Viscoelastic Rod Research Articles

Transient Response in a Viscoelastic Material With Temperature-Dependent Properties and Thermomechanical Coupling

The transient response of a semi-infinite, viscoelastic rod after application of a sinusoidal stress variation at one end has been investigated by a numerical method. Account has been taken of temperature dependence of properties and of thermomechanical coupling. It is found that, with values of physical properties typical for polymeric materials, temperature approaches steady state several orders of magnitude more slowly than would be the case for stress and strain in the absence of thermomechanical coupling.

The Transient Response of a Viscoelastic Torsional Pendulum

The pendulum consists of a circular viscoelastic rod fixed at one end and attached to a disk at the other end. The disk, initially at rest, is subjected to a step function of torque. The subsequent motion is analyzed in terms of normal modes and normal coordinates. The normal modes are found by separation of variables. The characteristic numbers associated with these modes depend only on the moments of inertia of the disk and rod. The normal coordinates satisfy integro-differential equations of the Volterra type. The mechanical properties of polyisobutylene at 25°C were represented in differential operator form. The Volterra integral equations were then solved by means of the Laplace transforms. An analysis of the numerical results shows that only the oscillatory part of the fundamental mode should persist after a short time. This result is in qualitative agreement with observations. This method of analysis may be applied to other dynamic problems in linear viscoelasticity provided the characteristic equation can be reduced to a form that does not involve the mechanical properties of the material.

Axial Vibrations of a Semiinfinite Viscoelastic Rod with External Elastic Constraint

This paper considers the response of a semiinfinite viscoelastic rod subject to an enforced sinusoidal displacement of its end. The rod has external elastic constraint along its length. Above a certain critical frequency, the steady-state solution consists of damped traveling waves moving away from the forced end. For lower frequencies, however, the wave travels out of the rod toward the forced end. A brief explanation of this interesting phenomenon is given by studying the work done on the rod. The transient analysis is performed, for the rod initially at rest, by applying a Fourier sine transform to the space variable. The resulting integral solution is integrated numerically for a purely viscous rod being forced at a frequency below the critical frequency. This solution shows how the disturbance is initially propagated away from the forced end and subsequently settles down to the steady-state solution of the wave traveling toward the forced end.

A note on disturbances in a certain type of visco-elastic solid deformed by a magnetic field

The present note is an attempt to study the propagation of disturbances in a semiinfinite visco-elastic rod which is of three-parameter type, and which is subjected to a static magnetic field.

Axial Vibrations of a Semiinfinite Viscoelastic Rod with External Elastic Constraint

The response is considered of a semiinfinite viscoelastic rod, with uniform external elastic constraint along its length, to an enforced sinusoidal displacement of its end. Above a certain critical frequency, the steady-state solution consists of damped traveling waves moving away from the forced end. For lower frequencies, however, the waves travel out of the rod toward the forced end. A brief explanation of this interesting phenomenon is given by studying the work done on the rod. The transient analysis is performed, for the rod initially at rest, by applying a Fourier sine transform to the space variable. The resulting integral solution is integrated numerically for a purely viscous rod being forced at a frequency below the critical frequency. This solution shows how the disturbance is initially propagated away from the forced end and subsequently settles down to the steady-state solution of the wave traveling toward the forced end.

A note on stress pulses in visco-elastic rods

Abstract This note gives a brief mathematical treatment of the relationship between the transient stress in a semi-infinite visco-elastic rod and the attenuation coefficient and phase velocity as functions of steady state frequency. Except in the case of a delta function stress input, the expression obtained disagrees with Kolsky's result (1956). The reason for the failure of the latter is pointed out.

The propagation of dynamic stresses in visco-elastic rods

A n account is given of the propagation of stress in thin visco-elastic rods when the ends of the rods satisfy a wide variety of boundary conditions. It is assumed that the material of the rods satisfies a stress-strain relation of either of the types ϵ(t)= ∫ −∞ t x (t − τ) dω(τ) dτ dτ, ω(t) = ∫ −∞ t φ(t − τ) dϵ(τ) dτ dτ and that the strains are infinitesimal. General solutions of the equations of motion are derived by use of the theory of Laplace transforms and their applicability demonstrated by the consideration of special problems. The theory of possible experiments to determine the functions x ( t), φ ( t) for any given material is also developed.