Transversal inertial effect on one-dimensional dynamic viscoelastic constitutive relation

In this paper, transversal inertial effect on one-dimensional dynamic viscoelastic constitutive relation was studied. In terms of energy equilibrium, the viscoelastic constitutive relation was derived based on the Voigt model. A differential equation for one-dimensional waves propagated in a viscoelastic bar was obtained with considering transversal inertial equation. From the solution of the equation motion, the relations between relaxation time, modulus and wave velocity, frequency, coefficient of attenuation, and transversal inertial effect are established. These results supply a theoretical method to determine the relaxation time and modulus of viscoelastic materials by means of ultrasonic wave technique.