Wave component solutions of free vibration and mode damping loss factor of finite length periodic beam structure with damping material

Free vibration and mode damping loss factor of the finite periodic beam structure with viscoelastic damping material are investigated in this paper based on wave component method. A simple iterative operation for the natural vibration modes of the beam structure is firstly proposed by considering that the mode shape can be formed through superposition of the wave shapes of the wave components of the beam structure at the corresponding natural frequency. And then, wave component solution of the mode damping loss factor of the beam structure is obtained and analyzed based on the modal stain energy method. It is found that the kinetic energy of the unit cell of propagative wave component is always the same with the strain energy, and for non-propagative wave component these two quantities will never be equal. In numerical examples, the proposed iterative operation is validated.