Torsional vibration of a sandwich shaft with damping interlayer

This paper presents an analytical method of solving torsional vibration problems concerning a sandwich circular shaft with a viscoelastic soft and light interlayer. The elasticity and damping coefficients of the interlayer are assumed to be dependent on its geometrical characteristic and viscoelastic properties of the interlayer material. Complex functions of a real variable are applied in the solution to free and forced vibration problems. Then, the property of orthogonality of complex modes of the free vibration, which is the basis for solving the free vibration problem for arbitrary initial conditions, has been demonstrated. The solution to the problem of real stationary forced vibration has been obtained on the grounds of the complex stationary modes of vibration.