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.

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A stress function theory for linearly viscoelastic solids is developed in this paper. If body forces and inertial forces are neglected, the stresses, strains, and displacements are biharmonic functions of the space variables. The displacements are expressed in terms of harmonic functions by an extension of the Neuber-Papkovitch theory. Axially symmetric stresses and strains are given in terms of a single biharmonic function. As the analysis does not involve boundary conditions, it is valid for problems involving moving leads and moving boundaries. The theory may be used to formulate stress analysis problems in terms of Volterra integral equations, using creep or relaxation functions as the kernel. The integral equations governing the stresses in a viscoelastic propellant grain subjected to the combined effects of internal pressure and erosion are derived.

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