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基于薄板的小挠度理论和叠加原理,考虑横向变温情况,将温度作用下的三边简支一边自由矩形薄板看作是面内温差作用下的四边简支矩形薄板和自由边上挠度作用下的三边简支一边自由矩形薄板的叠加,得到了温度作用下三边简支一边自由混凝土矩形薄板的挠度和弯矩解析解.首先通过在自由边界上试设具有待定参数的挠度函数,采用李维解法推导出三边简支一边自由矩形薄板在自由边界挠度作用下的挠度方程;其次利用横向变温作用下四边简支矩形薄板的求解得到待定参数;再采用叠加原理得出横向变温作用下三边简支一边自由矩形薄板的挠度和弯矩解析解;最后利用MATLAB编制程序得到了横向变温作用下三边简支一边自由矩形薄板的计算系数用表,为工程结构中三边简支一边自由混凝土矩形薄板在热环境下的设计计算提供了理论依据. 相似文献
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研究了切向均布随从力作用下,带有中间线支承的矩形薄板的稳定性问题.建立板的运动微分方程,利用微分求积法得到复特征方程.求解复特征方程,得出线支承板复频率随着随从力的变化关系,以及线支承刚度对板失稳形式和临界值的影响.对随从力作用下中间支承四边固支矩形薄板的计算结果表明:对于四边固支板,当边长比为1时,发现存在一个临界线支承刚度值,当线支承刚度小于该值时,板失稳为颤振失稳,当支承刚度大于该值时,板失稳为屈曲失稳;当边长比为2时,板失稳形式保持为屈曲失稳. 相似文献
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Maxwell模型薄板的自由振动 总被引:3,自引:0,他引:3
本文利用Maxwel粘弹性模型建立了粘弹性薄板的振动微分方程,给出四边简支粘弹性矩形薄板的固有频率解析解.对粘弹性矩形薄板的振动特性进行了讨论 相似文献
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分数阶微分型双参数黏弹性地基矩形板受荷响应 总被引:5,自引:0,他引:5
基于考虑水平剪切变形和竖向压缩变形的双参数地基模型,利用分数阶微分建立了黏弹性地基上矩形薄板荷载作用下的挠度方程;根据弹性-黏弹性对应原理,通过Laplace变换将四边简支矩形板弹性问题的解推广求解分数阶微分黏弹性问题;通过算例表明分数阶微分型黏弹性模型比经典黏弹性模型的适应性,并分析了模型参数对挠度-时间关系的影响. 相似文献
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变厚度矩形薄板的一般解 总被引:1,自引:0,他引:1
本文应用“两步级数展开”法构造了任意变厚度各向同性弹性矩形薄板的一般理论解。文中研究了四边简支、四边固支以及两对边简支另两边含自由边的矩形板的一般解和一些特例。最后,用数值算例证实了本文方法的有效性。 相似文献
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任意变厚度矩形薄板的屈曲和振动 总被引:3,自引:1,他引:2
本文采用两步级数展开法获得了任意变厚度矩形薄板的屈曲和振动问题的一般解,并详细研究了四边简支变厚度矩形板的屈曲和振动问题的解.针对两种变厚度板,计算了失稳临界荷载、失稳波形以及基频,并与前人的结果做了比较,分析结果表明本文方法简单收敛快。 相似文献
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基于平面闸门研究了两种边界条件下矩形薄板在水荷载作用下的挠度、内力、应力的分布规律。利用单三角级数分别构造了两对边简支一边固支一边自由以及三边固支一边自由矩形薄板在水压力作用下的挠曲变形函数,并依据最小势能原理求解了挠曲变形函数系数,最后根据薄板小挠度弯曲理论得到了两种边界条件下矩形薄板的内力与应力函数,并对挠度、内力、应力的分布规律进行了比较分析。结果表明,在相同静水压力作用下,两对边简支一边固支一边自由和三边固支一边自由矩形薄板的挠度以及内力分布规律不尽相同,其中三边固支一边自由矩形薄板挠度及背水面出现的最大拉应力值较两对边简支一边固支一边自由矩形薄板的要小。 相似文献
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针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法(DTM),研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。 相似文献
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针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法(DTM),研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。 相似文献
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An exact solution procedure is formulated for the stability analysis of viscoelastic rectangular plate with two opposite edges simply supported and other two edges clamped as well as the viscoelastic rectangular plate with one edge clamped and other three edges simply supported under the action of tangential follower force. Firstly, by assuming the transverse displacement (W) as independent functions which automatically satisfies the simply supported boundary conditions, the governing partial differential equation is reduced to an ordinary differential equation with variable coefficients. Then, by the normalized power series method and applying the boundary conditions yield the eigenvalue problem of finding the roots of a fourth-order characteristic determinant. The results show that the aspect ratio λ and the dimensionless delay time H have great effects on the types of instability and the critical loads of the viscoelastic plates. 相似文献
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The dynamic characteristics and stability of axially moving viscoelastic rect- angular thin plate are investigated.Based on the two dimensional viscoelastic differential constitutive relation,the differential equations of motion of the axially moving viscoelastic plate are established.Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method.The effects of the aspect ratio,moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed. 相似文献
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IntroductionDuringthelateseventies,ZhangFufanobtainedtheexactsolutionstothebendingproblemofrectangularcantileverplatesandrect... 相似文献
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Yu. V. Nemirovsky T. P. Romanova 《Journal of Applied Mechanics and Technical Physics》2011,52(2):288-302
A general solution is obtained for the problem of dynamic bending of an ideal rigid-plastic doubly connected plate with arbitrary simply supported or clamped curvilinear contours subjected to short-time high-intensity explosive dynamic loading uniformly distributed over the surface. The plate rests on a viscoelastic foundation. It is demonstrated that there are several mechanisms of plate deformation. Equations of dynamic deformation are derived for each mechanism, and implementation conditions are analyzed. Numerical examples are given. 相似文献
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Xing Ma John Butterworth Charles Clifton 《European Journal of Mechanics - A/Solids》2011,30(6):1024-1027
The buckling problem of an infinite thin plate resting on a tensionless Winkler foundation and subjected to shearing loads is investigated. The infinite plate is simplified to a one-dimensional mechanical model by assuming a lateral buckling mode function and a borderline function between contact and non-contact regions. After the governing differential equations for the plate sections in the contact and non-contact regions have been solved, the problem reduces to two nonlinear algebraic equations. Buckling coefficients for plates with simply supported edges and clamped edges are determined for a range of relative foundation stiffness factors. Comparison of the results with existing theory and finite element analyses shows good agreement. 相似文献
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自由正交异性矩形厚板的动态稳定 总被引:3,自引:0,他引:3
对在一条边上作用着均匀分布的非保守跟随力的四边自由正交异性矩形厚板的动态稳定进行了分析,通过把位移和剪力展成重傅立叶级数解,把微分方程简化成了代数方程。计算表明厚度的微小变化会引起颤振载荷明显的减小。这个明显减小是因为存在剪切变形。 相似文献
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An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal
gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined.
We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here
the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion
has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first
two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and
aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported
on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish
the accuracy and versatility. 相似文献
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The effects of a piezoelectric layer on the stability of viscoelastic plates subjected to the follower forces are evaluated. The differential equation of motion of the viscoelastic plate with the piezoelectric layer is formulated using the two-dimensional viscoelastic differential constitutive relation and the thin plate theory. The weak integral form of the differential equations and the force boundary conditions are obtained. Using the element-free Galerkin method, the governing equation of the viscoelastic rectangular plate with elastic dilatation and Kelvin–Voigt distortion is derived, subjected to the follower forces coupled with the piezoelectric effect. A generalized complex eigenvalue problem is solved, and the force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force; this force is used to improve the stability of the non-conservative viscoelastic plate. For the viscoelastic plate with various boundary conditions, the results for the instability type and the critical loads are presented to show the variations in these factors with respect to the location of the piezoelectric layers and the applied voltages. The stability of the viscoelastic plates can be effectively improved by the determination of the optimal location for the piezoelectric layers and the most favorable voltage assignment. 相似文献