State-Vector Equation With Damping and Vibration Analysis of Laminates
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摘要: 基于考虑弹性体粘滞阻尼的修正后的Hellinger-Reissner (H-R)变分原理，推导了相应的状态向量方程．结合精细积分法和Muller法为四边简支矩形层合板的简谐振动分析提出了新的方法．依据线性阻尼振动理论，简要地给出了复合材料层合板欠阻尼、临界阻尼和过阻尼3种自由运动的通解公式．通过数值实例研究了粘滞阻尼对复合材料层合板振动的影响．丰富了状态向量方程的理论体系和应用领域．Abstract: Based on the modified mixed Hellinger-Reissner(H-R) variational principle for elastic bodies with damping,the state-vector equation was directionally derived from the principle.A new solution for the harmonic vibration of simply supported rectangular laminates with damping was proposed by using the precise integration method and Muller method.The general solutions for the free vibration of underdamping,critical damp and overdamping of composite laminates were given simply in terms of the linear damping vibration theory.The effect of viscous damping force on the vibration of composite laminates was investigated through numerical examples.The state-vector equation theory and its application areas are extended.
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Key words:
- laminated plates /
- damping /
- vibration /
- H-R variational theorem /
- state-vector equation
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[1] 钟万勰. 条形域平面弹性问题和哈密尔顿体系[J].大连理工大学学报,1991,31(4)：373-384. [2] 钟万勰.弹性力学求解新体系[M].大连：大连理工大学出版社,1995. [3] 唐立民. 弹性力学的混合方程和Hamilton正则方程[J].计算结构力学及其应用，1991,8(4)：343-349. [4] Steele C R， Kim Y Y.Modified mixed variational principle and the state-vector equation for elastic bodies and shells of revolution[J].Journal of Applied Mechanics,1992,59(3)：587-595. doi: 10.1115/1.2893764 [5] FAN Jia-rang, YE Jian-qiao.A series of solution of the exact equation for thick orthotropic plates[J].International Journal of Solids and Structures,1990,26(7)：773-778. doi: 10.1016/0020-7683(90)90006-H [6] 范家让. 强厚度叠层板壳的精确理论[M].北京：科学出版社,1996. [7] Ting T C T.Anisotropic Elasticity： Theory and Application[M].New York: Oxford University Press,1996. [8] Reissner E. On a variational theorem in elasticity[J].Journal Mathematics Physics,1950，29(1)：90-95. [9] Johnston R L.Numerical Methods[M].New York: John Wiley, 1982. [10] 姚伟岸. 电磁弹性固体三维问题的广义变分原理[J].计算力学学报,2003,20(4):487-489. [11] 丁皓江, 江爱民.横观各向同性磁电弹性体的基本解和边界积分方程[J].中国科学,E辑,2003,33(9):845-855. [12] 卿光辉，邱家俊，刘艳红. 磁电弹性体修正后的H-R混合变分原理和状态向量方程[J]. 应用数学和力学，2005，26（6）：665-670. -
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