On the modal decoupling of linear mechanical systems with frequency-dependent viscoelastic behavior

• .General method to evaluate modal-based FRF for frequency-dependent damped systems.
• In Time-domain, it reduces to a set of uncoupled second order damped oscillators.
• In Frequency-domain, it allows a complete modal decomposition of the FRF's.
• For linearly viscous damping, it is based on an eigensolution.For frequency-dependent viscoelastic materials, it is based on iterative eigensolutions.The agreement between the modal-decomposed FRF and the direct one is full.

Linear Multi-Degree of Freedom (MDOF) mechanical systems having frequency-dependent viscoelastic behaviors are often studied and modelled in frequency or Laplace domains. Indeed, once this modelling process is carried out, it is not generally possible to reduce the obtained MDOF damped mechanical system to a set of uncoupled damped modal oscillators apart from some special cases. In this paper a general procedure has been proposed to transform a coupled linear mechanical system having frequency-dependent viscoelastic characteristics to a set of independent damped modal oscillators. The procedure is based on a linear co-ordinate transformation procedure using matrices in real field only. The approach is exact and based on the solution of one associated eigenproblem for the case of linearly viscous damping. In the general case of frequency-dependent viscoelastic materials, the approach includes an iterative procedure solving local eigenproblems.Some numerical results are reported to show the capabilities of the proposed approach.