Sergio Bellizzi

Mode coupling instability mitigation in friction systems by means of nonlinear energy sinks: numerical highlighting and local stability analysis

In this paper, we study the problem of passive control of friction-induced vibrations due to mode coupling instability in braking systems. To achieve that, the well-known two degrees of freedom Hultén’s model, which reproduces the typical dynamic behavior of friction systems, is coupled to two ungrounded nonlinear energy sinks (NES). The NES involves an essential cubic restoring force and a linear damping force. First, using numerical simulations it is shown that the suppression or the mitigation of the instability is possible and four steady-state responses are highlighted: complete suppression, mitigation through periodic response, mitigation through strongly modulated response, and no suppression of the mode coupling instability. Then the system is analyzed applying a complexification-averaging method and the resulting slow-flow is finally analyzed using geometric singular perturbation theory. This analysis allows us to explain the observed steady-state response regimes and predict some of them. The boundary values of the friction coefficient for some of the transitions between these regimes are predicted. However, the appearance of a three-dimensional super-slow flow subsystem highlights the limitation of the local linear stability analysis of the slow-flow to predict all these boundaries.

Experimental Study of an Acoustic System Coupled to a Nonlinear Membrane Under Multi-Frequency Forcing

In this paper, an experimental study of the coupling of a 2 degree-of-freedom acoustic medium to a nonlinear visco-elastic membrane under multi-frequency forcing is presented. When the excitation is sinusoidal, we observe classical results: non-linear effects tend to damp pressure in the linear system. When the excitation is quasi-periodic with two frequencies, various aspects of quasi-periodic regimes are observed. Some regimes exhibit only the two excitation frequencies in their spectrum, other display a more complicated, but mostly discrete, spectrum. These stable quasi-periodic regimes can disappear leaving to Strongly Modulated Quasi-Periodic Responses (SMQPR). Various structures have been extracted from SMQPRs using signal processing tools (RMS analysis, Fourier analysis, histogram analysis). They are compared with theory and the NES efficiency is assessed. The system behaves in general as expected: the periodic, quasi-periodic or SMQPR regimes correspond to theoretical findings.Copyright

Sliding window POD analysis of vibrating structures. Application to nonlinear forced structure under axial flow

In this paper, a multivariate data analysis method combining the Proper Orthogonal Decomposition (POD) and a time-frequency analysis (TEA) is presented. The POD method is a tool adapted to the study of multi-degrees of freedom systems, which can give some insight of the behavior of complex nonlinear systems, whereas TEA is suitable for scalar signal with multi-frequency components. The method presented here is of principal interest in the case of swept-sine excitation of complex multi-DOF systems. It will be first applied to a synthetic signal, then mechanical simulations and finally experimental results.© 2013 ASME

Smooth decomposition analysis and order reduction of nonlinear mechanical systems under random excitation

This paper presents a possible alternative procedure to the Karhunen-Loeve approach to construct reduced order models which capture accurately the dynamics of nonlinear discrete mechanical systems under random excitation. This procedure combines the Smooth Decomposition method and the Petrov-Galerkin approximation. The smooth decomposition method is a multivariate-data analysis method characterizing coherent structures (the smooth modes) as the eigenvectors of the generalized eigenproblem defined from the covariance matrix of the displacement field and the covariance matrix of the velocity field. The Petrov-Galerkin approximation is used to project the dynamics in a subspace generated by a set of the smooth modes. The Petrov-Galerkin approximation preserves the second order structure of the equations of motion. The procedure is considered for a mechanical system including a strongly nonlinear end-attachment. The efficiency of the approach is analyzed comparing the power spectral density functions of the reduced-order model and of the original system.Copyright