| 周平,赵德有.基于动态刚度阵法的加筋板间能量流研究[J].,2008,(1):98-104 |
| 基于动态刚度阵法的加筋板间能量流研究 |
| Analysis of energy flow in stiffened thick plate structures based on dynamic stiffness matrix technique |
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| DOI：10.7511/dllgxb200801019 |
| 中文关键词: 动态刚度阵 加筋板 Mindlin-Engesser模型 能量流 |
| 英文关键词: dynamic stiffness matrix stiffened plate Mindlin-Engesser model energy flow |
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| 中文摘要: |
| 采用动态刚度阵法研究耦合加筋板间的能量传输关系. 首先以带加筋的中厚矩形板为研究对象，推导了加筋板的动态刚度阵，为动态刚度阵方法提供了一种新单元. 板的运动微分方程由Mindlin厚板理论给出，同时还考虑了板平面内的振动. 对于板上加强筋的处理，则通过Hamilton原理对板的运动方程作相应的修正，最终得到加筋板的运动微分方程. 而方程的解析解直接用于单元刚度阵的推导，所得加筋板单元的动态刚度阵结合均方响应表达式即可计算出加筋板的平均振动能量. 最后以L形耦合加筋板间为例，采用动态刚度阵法计算其在中高频区域内的振动能量比，并通过与统计能量分析方法和有限元方法的计算结果比较，验证了方法的可行性和高效性. |
| 英文摘要: |
| The dynamic stiffness matrix technique is applied to analyze the energy flow of the coupled stiffened plates. At first, a new dynamic stiffness matrix of stiffened moderate thick plate is derived. The plate differential equations are based on Mindlin thick plate theory and include the in-plane vibrations. The stiffeners are taken to be smeared over the surface of the element, and Hamilton′s principle is used to derive the appropriate modifications which must be made to the plate differential equations. The resulting differential equations are solved exactly to yield the dynamic stiffness matrix for the element. Any number of elements may be assembled to model the cross-section of a building-up structure by using classical finite element techniques. The equation governing the complete structure can also be solved by employing classical techniques to obtain the dynamic responses of structures. Combined with the formulation of mean squared displacement for the stiffened plate, the averaged vibratory energy of each stiffened plate can be obtained. Finally, a numerical example of L-shaped stiffened plate is considered and the energy flow between each plate is calculated by dynamic stiffness matrix method. To verify the efficiency and feasibility of the presented method, the calculated results are compared with those obtained by finite element method and statistical energy analysis method. |
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