Finite Element Model for Hysteretic Friction Damping of Traveling Wave Vibration in Axisymmetric Structures

A finite element method is developed to treat the steady-state vibration of two axisymmetric structures—a base substructure and an attached damper substructure—that are driven by traveling wave excitation and that couple through a spatially distributed hysteretic friction interface. The base substructure is representative of a rotating brake rotor or gear, and the damper is a ring affixed to the base under preload and intended to control vibration through friction along the interface. In the axisymmetric approximation, the equation of motion of each substructure is reduced in order to the number of nodal degrees of freedom through the use of a propagation constant phase shift. Despite nonlinearity and with contact occurring at an arbitrarily large number of nodal points, the response during sticking, or during a combination of sticking and slipping motions, can be determined from a low-order set of computationally tractable nonlinear algebraic equations. The method is applicable to element types for longitudinal and bending vibration, and to an arbitrary number of nodal degrees of freedom in each substructure. In two examples, friction damping of the coupled base and damper is examined in the context of in-plane circumferential vibration (in which case the system is modeled as two unwrapped rods), and of out-of-plane vibration (alternatively, two unwrapped beams). The damper performs most effectively when its natural frequency is well below the base’s natural frequency (in the absence of contact), and also when its natural frequency is well separated from the excitation frequency.

Finite Element Model for Hysteretic Friction Damping of Traveling Wave Vibration in Axisymmetric Structures

A finite element method is developed to treat the steady-state vibration of two axisymmetric structures—a base substructure and an attached damper substructure—that are driven by traveling wave excitation, and that couple through a spatially-distributed hysteretic friction interface. The base substructure is representative of a rotating brake rotor or gear, and the damper is a ring affixed to the base under preload and intended to control vibration through friction along the interface. In the axisymmetric approximation, the equation of motion of each substructure is reduced in order to the number of nodal degrees of freedom through the use of a propagation constant phase shift. Despite nonlinearity and with contact occurring at an arbitrarily large number of nodal points, the response during sticking, or during a combination of sticking and slipping motions, can be determined from a low-order set of computationally tractable nonlinear algebraic equations. The method is applicable to element types for longitudinal and bending vibration, and to an arbitrary number of nodal degrees of freedom in each substructure. In two examples, friction damping of the coupled base and damper is examined in the context of in-plane circumferential vibration (in which case the system is modeled as two unwrapped rods), and of out-of-plane vibration (alternatively, two unwrapped beams). The damper performs most effectively when its natural frequency is well below the base’s natural frequency (in the absence of contact), and also when its natural frequency is well-separated from the excitation frequency.

Hysteretic Friction for the Transient Rolling Contact Problem of Linear Viscoelasticity

The problem of a smooth rigid indentor under variable loading moving across a viscoelastic half-space in one direction with variable speed is considered. The motion is assumed to be frictionless and the standard linear model is adopted to describe the viscoelastic material response. An integral equation is derived and a numerical algorithm for its solution subject to appropriate subsidiary conditions is constructed. The contact interval length, pressure, and coefficient of hysteretic friction are presented and the results discussed.