本文以平面内田字型耦合薄板结构为研究对象，提出了一种计算弹性约束边界条件耦合板振动响应的解析方法。利用耦合部位的平衡条件和连续性条件，建立了耦合板结构的边界耦合方程。使用改进的傅里叶级数作为每个子板的弯曲位移函数，从而使得微分形式的边界耦合方程和各子板的运动方程离散为简单的线性方程组。ANSYS有限元软件仿真验证了本文所建立的理论模型的正确性。利用本文建立的理论模型，分析了边界约束刚度的附带阻尼对耦合板结构振动响应的影响，结果表明：在横向约束刚度较软的情况下，横向约束刚度附带的边界阻尼可以明显削弱低阶共振响应。在求得结构位移的基础上，进一步给出了耦合板结构功率流的表达式，并对耦合板结构内的振动功率流传递特性进行了仿真研究，结果表明：增大边界约束刚度能有效阻碍功率流的在边界处的流动；当外激励频率为低阶共振频率时，功率流更容易从受激板流向与受激板相同材质的接受板。
Abstract
In this paper, the vibration response of in-plane Four-Palace type coupled plates was studied; an analytical method which calculates the vibration of coupled plates with elastic edges was proposed. Based on balance condition and continuity condition on coupling sides, the coupled equations of Four-Palace type coupled plates on coupling sides were established. The improved Fourier expansions were used to express the bending vibration displacement of these plates, and they were substituted into coupled boundary equations and vibration equations, then these differential equations were changed into simple linear systems of equations, so the natural frequencies, modal shape and displacement of coupled plates are obtained conveniently. The present theoretical model and method were checked by the finite element software ANSYS. Using the present theoretical model, the effect of boundary damping of elastic constraints on vibration response of coupled plates was considered. The results shows that the boundary damping of translational constraints could reduce low order resonance responses significantly when the translational constraints have small stiffness values. Using the obtained displacement of plates, the expressions of power flow for coupled plates were provided, and then the vibration power flow transfer characteristics of coupled plates were studied. The results shows that increasing restraint stiffness of edges can effecively hinders the power flow through the edges, and the power tends to flow into accepted plate with the same materials as excited plate.
关键词
田字型耦合板 /
功率流 /
弹性约束边界 /
边界阻尼
{{custom_keyword}} /
Key words
Four-Palace type coupled plates /
power flow /
elastic edges restraints /
boundary damping
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Tian Ran Lin, Andy C.C.Tan, Cheng Yan eta. Vibration of L-shaped plates under a deterministic force or moment excitation: a case of statistical energy analysis application[J]. Journal of Sound and Vibration, 2011, 330: 4780-4797.
[2] Xianhui Li. A scaling approach for high-frequency vibration analysis of line-coupled plates[J]. Journal of Sound and Vibration, 2013, 332: 4054-4058.
[3] 游进, 李鸿光, 孟光. 耦合板结构随机能量有限元分析[J]. 振动与冲击, 2009, 28(11): 43-46.
YOU Jin, LI Hongguang, Meng Guang. Random energy finite element analysis of coupled plate structures[J]. Journal of Vibration and Shock, 2009, 28(11):43-46.
[4] J M Cuschieri, M D McCollum. In-plane and out-of-plane waves’ power transmission through an L-plate junction using the mobility power flow approach[J]. Journal of the Acoustical Society of America, 1996, 100(2): 857-870.
[5] Jingtao Du, Wen L.Li, Zhigang Liu eta. Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints[J]. Journal of Sound and Vibration, 2011, 330: 788-804.
[6] 薛开, 王久发, 王威远等. 耦合板在任意边界条件下的自 由振动分析[J]. 振动与冲击, 2013, 32(22): 178-182.
Xue Kai, Wang Jiufa, Wang Weiyuan et al. Free vibration analysis of coupled rectangular plates with general elastic boundary conditions[J]. Journal of Vibration and Shock, 2013, 32(22): 178-182.
[7] 史冬岩, 石先杰, 王青山等. T型耦合板结构振动特性研究 [J]. 振动与冲击, 2014, 33(4): 185-198.
Shi Dongyan, Shi Xianjie, Wang Qingshan et al. Vibration analysis of a T-coupled plate structure[J]. Journal of Vibration and Vibration, 2014, 33(4): 185-198.
[8] Yuehua Chen, Guoyong Jin, Minggang Zhu eta. Vibration behaviors of a box-type structure built up by plates and energy transmission through the structure[J]. Journal of Sound and Vibration, 2012, 331: 849-867.
[9] Zhiguang Song, Fengming Li. Vibration and aeroelastic properties of ordered and disordered two-span panels in supersonic airflow[J]. International Journal of Mechanical Sciences. 2014, 81: 65-72.
[10] C.Johansson, C.Pacoste, R.Karoumi. Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads[J]. Computers and Structures. 2013, 119: 85-94.
[11] S.A.Eftekhari, A.A.Jafari. High accuracy mixed finite element-Ritz formulation for free vibration analysis of plates with general boundary conditions[J]. Applied Mathematics and Computation, 2012, 219: 1312-1344.
[12] 张安付, 盛美萍, 赵芝梅等. 基于傅里叶级数展开的多跨 耦合板功率流研究[J]. 振动与冲击, 2013, 32(14): 103-108.
AnfuZhang, MeipingSheng, Meizhi Zhao eta. Power flow analysis of a multi-span coupled plate using Fourier series expansion[J]. Journal of Vibration and Shock, 32(14): 103-108.
[13] W L Li, Xuefeng Zhang and Jingtao Du et al, An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports[J]. Journal of Sound and Vibration, 2009, 321: 254-269.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2641 KB)
