Some Properties of Motion Equations Describing the Nonlinear Dynamical Response of a Multibody System with Flexible Elements

The industrial applications use instruments and machines operating at high speeds, developing high forces, low temperatures, corrosive environments, extreme pressures, and so forth. Under these conditions, the elasticity of elements such a machine is built of cannot be ignored anymore, and models are needed to more accurately “grasp” the mechanical phenomena accompanying the operation. The vibrations and the loss of stability are the main effects occurring under these conditions. For the study on this kind of systems with rigid motion and elastic elements, numerous models have been elaborated, the main idea being the discretization of the elements and the use of finite element method. Finally, second-order differential equations with variable coefficients are obtained; these equations are strong nonlinear ones due to the time-dependent values of angular speed and acceleration, and they can be linearized considering a very short period of time, in which the motion is considered to be “frozen.” The aim of this paper is to present some characteristic properties of these systems.

[1]  W. Cleghorn,et al.  Dynamic finite-element analysis of a planar high-speed, high-precision parallel manipulator with flexible links , 2005 .

[2]  Sorin Vlase,et al.  A Method of Eliminating Lagrangian Multipliers from the Equation of Motion of Interconnected Mechanical Systems , 1987 .

[3]  T. Liu,et al.  THE MODELLING AND VIBRATION CONTROL OF BEAMS WITH ACTIVE CONSTRAINED LAYER DAMPING , 2001 .

[4]  Xianmin Zhang,et al.  Dynamic responses of flexible linkage mechanisms with viscoelastic constrained layer damping treatment , 2001 .

[5]  Pietro Fanghella,et al.  An explicit independent-coordinate formulation for the equations of motion of flexible multibody systems , 2003 .

[6]  Brian S. Thompson,et al.  A survey of finite element techniques for mechanism design , 1986 .

[7]  Zhang Xianmin,et al.  Simultaneous optimal structure and control design of flexible linkage mechanism for noise attenuation , 2007 .

[8]  J. Mayo,et al.  Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: Geometric stiffness , 1996 .

[9]  S. Vlase.  DYNAMICAL RESPONSE OF A MULTIBODY SYSTEM WITH FLEXIBLE ELEMENTS WITH A GENERAL THREE-DIMENSIONAL MOTION , 2012 .

[10]  G. N. Sandor,et al.  A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms , 1972 .

[11]  R. G. Fenton,et al.  Finite element analysis of high-speed flexible mechanisms , 1981 .

[12]  B. Bahgat,et al.  Finite element vibrational analysis of planar mechanisms , 1976 .

[13]  P. Nath,et al.  Kineto-elastodynamic analysis of mechanisms by finite element method , 1980 .

[14]  Xian-min Zhang,et al.  Dynamic analysis of flexible linkage mechanisms under uniform temperature change , 2009 .

[15]  Sorin Vlase,et al.  Elimination of lagrangian multipliers , 1987 .