A semi-analytical method is used to illustrate the behavior of a multimodal nonlinear electromechanical system which is under base-excitation. System is considered as piezo-ceramic patches attached to a cantilever beam coupled to a resistive load. The cantilever beam is modeled as a nonlinear Timoshenko beam using Assumed Mode method and equations of motion are derived through Lagrange's equati...

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems, thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, this transform is inherently limited to the analysis of single-degree-of-freedom syst...

In this paper, forced responses are investigated in a two degree-of-freedom linear system with a linear coupling to a Nonlinear Energy Sink (NES) subjected to quasi-periodic excitation. The quasi-periodic regimes associated to quasi-periodic forcing in the regime of 1:1-1:1 are studied analytically using the complexification method combined to the averaging method in terms of multi-time paramet...

The investigations on the dynamics of hierarchical oscillator chains provide basic theories for fields acoustic metamaterial and passive guidance energy flow. In present study, characteristics stiffness-dominated transfer a reduced cross-scale chain that generates chaotic vibrations are studied. semi-analytical solutions obtained by complexification-averaging method least-square thoroughly sear...

The quasi-zero stiffness (QZS) isolator shows excellent characteristics of low-frequency vibration isolation. However, the jump behavior caused by strong nonlinearity is a primary reason for failure QZS isolators. In order to grasp effective frequency range and mechanism horizontal comprehensively, dynamics were studied in following two cases. first case, subject base displacement excitation; s...

in this article we consider the averaging method for differential inclusions with fuzzy right-hand side for the case when the limit of a method of an average does not exist.

This article presents a method for identifying the parameters of simplified 2 degree freedom model representative linear primary system coupled to non-linear absorber in forced harmonic regime over wide range amplitudes and forcing frequencies covering different dynamical regimes. is priori difficult operation because it necessary combine two apparently contradictory steps. The first step consi...