Global bifurcations and chaos in a harmonically excited and undamped circular plate

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The method of multiple scales is used to obtain an autonomous system from a non-autonomous system of ordinary differential equations governing non-linear oscillations of an imperfect circular plate. The Melnikov's method for heteroclinic orbits of the autonomous system is used to obtain the criteria for chaotic motion. It is shown that the existence of heteroclinic orbits in the unperturbed system implies chaos arising from breaking of heteroclinic orbits under perturbation. The validity of the result is checked numerically. It is also observed numerically that chaos can appear due to breaking of invariant tori under perturbation.     

Physically and geometrically nonlinear deformation of thin-walled conical shells with a curvilinear hole

The elastoplastic state of thin conical shells with a curvilinear (circular) hole is analyzed assuming finite deflections. The distribution of stresses, strains, and displacements along the hole boundary and in the zone of their concentration are studied. The stress-strain state around a circular hole in shells subject to internal pressure of prescribed intensity is analyzed taking into account two nonlinear factors __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 73–79, April 2007.     

Some checks of Taylor''s hypothesis in a slightly heated turbulent circular jet

Taylor's hypothesis has been examined by comparing temporal variations of the temperature fluctuation θ with the corresponding spatial variations. The comparison is made on the axis of a circular jet in the self-preserving region of the flow for streamwise separations extending to about 10 Kolmogorov microscales. The use of the hypothesis yields reliable estimates of streamwise temperature correlations and also of second- and third-order moments of streamwise temperature increments. Fourth-order moments of these increments are estimated less accurately. Departures from the hypothesis are smaller than in the plane jet; consistently, local isotropy appears to be more closely satisfied in the circular jet.     

大湍流度高雷诺数时并列双圆柱的平均和脉动压力分布

本文通过风洞实验研究了来流湍流度,Iu=10％雷诺数分别为Re=1.95×10~9和Re=6.5×10~5时单个圆柱和不同间距比下并列双圆柱的平均和脉动压力分布。结果表明:在Re=1.95×10~5时单个圆柱的平均压力分布类似于低湍流度高超临界雷诺数时的压力分布;当雷诺数增大至6.5×10~5时,绕圆柱表面流动的分离点前移和背压绝对值提高,总的阻力系数随之增加。并列双圆柱的间距比变化对圆柱表面压力分布影响很大,在极小间距比(N/d=1.05)时,双圆柱间的缝隙流使附近柱面产生高达-5的压力系数峰值(Re=6.5×10~5),同时脉动压力也大为增加;在较小间距比时(1.5     

FRP加固金属裂纹板的断裂力学分析

传统的金属结构加固方法会形成新的疲劳源,而粘贴FRP加固则具有明显的优势．提出了“三维实体-弹簧-壳元”有限元模型,金属板采用三维实体单元, FRP采用壳单元,用弹簧单元来模拟FRP与金属板之间的胶层,对金属裂纹板粘贴FRP加固后的性能进行了线弹性断裂力学分析,并对影响金属板裂纹前缘应力强度因子的参数进行了讨论．分析结果表明,采用高弹性模量的FRP和增加FRP的厚度对改善加固效果非常明显．     

Nonlinear vibration analysis of viscoelastic plates based on a refined Timoshenko theory

Nonlinear vibrations of viscoelastic orthotropic and isotropic shells are mathematically modeled using a geometrically nonlinear Timoshenko theory. Nonlinear problems are solved by using the Bubnov-Galerkin method and a numerical method based on quadrature formulas. Results obtained from different theories are compared and analyzed. For each problem, the Bubnov-Galerkin method is tested for convergence. The influence of the viscoelasticity and inhomogeneity of materials on the vibrations of plates is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 120–131, May 2006.     

LARGE DEFLECTION PROBLEM OF THIN ORTHOTROPIC CIRCULAR PLATE ON ELASTIC FOUNDATION WITH VARIABLE THICKNESS UNDER UNIFORM PRESSURE

ＬＡＲＧＥＤＥＦＬＥＣＴＩＯＮＰＲＯＢＬＥＭＯＦＴＨＩＮＯＲＴＨＯＴＲＯＰＩＣＣＩＲＣＵＬＡＲＰＬＡＴＥＯＮＥＬＡＳＴＩＣＦＯＵＮＤＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＴＨＩＣＫＮＥＳＳＵＮＤＥＲＵＮＩＦＯＲＭＰＲＥＳＳＵＲＥ（王嘉新）（刘杰）ＬＡＲＧ...     

固接圆环板在集中力作用下的求解

本文根据板的基本理论，在文献￣［１］的基础上对因接圆环板在集中力作用下进行了求解，进而提出计算固接圆环板在非对称载荷作用下应力与应变的方法，并编制了计算程序。本文中还进行了有限元分析，二者符合较好。本文的方法和程序可用于有关的工程计算设计。     

含双圆孔平板弹性波散射与动应力分析

利用复变量及局部坐标系方法，对平板中含双圆孔弹性波的衍射与动应力集中问题进行了研究，给出了不同方向入射弯曲波条件下该问题一般解的函数逼近序列和边界条件的表达式用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解给出了双圆孔附近的动应力集中系数的数值结果，分析了孔间距对动应力分布的影响     

General mathematical theory of large deflections of thin plates with some holes

The theoretical analysis and the numerical computations for the problem of a thin plate with large deflection and some holes become much more difficult due to the multi-valued properties of the stress functionF and the single-valued demands on the displacements. The necessary and sufficient conditions which can assureF to be single-valued are obtained in this paper. At the same time, we prove that the single-valued demands on the displacements are equivalent to 3m functional constraint equationsDC(w,F)=0, wherem is the number of holes. From these conclusions, the single-valued governing-equations of the problem of plates with large deflection and some holes are derived. It is a system of fourth order partial differential equations with 3m unknown constants and constrained equations. A numerical method for solving this problem is presented. The problem of the critical load is considered and an iterative scheme for computing the buckled states is given when a critical load λ is ‘single’.