A Unified Approach to Dynamic Contact Problems in Viscoelasticity

In this paper we consider mathematical models describing dynamic viscoelastic contact problems with the Kelvin–Voigt constitutive law and subdifferential boundary conditions. We treat evolution hemivariational inequalities which are weak formulations of contact problems. We establish the existence of solutions to hemivariational inequalities with different types of non-monotone multivalued boundary relations. These results are consequences of an existence theorem for second order evolution inclusions. In a particular case we deliver sufficient conditions under which the solution to a hemivariational inequality is unique. Finally, applications to several unilateral and bilateral problems in contact mechanics are provided.*Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

Variational methods of solving dynamic problems for fluid-containing bodies

A variational approach to solving linear and nonlinear problems for a body with cavities partially filled with a perfect incompressible fluid is enunciated. The approach applies a nonclassical variational principle to describe the spatial motion of a finite fluid with a free surface and the classical variational principle, which is widely used in rigid body dynamics. These principles are used to formulate variational problems that are the basis of direct methods of solving nonlinear and linear dynamic problems for body-fluid systems. The approach allows us to derive an infinite system of nonlinear ordinary differential equations describing the joint motion of the rigid body and fluid and to develop an algorithm for determining the hydrodynamic coefficients. Linearized differential equations of motion of the mechanical system are presented and approximate methods are given to solve linear boundary-value problems and to determine the hydrodynamic coefficients.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 37–77, October 2004.The study was partially sponsored by the German Research Fund (der Deutsche Forschungsgemeinschaft), Grant 436 UKR113/33/0-3.     

混合状态Hamiltonian元的半解析解和叠层板的计算

本文给出混合状态方程的一种强有力的半离散半解析解法,并给出了矩形域和叠层板的算例,讨论了可能的发展和应用。     

具有损伤耦合效应的弹塑性蠕变问题结构分析的变分原理

本文基于连续介质损伤力学中有效应力的概念,研究弹塑性蠕变问题中的损伤耦合,并应用由最优控制理论基本思想发展起来的参变量变分原理建立起用于弹塑性蠕变损伤问题结构分析的变分原理.文中给出了原理的证明.该原理的物理意义明确,表达式简单且规范,容易为数值手段实现.     

耦合热弹性问题的分区变分原理及其广义变分原理

本文在文献[1]和[2]的基础上建立并论证了耦合热弹性问题的分区变分原理及其分区广义变分原理     

有限变形弹性动力学的非传统Gurtin型变分原理

根据古典阴阳互补和现代对偶互补的基本思想，通过作者早已提出的一条简单而统一的途径，系统地建立了有限变形弹性动力学的各类非传统Gurtin型变分原理，给出一个以卷积表示的重要关系式，可以认为，该式是有限变形动力学的广义虚功原理的表式。从该式出发，不仅能得到有限变形动力学的虚功原理，而且通过给出的一系列广义Legendre变换，还能系统地成对导出5类变量，3类变量，2类变量和1类变量非传统Gurtin型变分原理的互补泛函。通过这条途径还能清楚地阐明这些原理之间的内在联系。     

考虑畸变影响的箱梁横向弯矩计算方法

为研究偏心垂向荷载作用下梯形截面单室箱梁的横向弯矩,对框架分析法计算箱梁横向弯矩的方程进行优化,并在刚性支承法的基础上提出一种更加简单的横向弯矩计算方法;与框架分析法不同,横向弯矩可采用能量变分法求解,建立以箱梁顶板剪力差为未知量的四阶控制微分方程,采用比拟的弹性地基梁解法解出剪力差,得出梯形截面单室箱梁横向弯矩的能量变分法解。对几种箱梁横向弯矩计算方法用两个算例进行验证,结果表明,能量变分法解将箱梁底板上的弯矩误差绝对值由15.41%降到了9.68%;本文方法得出的横向弯矩结果和有限元结果吻合较好,弯矩误差绝对值最大不超过6.01%;本文方法和能量变分法可有效降低箱梁底板上的弯矩误差,计算精度得到提高。     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORYFOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDERUNIFORM SURFACE LOADING (Ⅰ)

I.1ntroductionTheaxisymmetricproblemofthreedimensionalelasticcircularplatecanbetreatedasthreedimensionalaxisymmetricproblemofelasticity.Weconsideracircularplatewithauniformthicknessh,andsetupacircumferentialcoordinates(r,o)onitsmidd1esurfacewithabscissazp…     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Adaptive synchronization of chaotic systems with less measurement and actuation

We investigate the synchronization problem between identical chaotic systems only when necessary measurement(output) and actuation(input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.