The harmonic oscillations of a viscoelastic rod of triangular cross-section

Two exact solutions of the plane strain problem of the harmonic oscillations of a viscoelastic rod, the cross-section of which is a right triangle, are proposed. Either the normal displacement and the shear stress or the shear displacement and the normal stress of the side surface of the rod are given. Six dimensionless parameters which affect the dynamic deformation process are derived. Two parameters characterize the contribution of the viscous properties with respect to the elastic properties, two others define the logarithmic decrement of the longitudinal and shear harmonic waves, and two other parameters affect the wavelength of the corresponding wave and the velocity of motion of the wave front of these waves. The velocities of both types of waves and their wavelengths turn out to be greater than the velocities and wavelengths of the corresponding elastic waves. It is shown that, for certain values of the viscosity and the oscillation frequency, pseudo-resonance frequencies are possible which are higher than the resonance frequencies for an elastic medium.