软芯三明治梁受移动点载荷作用的动力响应
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摘要
为了得到软芯三明治梁在移动集中载荷下的动力响应,基于扩展的高阶三明治梁理论和Hamilton原理,建立了任意节点的弱形式求积三明治梁单元,利用微分求积法的权系数显式表达式给出了单元刚度矩阵和质量矩阵的公式,并验证了刚度矩阵和简化质量矩阵的正确性和方法的有效性,结果表明弱形式的求积单元法具有精度和计算效率高的优点。然后,采用中心差分法首次给出了两端固支软芯三明治梁在移动集中载荷作用时的动力响应。本文的研究拓展了弱形式求积法的应用范围。
To analyze the dynamic response of soft core sandwich beams under a moving point load,an Nnode weak form quadrature sandwich beam element is established based on the extended high order sandwich panel theory and Hamilton principle.The formulas to calculate the element stiffness and mass matrices are given using the explicit formulas of the weighting coefficients existing in the differential quadrature method.The correctness and efficiency of the element stiffness and mass matrices are verified.It is shown that the weak form quadrature element method has advantages of high accuracy and computational efficiency.The dynamic response of a soft core sandwich beam with both ends clamped and subjected to a moving point load is obtained by using the finite difference method for the first time.Present research extends the application range of the weak form quadrature element method.
To analyze the dynamic response of soft core sandwich beams under a moving point load,an Nnode weak form quadrature sandwich beam element is established based on the extended high order sandwich panel theory and Hamilton principle.The formulas to calculate the element stiffness and mass matrices are given using the explicit formulas of the weighting coefficients existing in the differential quadrature method.The correctness and efficiency of the element stiffness and mass matrices are verified.It is shown that the weak form quadrature element method has advantages of high accuracy and computational efficiency.The dynamic response of a soft core sandwich beam with both ends clamped and subjected to a moving point load is obtained by using the finite difference method for the first time.Present research extends the application range of the weak form quadrature element method.
引文
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[5]陈树霖,刘莉,董威利.月球探测器着陆腿动力学建模与仿真[J].南京航空航天大学学报,2014,46(3):469-474.Chen Shulin,Liu Li,Dong Weili.Dynamics modeling and simulation for landing legs of lunar lander[J].Journal of Nanjing Aeronautics&Astronautics,2014,46(3):469-474.
[6]Yuan Z,Kardomateas G,Frostig Y.Finite element formulation based on the extended high-order sandwich panel theory[J].AIAA Journal,2015,53(10):3006-3015.
[7]Wang X.Differential quadrature and differential quadrature based element methods:Theory and applications[M].Waltham,MA,USA:Elsevier Inc.,2015.
[8]Wang Y,Wang X.Static analysis of higher order sandwich beams by weak form quadrature element method[J].Composite Structures,2014,116:841-848.
[9]Wang Y,Wang X.Free vibration analysis of softcore sandwich beams by the novel weak form quadrature element method[J].Journal of Sandwich Structures and Materials,2016,18(3):294-320.
[10]Wang X,Jin C.Differential quadrature analysis of moving load problems[J].Advances in Applied Mathematics and Mechanics,2016,8(4):536-555.
[11]Kudela P,Krawczuk M,Ostachowicz W.Wave propagation modeling in 1Dstructures using spectral finite elements[J].Journal of Sound and Vibration,2007,300:88-100.
[12]刘剑.求解动力学问题的微分求积法研究[D].南京:南京航空航天大学,2008.Liu Jian.On the differential quadrature method for analyzing dynamic problems[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2008.
[2]Phan C,Frostig Y,Kardomateas G.Analysis of sandwich beams with a compliant core and with inplane rigidity—Extended high-order sandwich panel theory versus elasticity[J].Journal of Applied Mechanics,2012,79(4):041001-1-11.
[3]Frostig Y,Phan C,Kardomateas G.Free vibration of unidirectional sandwich panels,Part I:Compressible core[J].Journal of Sandwich Structures&Materials,2013,15(4):377-411.
[4]袁慎芳,闫美佳,张巾巾,等.一种适用于梁式机翼的变形重构方法[J].南京航空航天大学学报,2014,46(6):825-830.Yuan Shenfang,Yan Meijia,Zhang Jinjin,et al.Shape reconstruction method of spar wing structure[J].Journal of Nanjing Aeronautics&Astronautics,2014,46(6):825-830.
[5]陈树霖,刘莉,董威利.月球探测器着陆腿动力学建模与仿真[J].南京航空航天大学学报,2014,46(3):469-474.Chen Shulin,Liu Li,Dong Weili.Dynamics modeling and simulation for landing legs of lunar lander[J].Journal of Nanjing Aeronautics&Astronautics,2014,46(3):469-474.
[6]Yuan Z,Kardomateas G,Frostig Y.Finite element formulation based on the extended high-order sandwich panel theory[J].AIAA Journal,2015,53(10):3006-3015.
[7]Wang X.Differential quadrature and differential quadrature based element methods:Theory and applications[M].Waltham,MA,USA:Elsevier Inc.,2015.
[8]Wang Y,Wang X.Static analysis of higher order sandwich beams by weak form quadrature element method[J].Composite Structures,2014,116:841-848.
[9]Wang Y,Wang X.Free vibration analysis of softcore sandwich beams by the novel weak form quadrature element method[J].Journal of Sandwich Structures and Materials,2016,18(3):294-320.
[10]Wang X,Jin C.Differential quadrature analysis of moving load problems[J].Advances in Applied Mathematics and Mechanics,2016,8(4):536-555.
[11]Kudela P,Krawczuk M,Ostachowicz W.Wave propagation modeling in 1Dstructures using spectral finite elements[J].Journal of Sound and Vibration,2007,300:88-100.
[12]刘剑.求解动力学问题的微分求积法研究[D].南京:南京航空航天大学,2008.Liu Jian.On the differential quadrature method for analyzing dynamic problems[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2008.