Influence of the Nonlinear Characteristics of Elastic Elements on the Bifurcations of Equilibrium States of a Double Pendulum with Follower Force

A generalized mathematical model of an inverted double pendulum with asymmetric follower force is developed. The model accounts for all possible types of springs: hard, soft, and linear. The influence of equitype springs on the equilibrium states is examined__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 103–109, February 2005.     

Evolution of Limit Cycles in the Stability Domain of a Double Pendulum under a Variable Follower Force

It is shown that stable and unstable limit cycles are born at a certain value of the follower force. As the absolute value of the force increases, the cycles move with different velocities in opposite directions. The unstable limit cycle moves toward the origin in the four-dimensional phase space. At a certain value of the follower force, this cycle gets at the origin, disturbing its stability as a singular point of the dynamic system. If the absolute value of the follower force decreases, then death of both cycles is possible. In this case, the attraction domain of the origin becomes infinite     

Divergent Bifurcations of a Double Pendulum under the Action of an Asymmetric Follower Force

The paper studies the influence of the orientation parameter of the follower force on the behavior of the pendulum with a simple zero eigenvalue in the linearization matrix     

Stability domains of the vertical equilibrium state of a triple simple pendulum

The stability boundaries for the vertical equilibrium position of a triple simple pendulum subject to asymmetric follower force are analyzed. The effect of the upper spring and the magnitude of the follower force on the roots of the characteristic equation is studied Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 122–134, October 2008.     

Influence of material and geometrical nonlinearities on the bifurcations of equilibrium states of a two-link pendulum

The equilibrium states of an inverted two-link simple pendulum with an asymmetric follower force are classified depending on the characteristics of the springs (hard, soft, or linear) at the upper end and at the hinges. Phase portraits are plotted. The bifurcation points on the equilibrium curves are identified. Emphasis is on fold and cusp catastrophes __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 115–128, August 2007.     

Asymptotic stability boundaries for the equilibrium positions of a double pendulum with vibrating point of suspension

The mechanisms whereby a double pendulum with vibrating point of suspension loses stability in equilibrium positions are studied. Stability conditions for the equilibrium positions in critical cases are established __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 120–133, July 2008.     

Influence of Geometrical Parameters on the Critical Load in Three-Dimensional Stability Problems for Rectangular Plates and Beams

Two- and three-dimensional stability problems for a rectangular plate under uniaxial compression are solved by the mesh method. It is shown that the difference between the critical loads obtained in the three- and two-dimensional problems is not greater than 5% for arbitrary fixation conditions and arbitrary length and thickness ratio of the plate     

弹性体表面分层压缩失稳问题的数学弹性力学解

采用数学弹性力学的稳定平衡方程并结合富氏积分变换的方法研究了含表面平行裂纹的弹性体在压缩载荷下的表面分层失稳问题。导出了一级显式的精确齐次奇异积分方程组,然后.通过Gauss-Chebyshev积分公式,得到一组齐次代数方程组,从而求出临界压缩载荷。并将结果与经典的材料力学梁板稳定的研究方法所得结果进行了比较,指出经典方法误差太大而不适于求解此问题。最后,利用数学弹性力学解求出的等效弹性支承常数给出一个简单精确的临界压缩载荷计算公式。     

表面力仪及固体表面微观接触机理的实验研究

利用以等色序条纹技术为核心的表面力仪,使２个分子级光滑的圆柱状云母表面在一定载荷下接触,测量其接触区尺寸和接触表面和变形情况。在两表面间使用不同介质以进行有粘着接触和无粘着接触２种条件下的实验,并将测量结果与Ｈｅｒｔｚ理论（无粘着接触）和ＪＫＲ理论（有粘着接触）进行对比。发现在无粘着接触条件下的试验结果与Ｈｅｒｔｚ理论相吻合;而在有粘着接触条件下则测量到了ＪＫＲ理论所预言的“颈缩”现象。