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考虑轴和盘的质量及轴的几何非线性,建立了在周期轴向载荷作用下具不对称粘弹性支承弹性盘轴转子系统的非线性动力学方程.基于Lyapunov运动稳定性理论和Floquet判据,对系统的线性和非线性动力稳定性进行了分析. 相似文献
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《应用力学学报》2020,(5)
研究四边简支载流纳米板在电磁场及机械载荷作用下的磁弹性稳定问题。结合非局部理论与板壳磁弹性理论,导出考虑尺度效应的纳米板的磁弹性动力学方程,得出载流纳米板在磁场及机械载荷作用下的磁弹性动力稳定方程;利用伽辽金原理将稳定性方程整理为特殊函数马丢方程的标准形式,根据其系数的本征值关系,判别磁弹性稳定问题的最低失稳临界状态;通过数值模拟得到纳米板失稳临界电流密度与相关参数之间的关系图及变化规律。结果表明:磁感应强度、板长与板厚、外加机械载荷及小尺度参数均会影响纳米板的稳定性;当小尺度参数取1nm时,板长在200nm~450nm、板厚在1nm~10nm的区间内,纳米板的稳定性随着磁感应强度、板长及板厚的变化而急剧变化。在这个灵敏区间内改变磁感应强度、板长及板厚的大小,可以有效地提高纳米板的稳定性。 相似文献
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通过试验和有限元方法分析了单轴压缩下加筋板的失效模式.研究了三种预置损伤位置及四种损伤尺寸的复合材料T型加筋板的线性及非线性屈曲行为,比较了损伤对临界屈曲载荷和最大失效载荷的影响.研究结果表明:损伤位置在桁条间蒙皮时,损伤的尺寸对其临界屈曲载荷和最大失效载荷影响较小;损伤位置在桁条区蒙皮时,加筋板的临界屈曲载荷随损伤尺寸的增加而明显降低,最大降低50%;损伤位置在桁条边凸缘处蒙皮时,加筋板最大失效载荷所受影响随损伤尺寸的增加而明显降低,最大降低25%.从而得到了复合材料加筋板临界屈曲载荷比和最大失效载荷比与损伤位置及尺寸的关系图. 相似文献
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《力学学报》2017,(6)
由于周期性隔振结构动力计算中较少考虑轨道交通载荷及材料黏弹性,因此,本文以黏弹性层状周期板为研究对象,提出了垂向移动简谐载荷下,可以考虑材料黏弹性及板内横向剪切变形的黏弹性层状周期板动力计算近似理论并给出解析解答.设板中性面的横向剪切变形为横截面的整体剪切变形,利用Reissner-Mindlin假设及提出的剪切变形补充计算条件,得到了中性面法线转角与中性面剪应力的关系.基于平衡方程和应力连续条件,建立了黏弹性层状周期板振动控制方程,推导了对边简支对边自由条件下,板垂向位移的简化Fourier级数形式解.与经典层合板模型和有限元计算结果进行了比较,验证了本文解答的有效性.结果表明:(1)黏弹性层状周期板可以显著降低单一材料板在自振频率处的振动响应,但会引起局部低频频段的振动放大;(2)板的垂向位移随着载荷速度的增大而增大,当载荷速度超过300 km/h后,其对板振动响应的影响减弱;(3)黏弹性层剪切模量存在最佳设计值,可使结构的隔振性能最佳;(4)黏弹性层的阻尼特性在低频范围内对结构振动影响较小;(5)可在满足工程实际的情况下适当增加板长,以提高结构的隔振性能. 相似文献
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本文在考虑大变形、忽略阻尼影响的情况下,基于高散加筋板模型,对具有弹性约束边界的加筋板在流固冲击载荷下的非线性瞬态响应进行了理论研究.取样条函数作为挠度试函数,运用加权残值法求得加筋板动力响应的控制方程,采用四阶Runge-Kutta法求解该方程,并用Fortran语言编制了相应的计算程序.构造的B样条函数能适应板侧边上的任意弹性转动约束.文中不仅分析了不同的冲击载荷形式对加筋板动力特性的影响,还讨论了载荷峰值、冲击栽荷持续时问、加强筋和弹性转动约束的影响. 相似文献
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由于周期性隔振结构动力计算中较少考虑轨道交通载荷及材料黏弹性,因此,本文以黏弹性层状周期板为研究对象,提出了垂向移动简谐载荷下,可以考虑材料黏弹性及板内横向剪切变形的黏弹性层状周期板动力计算近似理论并给出解析解答.设板中性面的横向剪切变形为横截面的整体剪切变形,利用Reissner-Mindlin假设及提出的剪切变形补充计算条件,得到了中性面法线转角与中性面剪应力的关系.基于平衡方程和应力连续条件,建立了黏弹性层状周期板振动控制方程,推导了对边简支对边自由条件下,板垂向位移的简化Fourier级数形式解.与经典层合板模型和有限元计算结果进行了比较,验证了本文解答的有效性.结果表明:(1)黏弹性层状周期板可以显著降低单一材料板在自振频率处的振动响应,但会引起局部低频频段的振动放大;(2)板的垂向位移随着载荷速度的增大而增大,当载荷速度超过300 km/h后,其对板振动响应的影响减弱;(3)黏弹性层剪切模量存在最佳设计值,可使结构的隔振性能最佳;(4)黏弹性层的阻尼特性在低频范围内对结构振动影响较小;(5)可在满足工程实际的情况下适当增加板长,以提高结构的隔振性能. 相似文献
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为研究黏弹性地基上功能梯度材料板的自由和强迫振动特性,基于Reddy高阶剪切变形理论以及由Shen导得的广义Karman型方程,用双重Fourier级数法推导了三参数黏弹性地基上四边简支功能梯度材料板自由振动和动力响应的解析解,计算了各模态自振频率和半波冲击载荷作用下的动力响应,讨论了材料组分指数、黏弹性地基参数、边厚比等因素对自由振动和动力响应的影响.结果表明,黏弹性地基的剪切和压缩刚度显著提升了功能梯度材料板的振动频率,减小了动力响应;另外,地基的黏性对振动频率和动力响应也有一定的影响. 相似文献
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粘弹性圆薄板的动力学行为 总被引:4,自引:0,他引:4
基于线性粘弹性力学的Boltzmann叠加原理,给出粘弹性圆薄板动力学分析的初边值问题。通过一定的简化后得到描述薄板力学行为的四维非线性非自治动力系统。综合使用非线性动力学中的数值分析方法,研究了参数对粘弹性圆薄板动力学行为的影响。同时计算了吸引子的Lyapunov维、相关维和点形维。 相似文献
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Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage are presented. The Galerkin method is applied to simplify the set of equations. The numerical methods in nonlinear dynamics are used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plate with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system are investigated in detail. At the same time, the effect of damage on the dynamical behavior of plate is also discussed. 相似文献
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M. Shariyat 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(9):1253-1268
A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling
analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed
so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the
layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied.
Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties
and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account.
Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time.
Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency
of the proposed theory and the relevant solution algorithm. 相似文献
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姜稚清 《应用数学和力学(英文版)》1983,4(4):559-570
In this paper,Neale’S generalized variational principle aboutincremental boundarg-value problems is utilized to study theeffect of initial imperfections in geometry on tbe criticalloads of elasticoplastic buckling of thin annular plates.Thecalculations show that.if the effect of initial imperfectionsin geometrg is taken into account in the solutions by J_2 in-cremental theorg.the results are very close to the bifurca-tional buckling loads of the perfect annular Plates accordingto the plastic deformation theorg. 相似文献
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Yong-Gang Wang Xiao-Meng Li Dan Li Xin-Zhi Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(12):1925-1933
An integrated mathematic model and an efficient algorithm on the dynamical behavior of homogeneous viscoelastic corrugated
circular plates with shallow sinusoidal corrugations are suggested. Based on the nonlinear bending theory of thin shallow
shells, a set of integro-partial differential equations governing the motion of the plates is established from extended Hamilton’s
principle. The material behavior is given in terms of the Boltzmann superposition principle. The variational method is applied
following an assumed spatial mode to simplify the governing equations to a nonlinear integro-differential variation of the
Duffing equation in the temporal domain, which is further reduced to an autonomic system with four coupled first-order ordinary
differential equation by introducing an auxiliary variable. These measurements make the numerical simulation performs easily.
The classical tools of nonlinear dynamics, such as Poincaré map, phase portrait, Lyapunov exponent, and bifurcation diagrams,
are illustrated. The influences of geometric and physical parameters of the plate on its dynamic characteristics are examined.
The present mathematic model can easily be used to the similar problems related to other dynamical system for viscoelastic
thin plates and shallow shells. 相似文献
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The integro-partial differential equations governing the dynamic behavior of viscoelastic plates taking account of higher-order shear effects and finite deformations are presented. From the matrix formulas of differential quadrature, the special matrix product and the domain decoupled technique presented in this work, the nonlinear governing equations are converted into an explicit matrix form in the spatial domain. The dynamic behaviors of viscoelastic plates are numerically analyzed by introducing new variables in the time domain. The methods in nonlinear dynamics are synthetically applied to reveal plenty and complex dynamical phenomena of viscoelastic plates. The numerical convergence and comparison studies are carried out to validate the present solutions. At the same time, the influences of load and material parameters on dynamic behaviors are investigated. One can see that the system will enter into the chaotic state with a paroxysm form or quasi-periodic bifurcation with changing of parameters. 相似文献
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The nonlinear, forced, damped vibrations of simply-supported rectangular sandwich plates with a viscoelastic core are studied. The general, nonlinear dynamic equations of asymmetrical sandwich plates are derived using the virtual work principle. Damping is taken into account by modelling the viscoelastic core as a Voigt-Kelvin solid. The harmonic balance method is employed for solving the equations of motion. The influence of the thickness of the layers and material properties on the nonlinear response of the plates is studied. 相似文献
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A. A. Movchan I. A. Movchan L. G. Sil’chenko 《Journal of Applied Mechanics and Technical Physics》2011,52(2):279-287
Analytical solutions using various hypotheses are obtained for the problem of buckling of an annular circular plate of a shape
memory alloy in the forward or reverse thermoelastic phase transformations under uniform radial compression. It is established
that, despite the axial symmetry of the body geometry, loads, and boundary conditions, the minimum critical loads for annular
plates correspond to nonaxisymmetric buckling modes, in contrast to continuous plates. 相似文献
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本文以正交异性板理论为基础,提出了一种波纹环形板非线性弯曲的Cheby-shev级数解法,推导出具有硬中心的波纹环形板在任意轴对称载荷作用下的弹性特征方程.文中计算了几个典型的算例,数值结果表明本文的方法对目前文献中常见的方法有一定的改进和推广. 相似文献