共查询到18条相似文献,搜索用时 58 毫秒
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以载流导线激发的磁场中轴向运动梁为研究对象,同时考虑外激励力作用,推导出梁的磁弹性非线性振动方程.通过位移函数的设定和伽辽金积分法,将非线性振动方程离散为常微分方程组.采用多尺度法得到系统的近似解析解.应用Matlab 和Mathematica 软件求解幅频响应方程,并对稳态解进行稳定性判定.通过具体算例得到前两阶假设模态的响应幅值随不同参数的变化规律.结果发现:系统在内共振条件下发生超谐波共振时,二阶假设模态幅值明显小于一阶;随着外激励的增大,多值解区域范围明显缩小;随着电流强度增加,振动幅值减小,表明载流导线能够起到控制共振的作用. 相似文献
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针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究.应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解,得到超谐波共振下系统的分岔响应方程.根据奇异性理论对非线性动力学系统的普适开折进行分析,求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图.通过数值算例,分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图,以及反映不同运动行为区域的动力学响应图形,讨论分岔参数对系统呈现的倍周期和混沌运动的影响.结果表明,可通过相应参数的改变实现对系统复杂动力学行为的控制. 相似文献
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研究静载荷作用下夹层圆板的超谐波共振问题.基于Hoff型夹层板理论,给出了静载荷作用下夹层圆板的非线性动力学方程.应用Galerkin法推导了静载荷作用下夹层圆板的轴对称非线性振动方程.运用多尺度法分别对系统的三次超谐波问题和二次超谐波问题进行了求解,并依据Lyapunov稳定性理论得到了系统稳态运动的稳定性判据.通过算例,得到了周边简支约束下夹层圆板三次超谐波共振和二次超谐波共振的幅频响应曲线图、振幅-静载荷响应曲线图、振幅-激励力幅值响应曲线图;研究了不同参数对系统振幅的影响规律,并对解的稳定性进行了分析. 相似文献
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研究轴向运动导电条形板的磁弹性1∶3主-内联合共振问题。以轴向运动导电条形板为研究对象,建立磁场中导电条形板的力学模型。利用哈密顿原理建立轴向运动导电条形板的振动方程。当夹支-铰支轴向运动导电条形板发生共振现象时,针对约束边界条件,通过对位移模态函数的设定,利用Galerkin积分法得到了双自由度非线性振动微分方程组。采用多尺度法得到了轴向运动导电条形板在主-内联合共振状态下的幅频响应方程组。通过算例分析,得到了关于一阶共振幅值和二阶共振幅值变化规律曲线图,讨论了磁场强度、轴向速度、外部激振力幅值和轴力对系统振动的影响。结果表明:系统发生主-内联合共振时,一阶共振和二阶共振均被激发,且幅值解呈现多值性和跳跃现象,表现出复杂的非线性特征。 相似文献
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本文研究了轴向变速黏弹性梁的组合参数共振和主参数共振稳定性.梁的材料黏弹性本构关系由Poynting-Thompson模型描述.使用多尺度法渐近展开求解,导出了其可解性条件.根据Routh-Hurwitz准则给出了组合参数共振和主参数共振稳定性条件.考虑Poynting-Thompson模型退化到Kelvin-Voigt模型的情况.通过数值算例对两个模型进行了失稳边界的比较. 相似文献
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1.接头端部的荷载考虑一个正交各向异性板单肢搭接粘接接头(图1).取单位宽度并承受外力T的作用.可写出 相似文献
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轴向运动梁非线性振动内共振研究 总被引:19,自引:2,他引:19
采用多元L-P方法分析轴向运动梁横向非线性振动的内共振,首先根据哈密顿原理建立轴向运动梁的横向振动微分方程,然后利用Galerkin方法分离时间和空间变量,再采用多元L-P方法进行求解,推导了内共振条件下频率-振幅方程的求根判别式,理论分析发现内共振与强迫力的振幅有关,而且可以从理论上决定这一界乎不同内共振的强迫力振幅的临界值,典型算例获得了轴向运动梁横向非线性振动内共振复杂的频率一振幅响应曲线,揭示了很多复杂而有趣的非线性振动特有的现象,多元L-P方法的数值结果,在小振幅时与IHB法的结果一致。 相似文献
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Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given . 相似文献
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构造了带有补充项的双重正弦傅里叶级数通解来求解各种边界条件的多层正交各向异性矩形薄板的弯曲、振动和稳定问题.将坐标轴取在中性面上,求出用挠度表示的应力表达式,然后由横截面上每单位宽度的应力合成板的内力;再将层合板的内力代入板的平衡方程中得到板的控制方程,将多层板的物理参数折算为等价的单层板物理参数;最后联立控制方程与边界条件,求得未知量的系数并代入本文的通解中.本文的通解不需要叠加即可求解各种边界条件的板的弯曲、振动和稳定问题;现有的对于单层板的研究都可以用本文的方法拓展到多层板领域;对于复杂边界条件的板,也可以使用该通解分析. 相似文献
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In the current paper we present the tensile force, the edge moment and edge transverse force acting on the single-lap joint and get the moment reduction factork for orthotropic plates. We use the variational method based on the principle of complementary energy. Considering Hooke's law for orthotropic materials, carrying out the variationV=0 and using the Euler-Poisson's equation we establish all the expressions of stresses in the joint for orthotropic plates. All numerical calculations can be made on a computer. 相似文献
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The transverse vibrations of a flexible connecting rod in an otherwise rigid slider-crank mechanism are considered. An analytical approach using the method of multiple scales is adopted and particular emphasis is placed on nonlinear effects which arise from finite deformations. Several nonlinear resonances and instabilities are investigated, and the influences of important system parameters on these resonances are examined in detail. 相似文献
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An exact solution for the bending of point-supported orthotropic rectangular thin plates 总被引:2,自引:0,他引:2
A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse load are arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past. 相似文献
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R. M. Kirakosyan 《International Applied Mechanics》2008,44(4):448-458
The existence of two correction coefficients traditionally introduced to account for the effect of the distribution of tangential
stresses over the thickness of a plate is discussed. The virtual-work principle is used to generalize the expressions for
the coefficients to the case of arbitrary loading. These expressions and hypotheses for displacements help to derive equations
for orthotropic rectangular plates subject to tangential surface loads. These equations account for the effect of the distribution
of tangential stresses over the thickness of the plate. Numerical examples are given. The results obtained are compared with
those produced by other theories
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 107–119, April 2008. 相似文献
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