共查询到18条相似文献,搜索用时 78 毫秒
1.
张剑锋 《计算结构力学及其应用》1996,13(2):201-207
本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收同中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。 相似文献
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分数导数型本构关系描述粘弹性梁的振动分析 总被引:3,自引:1,他引:2
本文研究粘弹性梁在周期激励作用下的受迫振动问题。梁的材料满足Kelvin-Volgt分数导数型本构关系。基于动力学方程、本构关系和应变-位移关系建立了小变形粘弹性梁的振动方程。采用分离变量法分析粘弹性梁的自由振动,导出模态坐标满足的常微分-积分方程和模态函数满足的常微分方程,对于两端简支的截面梁给出了固有频率和模态函数。对于简谐激励作用下粘弹性梁的受迫振动,利用模态叠加得到了稳态响应。最后给出数值算例说明本文方法的应用。 相似文献
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粘弹性材料的变形动力学模型 总被引:1,自引:0,他引:1
粘弹性材料的变形动力学模型周建平(长沙国防科技大学,410073)关键词粘弹性,本构关系,内变量,老化1引言许多工程材料,特别是聚合物材料的应力应变关系具有粘弹性特征,使得材料或结构在受力过程中发生蠕变或应力松弛现象.从微观上讲,这种粘弹性变形是由于... 相似文献
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基于内变量理论的一种广义粘弹性本构方程 总被引:1,自引:1,他引:1
以Biot理论为基础,将弹性应变与非弹性尖变均取作状态为量,引入耗散势,建立了一种率相关非弹性本构关系及演变方程,进而导出一种广义的粘弹性本构方程。 相似文献
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本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。 相似文献
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根据不可逆热力学原理和推广的Onsager原理建立了内变量演化的非线性方程;采用迭代方法得到了非线性方程的迭代解,并根据Lipschitz条件给出了迭代解的收敛条件。由此,建立了一维应力条件下的非线性粘弹性本构关系。将这一本构关系推广至三维应力情况,并考虑了状态方程和损伤演化,在剪切诱导材料粘性的前提下建立了混凝土损伤耦合的非线性粘弹性本构关系。在该关系式中:损伤演化方程与混凝土的粘性应变积累相关;状态方程服从三次多项式的形式。实验结果表明:此模型能够比较好地表征混凝土材料在达到强度极限前后的强化与软化的特征。 相似文献
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关于复合结构振动分析中粘弹性材料本构方程的形式 总被引:3,自引:1,他引:3
弹性——粘弹性材料复合结构的振动分析必然要涉及粘弹性材料的本构方程形式。就两种常用的形式:标准形式和分数阶导数形式,本文从粘弹性材料的力学性能曲线拟合和复合结构振动分析两方面比较了这两种本构方程形式的优劣,认为采用标准形式具有更多的优越性。 相似文献
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非线性粘弹性板的失稳条件 总被引:1,自引:0,他引:1
研究了给定面内周期激励作用下简支各向同性均匀粘弹性板平衡失稀问题,板的材料特性由Leaderman非线性本构关系描述,将板的动力学方程进行(Galerkin截断得到简化数学模型为弱非线性系统,采用平均法得到系统的平均化方程,对平均化方程进行稳定性分析得到了板平衡失稳的解析条件,对原系统用数值仿真进行研究,数值结果表明,随着激励幅值的增加或粘弹性材料系数的减少,系统平衡点推失稳,激励幅值和粘弹性材料系数的临界值均与解析结果接近。 相似文献
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A single integral type of constitutive equation for finite viscoelastic deformation is proposed. A special case, which is a viscoelastic generalization of the constitutive equation for a neo-Hookean elastic solid, is used to consider the finite deformation problem of shock wave propagation resulting from the sudden application of compressive force at the end of a semi-infinite viscoelastic bar. An approximate method is used to determine the shock front path and shock strength when the viscoelastic dissipative effect is small. 相似文献
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广义Maxwell黏弹性流体在两平板间的非定常流动 总被引:2,自引:0,他引:2
将分数阶微积分运算引入Maxwell黏弹性流体的本构方程,研究了黏弹性流体在两平板问的非定常流动.对于广义Maxwell黏弹性流体的分数阶导数模型,导出了对时间具有分数阶导数的特殊运动方程,利用分数阶微积分的Laplace变换理论,得到了流动的解析解. 相似文献
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EIGEN THEORY OF VISCOELASTIC MECHANICS FOR ANISOTROPIC SOLIDS 总被引:4,自引:0,他引:4
Guo Shaohua 《Acta Mechanica Solida Sinica》2001,14(1):74-80
Anisotropic viscoelastic mechanics is studied under anisotropic subspace. It is proved that there also exist the eigen properties
for viscoelastic medium. The modal Maxwell's equation, modal dynamical equation (or modal equilibrium equation) and modal
compatibility equation are obtained. Based on them, a new theory of anisotropic viscoelastic mechanics is presented. The advantages
of the theory are as follows: 1) the equations are all scalar, and independent of each other. The number of equations is equal
to that of anisotropic subspaces, 2) no matter how complicated the anisotropy of solids may be, the form of the definite equation
and the boundary condition are in common and explicit, 3) there is no distinction between the force method and the displacement
method for statics, that is, the equilibrium equation and the compatibility equation are indistinguishable under the mechanical
space, 4) each model equation has a definite physical meaning, for example, the modal equations of order one and order two
express the volume change and shear deformation respectively for isotropic solids, 5) there also exist the potential functions
which are similar to the stress functions of elastic mechanics for viscoelastic mechanics, but they are not man-made, 6) the
final solution of stress or strain is given in the form of modal superimposition, which is suitable to the proximate calculation
in engineering. 相似文献
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Summary A viscoelastic constitutive equation of rubber that is under small oscillatory load superimposed on large static deformation
is proposed. The model is derived through linearization of Simo's nonlinear viscoelastic constitutive model and reference
configuration transformation. Most importantly, in this model, static deformation correction factor is introduced to consider
the influence of pre-strain on the relaxation function. Natural statically pre-deformed state is served as reference configuration.
The proposed constitutive equation is extended to a generalized viscoelastic constitutive equation that includes widely used
Morman's model as a special case using objective stress increment. The proposed constitutive model is tested for dynamic behavior
of rubber specimens with different carbon black content. It is concluded from the test that the assumption that the effects
of static deformation can be separated from time effects, which is the basis of Morman's model, is only applicable to unfilled
rubber. The viscoelastic constitutive equation for filled rubber must include, therefore, the influence of the static deformation
on the time effects. The suggested constitutive equation with static deformation correction factor shows good agreement with
test values.
Received 4 January 2001; accepted for publication 13 June 2001 相似文献
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The differential quadrature method has been applied to investigate vibrations of viscoelastic thin plate with variable thickness. Firstly, the governing equations are derived in terms of the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation. Then, the convergence of the method is demonstrated based on the differential equation of uniform thickness elastic square plate, which is reduced from the differential equation of viscoelastic plate with varying thickness. Lastly, the effects of aspect ratio, thickness ratio and dimensionless delay time on the vibrations of the linear thickness viscoelastic plate with different boundary conditions have been studied. 相似文献
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黏弹性传动带1:3内共振时的周期和混沌运动 总被引:14,自引:0,他引:14
研究了参数激励作用下黏弹性传动带在1:3内共振时的周期解分岔和混沌动力学.
同时考虑传动带的线性外阻尼因素和材料内阻尼因素.
首先建立了具有线性外阻尼情况下的黏弹性传动带平面运动时的非线性动力学方程,
黏弹性材料的本构关系用Kelvin模型描述. 然后考虑黏弹性传动带的横向振动问题,
利用多尺度法和Galerkin离散法得到黏弹性传动带系统在1:3内共振时的平均方程.
最后利用数值模拟方法研究了黏弹性传动带系统的周期振动和混沌动力学,
得到了系统在不同参数下的混沌运动.
数值模拟结果说明黏弹性传动带系统存在周期分岔, 概周期运动及混沌运动. 相似文献