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An Efficient Reduced-Order Model to Investigate the Behavior of an Imperfect Microbeam Under Axial Load and Electric Excitation
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NONLINEAR PHENOMENA IN THE SINGLE-MODE DYNAMICS OF A CABLE-SUPPORTED BEAM
No full textIn this paper we discuss the practical usefulness of nonlinear dynamical analysis for the design of a planar cable-supported beam: we refer to a feasible case, assuming the value of the parameters corresponding to a realistic pedestrian footbridge. We consider a one degree of freedom model, obtained by the classical Galerkin reduction technique: the ensuing ordinary differential equation has both quadratic and cubic terms, due to geometric nonlinearities. Extensive numerical simulations are performed: they point out that this model, in spite of its apparent simplicity, is able to highlight the complex dynamics of the cable-supported beam, describing several common and uncommon nonlinear phenomena. Each of them is interpreted in terms of oscillations of the considered mechanical system; we explain the relevance of all the obtained results in the design of the examined structure under steady loads as wind and pedestrians, but also under transient phenomena as earthquake and gust; the ensuing issues, the most dangerous ranges and also the sensibility to perturbations are discussed in detail. In particular we deal with the importance, for an engineering design, of a careful interpretation of: isola bifurcation, transition to chaos both by period doubling cascade and reverse boundary crisis, multistability with coexistence of chaotic and periodic attractors, fractal basins boundaries, erosion of immediate basins, interrupted sequence of period doubling bifurcations. Also the effects of secondary attractors are analyzed, and it is shown that in general they cannot be neglected even if their range of existence is very small. We underline that all these investigations are performed choosing the excitation frequency far from resonances in order to alert the designer that the system dynamics may be complex independently of the activation mechanism due to resonance
Dynamical integrity for interpreting experimental data and ensuring safety in electrostatic MEMS
No full textMultistability in an electrically actuated carbon nanotube: a dynamical integrity perspective
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AN IMPERFECT MICROBEAM ELECTRICALLY ACTUATED: EXPERIMENTAL INVESTIGATION AND PARAMETER IDENTIFICATION
No full textNonlinear dynamics of an imperfect microbeam under an axial load and electric excitation
No full textThis study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Padé approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors. Copyright © 2011 by ASME
Subcombination internal resonance of the additive type in the response dynamics of micromachined resonators crossing the impacting threshold
No full textIn the present paper, a microbeam-based MEMS device is experimentally driven to experience a subcombination internal resonance (IR) of the additive type, where the second mode internally resonates with both the first and the third modes inducing a range of quasi-periodic dynamics. The main features of the experimental quasi-periodicity are analyzed, which inherently depend on the ratios established by the frequencies of the involved modes. Experimental Poincaré maps are established and tracked, exhibiting a specific underlying pattern. Numerical simulations are developed and the Fast Fourier Transform frequency trend lines are examined, showing the variations of the modes frequencies values while keeping the subcombination IR relationship. We investigate the evolution of the quasi-periodic waveform as increasing the excitation frequency. Special attention is devoted to the hardening dominance of the system, which influences the modes frequencies components. The last part of the paper is focused on the impacting regime. Since the microbeam is constituted by a dielectric layer (Silicon Nitride), impacts take place as raising the oscillation amplitudes. We analyze the experimental behavior at impacts, showing the possibility of dynamics with different characteristics, including both quasi-periodic, chaotic and periodic regions, all of them holding subcombination IR signature
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