频响曲线,并结合传递矩阵法计算结构的色散关系,将两种方法相结合来研究结构的振动带隙特性.构建带隙占比函数作为优化目标函数,将单胞结构的尺寸作为优化参数进行带隙特性优化.经过优化,使得在研究频段内带隙特性大大提高.通过与有限元法和振动实验相对比,验证了谱元法计算和优化结果的正确性.研究内容对于提高周期结构的振动带隙特性和减振应用提供有益参考. In order to improve the vibration reduction performance of hierarchical periodic beam,the vibration band-gap characteristics are optimized.Combined with previous studies,the dispersion relation of the infinite hierarchical periodic beam structure is chosen as the optimization object.The purpose of the optimization is to maximize the proportion of band-gaps in the whole frequency range.The spectral element method(SEM) is used to calculate the frequency response curves of the periodic beam,the dispersion relation curves of the structure is calculated by the transfer matrix method,and the two methods are combined to study the vibration band-gap characteristics of the structure.The frequency response curve of the finite hierarchical period beam is calculated to validate that the band-gap characteristic of the finite period beam is the same as that of the infinite period one.The band-gap ratio function is constructed as the optimization objective function,and the sizes of the unit-cell are used as the optimization parameters to optimize the band-gap characteristics.The structural parameters of the horizontal and vertical rods of the third L-shaped structure in the unit-cell are chosen as the optimization parameters group.After optimization,the band-gap characteristics in the considered frequency ranges are greatly improved.The optimization results of the vertical rod are extremely obvious,and the optimized band-gap ratio is increased to about 80%.Two vibration experiments are conducted to verify the un-optimized and the optimized results.Compared with the finite element method(FEM) and the vibration experiments,the correctness of the calculation results of the SEM is verified.In general,the hierarchical periodic beam structure can be optimized by applying the dispersion relation curves,and the vibration band-gap properties can be obviously enhanced.The research content provides a useful reference for improving the vibration band-gap characteristics of periodic structures and the application of vibration reduction.
作者 熊远皓 李凤明 Yuanhao Xiong;Fengming Li(College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin,150001)
出处 《固体力学学报》 CAS CSCD 北大核心 2021年第6期633-641,共9页 Chinese Journal of Solid Mechanics
基金 国家自然科学基金项目(11761131006)资助。
关键词 分级周期梁结构 谱元法 振动带隙 优化 振动实验 hierarchical periodic beam spectral element method(SEM) vibration band-gap optimization vibration experiment
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