A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental results is observed.

A robust finite element method is developed for the analysis of piezoelectric bodies. The method is general enough to account for the losses in material coefficients. The method is used to analyze the behavior of 3:1 PZT-rubber composite hydrophone. The effect of material properties, sizes and locations of the rubber phase on the response of the composite is studied. Also the viscoelastic properties of the rubber phase are studied for its effect on the sensitivity as well as on the dynamic response of the composite hydrophone.

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

Abstract A steady state formulation of the rolling contact problem with friction that allows the analysis of free rolling, cornering, acceleration, and braking is presented. This formulation is applied to the finite element analysis of tires. A layered shell finite element with shear deformation that allows for large deflection and rotation is developed. In each layer, orthotropic Hookean materials or Mooney-Rivlin type materials with fiber reinforcements can be used and the incompressibility constraint is enforced with Lagrange multipliers. The contact constraint is enforced with a penalty and the friction term, instead of the usual Coulomb friction, is regularized by a differentiable form that makes it more suitable for numerical analysis. A numerical example for a typical tire is also given.

International Journal for Numerical Methods in EngineeringVolume 22, Issue 1 p. 219-228 Article Numerical control of the hourglass instability O.-P. Jacquotte, O.-P. Jacquotte Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this authorJ. T. Oden, J. T. Oden Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this authorE. B. Becker, E. B. Becker Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this author O.-P. Jacquotte, O.-P. Jacquotte Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this authorJ. T. Oden, J. T. Oden Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this authorE. B. Becker, E. B. Becker Texas Institute for Computational Mechanics, The University of Texas at Austin, Austin, Texas, U.S.A.Search for more papers by this author First published: January 1986 https://doi.org/10.1002/nme.1620220116Citations: 16AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL References 1 T. Belytschko and J. M. Kennedy, 'Computer models for subassembly simulation', Nucl. Eng. Des., 49, 17– 38 (July 1978). 2 T. Belytschko and C. S. Tsay, 'A stabilization procedure for the quadrilateral plate element with one-point quadrature', Int. j. numer. methods eng., 19, 409– 419 (1983). 3 T. Belytschko, C. S. Tsay and W. K. Liu, 'A stabilization matrix for the bilinear Mindlin plate element', Comp. Meth. Appl. Mech. Eng., 29, 313– 327 (1981). 4 D. P. Flanagan and T. Belytschko, 'A uniform strain hexahedron and quadrilateral with orthogonal hourglass control', Int. j. numer. methods eng., 17, 679– 706 (1981). 5 O.-P. Jacquotte, 'Stability, accuracy, and efficiency of some underintegrated methods in finite element computations', Comp. Meth. Appl. Mech. Eng. (to appear). 6 O.-P. Jacquotte and J. T. Oden, 'Analysis of hourglass instabilities and control in underintegrated finite element methods', Comp. Meth. Appl. Mech. Eng., 43, 339– 363 (1984). 7 O.-P. Jacquotte and J. T. Oden, ' Analysis and treatment of hourglass instabilities in underintegrated finite element methods', in Innovative Methods in Nonli near Computational Mechanics (Eds. T. Belytschko, K. C. Park and W. K. Liu), Pineridge Press, Swansea, 1984. Citing Literature Volume22, Issue1January 1986Pages 219-228 ReferencesRelatedInformation

Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.