1,721,111 research outputs found
Fundamental competition of smooth and non-smooth bifurcations and their ghosts in vibro-impact pairs
No full textA combined analysis of smooth and non-smooth bifurcations captures the interplay of different qualitative transitions in a canonical model of an impact pair, a forced capsule in which a ball moves freely between impacts on either end of the capsule. The analysis, generic for the impact pair context, is also relevant for applications. It is applied to a model of an inclined vibro-impact energy harvester device, where the energy is generated via impacts of the ball with a dielectric polymer on the capsule ends. While sequences of bifurcations have been studied extensively in single- degree-of-freedom impacting models, there are limited results for two-degree-of-freedom impacting systems such as the impact pair. Using an analytical characterization of impacting solutions and their stability based on the maps between impacts, we obtain sequences of period doubling and fold bifurcations together with grazing bifurcations, a particular focus here. Grazing occurs when a sequence of impacts on either end of the capsule are augmented by a zero-velocity impact, a transition that is fundamentally different from the smooth bifurcations that are instead characterized by eigenvalues of the local behavior. The combined analyses allow identification of bifurcations also on unstable or unphysical solutions branches, which we term ghost bifurcations. While these ghost bifurcations are not observed experimentally or via simple numerical integration of the model, nevertheless they can influence the birth or death of complex behaviors and additional grazing transitions, as confirmed by comparisons with the numerical results. The competition between the different bifurcations and their ghosts influences the parameter ranges for favorable energy output; thus, the analyses of bifurcation sequences yield important design information.</p
Analysis of dry friction dynamics in a vibro-impact energy harvester
No full textVibro-impact (VI) systems provide a promising nonlinear mechanism for energy harvesting (EH) in many engineering applications. Here, we consider a VI-EH system that consists of an inclined cylindrical capsule that is externally forced and a bullet that is allowed to move inside the capsule, and analyze its dynamics under the presence of dry friction. Dry friction introduces a switching manifold corresponding to zero relative velocity where the bullet sticks to the capsule, appearing as sliding in the model. We identify analytical conditions for the occurrence of non-stick and sliding motions, and construct a series of nonlinear maps that capture model solutions and their dynamics on the switching and impacting manifolds. An interplay of smooth (period-doubling) and non-smooth (grazing) bifurcations characterizes the transition from periodic solutions with alternating impacts to solutions with an additional impact on one end of the capsule per period. This transition is preceded by a sequence of grazing-sliding, switching-sliding and crossing-sliding bifurcations on the switching manifold that may reverse period doubling bifurcations for larger values of the dry friction coefficient. In general, a larger dry friction coefficient also results in larger sliding intervals, lower impact velocities yielding lower average energy outputs, and a shift in the location of some bifurcations. Surprisingly, we identify parameter regimes in which higher dry friction maintains higher energy output levels, as it shifts the location of grazing bifurcations
Exploring effective TET through a vibro-impact nonlinear energy sink over broad parameter regimes
No full textIn recent times, the vibro-impact nonlinear energy sink (VINES) has emerged as a promising passive mechanism for vibration mitigation in engineering systems. The VINES system consists of a ball traveling within a cavity of an externally excited linear oscillator (LO). The ball impacts either end of the cavity, transferring energy from the LO to the ball and mitigating excess oscillations of the LO. Earlier studies of VINES analyzed scenarios with the mass of the ball to be small relative to the LO, with low forcing amplitude near the resonant frequency of the LO. Improvements in targeted energy transfer (TET), observed for an increased mass of the ball, motivate an investigation of VINES for larger mass ratios, using a recently developed semi-analytical map-based approach that provides the exact solution without the limitations of previous analyses. Complementary analytical and numerical approaches treat larger mass ratios and higher amplitudes of the external harmonic excitation for forcing frequencies away from the natural frequency of the LO, identifying parameter regimes for efficient and inefficient performance based on standard measures of energy transfer. The analysis identifies multiple regions for the desired behavior with two alternating impacts per forcing period and provides relevant stability conditions. Numerical results indicate chattering behavior in regimes where energy transfer is minimal, yielding performance that appears similar to resonance. This phenomenon can be directly related to the passive nature of the VINES design, where the natural frequency of the VINES system decreases as the mass of the ball, and thus that of the system, increases. Then the peak response of the LO is shifted away from its resonant frequency, allowing excellent energy transfer to be realized there.</p
Qualitative changes in bifurcation structure for soft vs hard impact models of a vibro-impact energy harvester
No full textVibro-impact phenomena in engineering systems, considered an adverse effect in some settings, are an intrinsic part of the mechanism in others. In energy harvesting, a vibro-impact component is often intentionally introduced to increase the power output or the system’s bandwidth. The impacts can be treated as “hard” for instantaneous impacts or “soft” for compliant materials. Since both types of models exhibit complex dynamics, a comparison is non-trivial. We develop a soft impact model for a vibro-impact energy harvester, calibrating it with the relevant hard impact model for large stiffness, and systematically compare the different phenomena and dynamics in various compliant regimes. Numerical results are used in two different parametric analyses, considering the bifurcation diagrams in terms of device size and external forcing parameters. Varying the natural frequency of the membranes that form the impact boundaries, we observe shifts in the bifurcation structure that promote period-1 orbits for increased softness parameters, often generating higher power output, but also introducing parameter sensitivities for increased softness. Complementary analytical results reveal unstable periodic orbits and co-existing behaviors, potentially missed by computational methods, that can influence the bifurcation structure and in turn the energy output. A non-dimensional formulation highlights the significance of ratios of external and natural frequencies in delineating soft and hard impact scenarios parametrically. The soft impact model exhibits new symmetry breaking bifurcations related to key quantities that characterize the soft impact dynamics, such as the effective restitution coefficients, the impact phase, and the contact time interval, not captured by hard impact models
Post-grazing dynamics of a vibro-impacting energy generator
No full textThe motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. This motion occurs beyond a grazing bifurcation, at which alternating top and bottom impacts are supplemented by a zero velocity impact with the bottom of the device. For periodic forcing, we obtain semi-analytical expressions for the asymmetric periodic motion with a ratio of 2:1 for the impacts on the device bottom and top, respectively. These expressions are derived via a set of nonlinear maps between different pairs of impacts, combined with impact conditions that provide jump discontinuities in the velocity. Bifurcation diagrams for the analytical solutions are complemented by a linear stability analysis around the 2:1 asymmetric periodic solutions, and are validated numerically. For smaller incline angles, a second grazing bifurcation is numerically detected, leading to a 3:1 asymmetry. For larger incline angles, period doubling bifurcations precede grazing bifurcations. The converted electrical energy per impact is reduced for the asymmetric motions, and therefore less desirable under this metric
Systematic matrix formulation for efficient computational path integration
No full textIn this work we introduce a novel methodological treatment of the numerical path integration method, used for computing the response probability density function of stochastic dynamical systems. The method is greatly accelerated by transforming the corresponding Chapman-Kolmogorov equation to a matrix multiplication. With a systematic formulation we split the numerical solution of the Chapman-Kolmogorov equation into three separate parts: we interpolate the probability density function, we approximate the transitional probability density function of the process and evaluate the integral in the Chapman-Kolmogorov equation. We provide a thorough error and efficiency analysis through numerical experiments on a one, two, three and four dimensional problem. By comparing the results obtained through the Path Integration method with analytical solutions and with previous formulations of the path integration method, we demonstrate the superior ability of this formulation to provide accurate results. Potential bottlenecks are identified and a discussion is provided on how to address them
Updatable Probabilistic Evaluation of Failure Rates of Mechanical Components in Power Take-Off Systems of Tidal Stream Turbines
Full text linkThis paper presents a method for the probabilistic evaluation of the failure rates of mechanical components in a typical power take-off (PTO) system of a horizontal-axis tidal stream turbine (HATT). The method is based on a modification of the method of the influence factors, when base failure rates, relevant influence factors and, subsequently, resulting failure rates are treated as random variables. The prior (i.e., initial) probabilistic distribution of the failure rates of a HATT component is generated using data for similar components from other industries, while taking into account actual characteristics of the component and site-specific operating and environmental conditions of the HATT. A posterior distribution of the failure rate is estimated numerically based on a Bayesian approach as new information about the component performance in an operating HATT becomes available. The posterior distribution is then employed to obtain the updated mean and lower and upper confidence limits of the failure rate. The proposed method is illustrated by applying it to the evaluation of the failure rates of two key components of the PTO system of a typical HATT—main seal and main bearing. In particular, it is shown that uncertainty associated with the method itself has a major influence on the failure rate evaluation. The proposed method is useful for the reliability assessment of both PTO designs of new HATTs and PTO systems of operating HATTs
On the analysis of the tristable vibration isolation system with delayed feedback control under parametric excitation
No full textIn this paper, the delayed feedback control of a tristable vibration isolation system (TVIS) under the stochastic parametric excitation is investigated. Firstly, theoretical solutions of the frequency response equation that governs the dynamical performance of the TVIS are derived. Meanwhile, the stability conditions are obtained. The controlled performance and response properties induced by the time delay, the feedback gains and the excitation amplitude are discussed. The existence of the time delay can considerably suppress the vibration amplitude. Particular phenomena induced by the time delay are observed. In addition, the first-order and second-order steady-state moments of the TVIS are obtained based on the Itô stochastic differential equations under the stochastic parametric excitation. The phenomenon of the time delay island about steady-state moments is found. The stationary probability density is discussed for the parametric resonance by means of the finite difference method. The variation of the noise bandwidth and the time delay can induce the transition of the stationary probability density between trivial solutions and non-trivial solutions. Overall, the response mechanism of the TVIS under the stochastic parametric excitation is revealed
Influence of impulse characteristics on realizing high-energy orbits in hybrid energy harvester
No full textEnergy harvesters based on non-linear systems are promising devices for extracting energy from mechanical vibrations. This paper presents a new design of energy harvester con-sisting of two coupled nonlinear systems; the Duffing oscillator and a system with quasizero stiffness. A numerical analysis of the dynamics of the harvester is carried out, presenting co-existing solutions and their energy efficiencies in both chaotic and periodic motion zones. The root mean squared (RMS) voltage results depend on the dimensionless excitation frequency, where high-energy orbits are coexisting with low-energy orbits. Therefore, the second part of the paper focuses on various strategies for jumps between the orbits using impulses. Different impulse characteristics and their sequences for periodic and chaotic zones are analyzed. Therefore, a detailed analysis is presented for many strategies using an impulse excitation di-agram (IED) as a numerical tool for accurately estimating the amplitude of the impulse, its duration, and the moment of initiation. The probability of achieving a given solution is also determined. The simulation results show that achieving the most effective orbit with a single impulse, as well as several impulses, requires similar energy. However, the advantage of the step-by-step method is the lower energy required to initiate a single impulse which enables the use of a smaller regulator. This work can be a valuable tool for designing various systems and strategies for changing the orbit of a solution
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