Free vibration of the system of two viscoelastic beams coupled by viscoelastic interlayer

Acoustic bulletin, Vol. 2 1, (1999) p.3-10
An analytical method of solution of the free vibration problem for composite system of two viscoelastic beams coupled by a viscoelastic interlayer has been proposed. The phenomenon of free vibration has been described using a homogenous system of conjugate partial differential equations. After the separation of variables in the differential equations the boundary problem has been solved and two complex sequences have been obtained: the sequence of frequencies and the sequence of modes of free vibration. The property of orthogonality of complex modes of free vibration has been demonstrated. Polyharmonic free vibration has been expanded into the complex Fourier series with respect to complex eigenfunctions. The coefficients at the eigenfunctions are determined by the initial conditions.
visco-elastic beam, the Winkler base, complex modes