Linear Multi-Degree of Freedom (MDOF) mechanical systems having frequency-independent or frequency-dependent viscoelastic behaviors are often studied and modelled in frequency or Laplace domains. Indeed, the experimental characterization of such mechanical properties is also naturally performed in frequency domain via input/output experimental tests and it includes the linear viscous damping as special case. However, once this identification and modelling process is performed, 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, such as the proportional viscous damping one. In this paper a general procedure has been proposed to transform a coupled linear mechanical system having genericfrequency-independent or frequency-dependent viscoelastic characteristics to a set of independent damped modal oscillators. The procedure is achieved via a linear co-ordinate transformation procedure using matrices in real field only. The approach is exact and based on the solution of an associated eigenproblem for the specific case of linearly viscous damping and frequency independent stiffness. In the general case of frequency-dependent viscoelastic materials, the approach is extended by an iterative procedure solving local eigenproblems to determine the suitable uncoupling transformation. As final consequence, a damped modal-based Frequency Response Function (FRF) of the system can be obtained so showing how the single damped-mode contribution can be isolated and a limited-frequency-band viscoelastic model can be finally achieved. Some numerical results on simple mechanical systems and also on a generic Finite Element (FE) models are reported to show the capabilities of the proposed approach.
On the modal decoupling of linear mechanical systems with frequency-dependent viscoelastic behavior / Mastroddi, Franco; Calore,. - In: MECHANICAL SYSTEMS AND SIGNAL PROCESSING. - ISSN 0888-3270. - STAMPA. - 70-71:(2016), pp. 769-787. [doi:10.1016/j.ymssp.2015.09.024]
On the modal decoupling of linear mechanical systems with frequency-dependent viscoelastic behavior
MASTRODDI, Franco
;
2016
Abstract
Linear Multi-Degree of Freedom (MDOF) mechanical systems having frequency-independent or frequency-dependent viscoelastic behaviors are often studied and modelled in frequency or Laplace domains. Indeed, the experimental characterization of such mechanical properties is also naturally performed in frequency domain via input/output experimental tests and it includes the linear viscous damping as special case. However, once this identification and modelling process is performed, 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, such as the proportional viscous damping one. In this paper a general procedure has been proposed to transform a coupled linear mechanical system having genericfrequency-independent or frequency-dependent viscoelastic characteristics to a set of independent damped modal oscillators. The procedure is achieved via a linear co-ordinate transformation procedure using matrices in real field only. The approach is exact and based on the solution of an associated eigenproblem for the specific case of linearly viscous damping and frequency independent stiffness. In the general case of frequency-dependent viscoelastic materials, the approach is extended by an iterative procedure solving local eigenproblems to determine the suitable uncoupling transformation. As final consequence, a damped modal-based Frequency Response Function (FRF) of the system can be obtained so showing how the single damped-mode contribution can be isolated and a limited-frequency-band viscoelastic model can be finally achieved. Some numerical results on simple mechanical systems and also on a generic Finite Element (FE) models are reported to show the capabilities of the proposed approach.File | Dimensione | Formato | |
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