摘要
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建立的理论模型的正确性。利用该理论模型,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。
Here,the vibration response of in-plane four-palace type coupled plates was studied. A method to calculate the vibration of coupled plates with elastic edges was proposed. Based on balance conditions and continuity conditions of coupling positions,the boundary coupled equations of four-palace type coupled plates were established. The improved Fourier series were used to express the bending vibration displacement functions of these plates,and they were substituted into boundary coupled equations and equations of motion of these plates,then these differential equations were converted into simpler linear algebraic equations,so the natural frequencies,modal shapes and displacements of coupled plates were solved conveniently. The presented theoretical model and method were verified with the finite element software ANSYS. Using the presented theoretical model,the effect of boundary damping of elastic constraints on the vibration response of coupled plates was analyzed. The results showed that the boundary damping of lateral constraints can reduce lower order resonance responses significantly when the lateral constraints have smaller stiffness values. Using the obtained displacements of plates,the expressions of power flow for coupled plates were derived,and then the vibration power flow transfer characteristics of coupled plates were simulated. The results showed that increasing restraint stiffness of edges can effecively hinder the power flow to flow along edges,and the power flow tends to flow into the accepted plate with the same material as that of the excited plate when the outernal excitation frequencies are the lower order resonance ones.
出处
《振动与冲击》
EI
CSCD
北大核心
2015年第23期194-201,共8页
Journal of Vibration and Shock
关键词
田字型耦合板
功率流
弹性约束边界
边界阻尼
four-palace type coupled plates
power flow
elastic boundary restraints
boundary damping
