This chapter addresses the prediction of vibratory resonances in nonsmooth structural systems via Nonsmooth Modal Analysis. Nonsmoothness in the trajectories is induced by unilateral contact conditions in the governing (in)equations. Semi-analytical and numerical state-of-the-art solution methods are detailed. The significance of nonsmooth modal analysis is illustrated in simplified one-dimensional space semi-discrete and continuous frameworks whose theoretical and numerical discrepancies are explained. This contribution establishes clear evidence of correlation between periodically forced and autonomous unilaterally constrained oscillators. It is also shown that strategies using semi-discretization in space are not suitable for nonsmooth modal analysis. The spectrum of vibration exhibits an intricate network of backbone curves with no parallel in nonlinear smooth systems. Terminology and acronyms The purpose of this chapter is to provide a general picture of the state-of-the-art vibratory analysis of nonsmooth systems. This topic lies at the interface between modal analysis of smooth nonlinear systems and nonsmooth contact dynamics dedicated to the time-evolution of nonsmooth systems, undergoing impact or dry friction, for instance. Some elementary concepts are succinctly recalled for the purpose of completeness. Unless otherwise stated, the epithet discrete (as in "discrete systems" or "discrete setting") designates semidiscretization in space, while continuous refers to everything else.
The influence of prestrain on viscoelastic properties E Ã and tan d of four different HTPB composite propellants was measured using Dynamic Mechanical Analysis (DMA). Nonlinear behaviour in terms of prestrain was observed and then modelled using a modified generalized Maxwell model. Prestrain was introduced as a variable of the stiffness of each Maxwell element using simple two-parameter relationships. An algorithm was proposed and numerically implemented to identify the model parameters from the measurements. The performance of the identification method is discussed in terms of accuracy and robustness. The good match between the predictions and the experimental measurements shows that the dependence on the uniaxial prestrain of the complex modulus of the studied composite propellants can be described with few Maxwell elements but with good accuracy.
International audienceHighly filled elastomers exhibit a complex nonlinear mechanical behaviour that is difficult to characterize experimentally. This paper presents a Dynamic Mechanical Analysis (DMA) method coupled with orthogonal prestrains, applied in two distinct steps. A localization operator between measurements at the arms of a cross shaped specimen and the stress and strain fields at its center was determined using elastic small strain finite element computations. The operator makes estimating the storage and loss moduli at the center of the specimen possible. A mathematical model is then fitted to the moduli values. These results are compared to DMA measurements of highly filled elastomers under uniaxial prestrain. Although the storage and loss moduli increase with the prestrain under both loadings, the nonlinear behaviour is quantitatively modified by adding an orthogonal prestrain. In addition, the modification of the behaviour under a horizontal prestrain is cancelled out by an increase of the vertical prestrain, which may be explained by fillers aligning in the direction of the prestrain
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