Damping of Free Elastic Vibrations in Linear Systems

The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 110–117, February 2005.     

Natural Vibrations of Complex Bodies

The paper sets forth a modified preconditioned conjugate-gradient method with shifted aggregated multilevel preconditioning (MPCG_AMIS). The method is intended to solve large-scale natural-vibration problems. Such problems are typical for the finite-element analysis of buildings and other complex structures and bodies. Using a proper shift in preconditioning improves considerably the spectral properties of the preconditioner and, hence, improves convergence. Using the MPCG_AMIS allows us to avoid lock of convergence, which is the case in the conventional PCG method. The performance of the method is illustrated by examples     

Forced Nonstationary Vibrations of a Sandwich Cylindrical Shell with Cross-Ribbed Core

The equations of nonaxisymmetric vibrations of sandwich cylindrical shells with discrete core under nonstationary loading are presented. The components of the elastic structure are analyzed using a refined Timoshenko theory of shells and rods. The numerical method used to solve the dynamic equations is based on the integro-interpolation method of constructing finite-difference schemes for equations with discontinuous coefficients. The dynamic problem for a sandwich cylindrical shell under distributed nonstationary loading is solved with regard for the discreteness of the core__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 60–67, February 2005.     

Principal Trajectories of Forced Vibrations for Discrete and Continuous Systems

Principal trajectories of forced vibration of linear and nonlinear continuous systems are introduced as such motions in which the system is equivalent to a Newtonian particle in the function space of the system configurations. The corresponding 'effective mass' of the particle gives physical characteristics of the system response, so that zero effective mass is associated with resonance. The methodology can be viewed as a complementary tool to the method of normal modes, when considering the class of forced vibrating systems, since the related basis accounts for the system physical properties as well as the external forcing factor. In particular, it is shown that a two degrees of freedom system can possess an infinite discrete set of in-phase and out-of-phase forced vibrations of the normal modes type. The corresponding forcing vector-functions obey the second Newton law due to the definition of principal trajectories.     

Control of Gear Vibrations at Their Source

Results are presented of study into the origin of spur gear vibrations and methods of reducing them at their source     

中心有刚体质量的环形薄板的非线性强迫振动

本文研究中心带有刚体质量外部固定铰支或活动铰支的环形薄板的非线性强迫振动。考虑板的弯曲变形、面内位移和几何非线性，用哈米尔顿原理建立板的运动方程，用Ｋａｎｔｏｒｏｖｉｃｈ平均法消去时间变量，然后用数值积分求得非线性振动的振幅随激振力的大小及激振力的频率而变化的关系。求解过程中用打靶法逐步改进未知参量，以保证边界条件的满足。最后讨论薄膜力、激振力的分布、板的内外半径比等因素对响应的影响     

Transverse Vibrations of Laminated Beams in Three-Dimensional Formulation

A new asymptotic method is proposed to describe the free and forced transverse vibrations of elastic laminated beams of arbitrary cross section using the three-dimensional elastic equations without additional hypotheses and constraints. For beams with layers of equal Poisson's ratio, the zero-order natural frequencies are equal to the natural frequencies predicted by classical beam theory based on the Bernoulli hypothesis. The method makes it possible to calculate the frequencies of free vibrations and amplitudes of forced vibrations with prescribed accuracy for the first natural modes __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 56–71, June 2005.     

Resonance Vibrations and Dissipative Heating of Thin-Walled Laminated Elements Made of Physically Nonlinear Materials

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations     

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

Technical Stability of Forced Motion in Nonstationary Automatic-Control Systems of Variable Structure

Sufficient conditions of technical stability are established for nonstationary automatic-control systems of variable structure. The case is considered where for appropriate controls and for all admissible initial perturbations from a predefined measurable set of initial states, the nonstationary parameters of a process under external actions vary within given ranges. The control process depends on the mismatch signal and its derivatives up to an order that is less by one than the order of the equations of motion. The associated system of differential equations contains discontinuous time-dependent coefficients. A relationship is established between the eigenvalues of the quadratic forms of the given Lyapunov functions and the technical-stability criteria. It is shown that the technical-stability conditions do not depend on the sliding-mode conditions for variable-structure control processes     

Stabilization of the Rotation Axis of a Solid by Coupled Perfectly Rigid Bodies

The problem of stabilizing the axis of a solid by coupled perfectly rigid bodies (PRBs) is solved. The solid executes a plane-parallel motion. The PRBs can rotate as a single rigid body about the centroidal axis of the solid and counterrotate about its transverse axes through equal angles. There is a particle inside the solid which causes its imbalance. It is established that the principal state (if any) of the system—rotation about the centroidal axis—is stable, whereas the rest (unwanted) states are unstable __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 122–129, August 2005.     

非定常俯抑振荡下的横向喷流数值模拟

采用高精度格式数值求解RANS方程,研究了定常状态下横向喷流流场,压力分布计算结果与实验结果基本吻合,并捕捉到喷流干扰流场中多种流动结构.在非定常计算过程中,飞行器的振动引起了法向力和俯仰力矩系数的相位滞后,推力放大因子随俯仰角周期变化.飞行器振动过程中,喷流流场的动态气动特性与稳态喷流有明显的区别,因此在利用横向喷流对飞行器进行姿态控制时,应该考虑由于飞行器姿态的变化对横向喷流所产生的非定常影响问题.     

Forced flexural-and-torsional vibrations of a cantilever beam of constant cross section

The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes it much easier to construct a Cauchy vector function as an analytic function of these matrices __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007.     

Rolling Rigid Bodies and Forces of Constraint: An Application to Affine Nonholonomic Systems

In the present paper we study the motion of a disk rolling without sliding on a rotating platform, deriving the differential equations directly by D'Alembert principle.     

Motion of a Sphere in a Liquid Caused by Vibrations of Another Sphere

The motion of an absolutely rigid sphere in a nonuniformly vibrating, ideal, incompressible liquid is considered. The liquid vibrates under the action of an absolutely rigid sphere vibrating in a specified manner. Refined conditions are obtained under which the inclusion sphere recedes from the vibrating sphere, approaches it, and does not perform mean motion. It is found that under nonuniform vibrations of the liquid, the motion of the inclusion can depend on the geometrical parameters of the hydromechanical system.     

Dynamics of a System of Bodies with Program-Variable Configuration

The dynamics of a system of rigid bodies with program-variable configuration is analyzed. A mathematical model is constructed using methods of analytical mechanics. The behavior of a microsatellite with a deployable gravity-gradient boom is analyzed as a numerical example     

Stability of Nonstationary Automatic-Control Systems of Variable Structure in Forced Motion

Conditions of stability in sliding mode are obtained for nonstationary dynamic automatic-control processes of variable structure. The nonstationary parameters of a control process subjected to external perturbations vary in given ranges, whereas the parameters of the switching plane remain constant for the appropriately chosen parameters of discontinuous logic control laws. The corresponding system of differential equations contains coefficients that vary stepwise in time together with the parameters of the controlled process. The general stability criteria for the solutions of variable-structure systems are used to analyze the stability of motion in sliding mode of an automatic variable-structure control system of the second order     

Medium frequency dynamic investigation of the railway wheelset-track system using a discrete-continuous model

Summary In the paper, dynamic interaction between elastic high-speed-train car wheelset and track is studied using a discrete-continuous mechanical model. The model enables to investigate the influence of the parametric excitation from the track as well as static and dynamic unbalances of wheels and brake disks on the dynamic response of the wheelset running at various speeds on the track of various average vertical stiffness. From the results of numerical simulation it follows that particularly severe periodic resonances occur for the track of large stiffness, yielding high vertical dynamic contact forces between the wheels and rails. The maximum dynamic response has been obtained for parameters corresponding to the conditions at which the phenomenon of grumbling noise generation is usually observed in reality. Received 21 January 1997; accepted for publication 29 February 1997     

Damping of mesh-induced errors in Free-Lagrange simulations of Richtmyer-Meshkov instability

Mesh-induced errors at material interfaces are identified as a source of unphysical behaviour in Lagrangian numerical simulations of Richtmyer-Meshkov instability. The mesh geometry introduces interface perturbations with wavelengths of the same order as the mesh resolution. When a shock propagates through the interface, these perturbations can grow, severely contaminating the predicted interface development. Here an algorithm is presented which damps small-scale interface perturbations. A body force is applied at the interface which depends upon the disturbance amplitude and growth rate, and which resembles surface tension. Using this technique, qualitative improvements are obtained in Free-Lagrange simulations of single-mode Richtmyer-Meshkov instability. Growth rate behaviour and the evolution of the instability are seen to agree well with previously published results. Received 9 March 2000 / Accepted 30 May 2000     

集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。