移动质量作用下双层叠合梁的动力学分析
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摘要
主要分析了移动质量作用下双层叠合梁的振动特性。在分析中移动质量的加速度是任意的。基于一些假设,列出了系统的应变能和势能,并利用广义哈密尔顿原理导出了横纵耦合的动力学方程,然后利用有限元法和Newmark法求解了该方程。数值算例表明:移动质量的速度越大,双层叠合梁的中点横向位移就越大;当移动质量位于梁中点时,中点的纵向位移为零。在其他条件相同情况下,双层叠合梁比单层梁具有较高的刚度-重量比。所得结论为设计强度高且重量轻的结构提供理论依据。
The simply supported double composite beam with moving mass is investigated. During the analysis,the acceleration of the moving mass can be arbitrary. With some assumptions, the strain energy and the kinetic energy of the system are gotten. Then the axial-bending coupled equations of motion are derived by the Hamilton's principle, and solved by the finite element method combined with Newmark method. The numerical examples show that, the larger the speed of moving mass the larger the maximum vertical displacement of the beam; the horizental displacement of centre point of the beam is zero when the moving mass on the centre point; under the same conditions, the double composite beams have higher stiffness-to-weight ratio than the single layer ones. The conclusions obtained here provide theoretical references for designing the structures with high strength and light weight.
The simply supported double composite beam with moving mass is investigated. During the analysis,the acceleration of the moving mass can be arbitrary. With some assumptions, the strain energy and the kinetic energy of the system are gotten. Then the axial-bending coupled equations of motion are derived by the Hamilton's principle, and solved by the finite element method combined with Newmark method. The numerical examples show that, the larger the speed of moving mass the larger the maximum vertical displacement of the beam; the horizental displacement of centre point of the beam is zero when the moving mass on the centre point; under the same conditions, the double composite beams have higher stiffness-to-weight ratio than the single layer ones. The conclusions obtained here provide theoretical references for designing the structures with high strength and light weight.
引文
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[3] M A Foda,Z Abduljabbar,A dynamic Green function formulation for the response of a beam structure to a moving mass[J].Journal of Sound and Vibration,1998(210):295- 306.
[4] J J Wu,Dynamic analysis of an inclined beam due to moving loads,Journal of Sound and Vibration,2005(288):107-131.
[5] T Kocatürk,M.Simsek,Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load[J].Computers & structures,2006(84):2113-2127.
[6] M Simsek,Vibration analysis of a functionally graded beam under a moving mass by using different beam theories[J].Composite Structures,2010(92):904-917.
[7] 陈上有,夏禾,战家旺,等.变速移动荷载作用下简支梁的动力响应分析[J].中国铁道科学,2007,28(6):41-46.Chen ShangYou,Xia He,Zhan JiaWang,etal.Dynamic response analysis of simply-supported beam under speed -varying loads[J].China Raily Way Science,2007,28(6):41-46.(In Chinese)
[8] M J Yan,E H Dowell,Gove rning equations for vibrating constrained-layer damping sandwich plates and beams,Journal of Applied Mechanics 39 (1972) 1041-1046.
[9] U Lee,J Kim,Dynamics of elastic-piezoelectric two-layer beams using spectral element method[J].International Journal of Solids and Structures,2000(37):4403-4417.
[10] 谢丽君.简支双层叠合梁的变形计算[J].机械强度,2012,34(5):777-780.Xie LiJun.Deformation computation of simply supported double composite beam[J].Journal of Mechanical Strength,2012,34(5):777-780 (In Chinese).
[2] J E Akin,M Mofid,Numerical solution for response of beams with moving mass[J].Journal of Structural Engineering,1989(115):120-131.
[3] M A Foda,Z Abduljabbar,A dynamic Green function formulation for the response of a beam structure to a moving mass[J].Journal of Sound and Vibration,1998(210):295- 306.
[4] J J Wu,Dynamic analysis of an inclined beam due to moving loads,Journal of Sound and Vibration,2005(288):107-131.
[5] T Kocatürk,M.Simsek,Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load[J].Computers & structures,2006(84):2113-2127.
[6] M Simsek,Vibration analysis of a functionally graded beam under a moving mass by using different beam theories[J].Composite Structures,2010(92):904-917.
[7] 陈上有,夏禾,战家旺,等.变速移动荷载作用下简支梁的动力响应分析[J].中国铁道科学,2007,28(6):41-46.Chen ShangYou,Xia He,Zhan JiaWang,etal.Dynamic response analysis of simply-supported beam under speed -varying loads[J].China Raily Way Science,2007,28(6):41-46.(In Chinese)
[8] M J Yan,E H Dowell,Gove rning equations for vibrating constrained-layer damping sandwich plates and beams,Journal of Applied Mechanics 39 (1972) 1041-1046.
[9] U Lee,J Kim,Dynamics of elastic-piezoelectric two-layer beams using spectral element method[J].International Journal of Solids and Structures,2000(37):4403-4417.
[10] 谢丽君.简支双层叠合梁的变形计算[J].机械强度,2012,34(5):777-780.Xie LiJun.Deformation computation of simply supported double composite beam[J].Journal of Mechanical Strength,2012,34(5):777-780 (In Chinese).