Stiffness Of Nonlinear Energy Sink Research Articles

Nonlinear Dynamic Response of Galfenol Cantilever Energy Harvester Considering Geometric Nonlinear with a Nonlinear Energy Sink

The nonlinear energy sink (NES) and Galfenol material can achieve vibration suppression and energy harvesting of the structure, respectively. Compared with a linear structure, the geometric nonlinearity can affect the output performances of the cantilever beam structure. This investigation aims to present a coupled system consisting of a nonlinear energy sink (NES) and a cantilever Galfenol energy harvesting beam with geometric nonlinearity. Based on Hamilton’s principle, linear constitutive equations of magnetostrictive material, and Faraday’s law of electromagnetic induction, the theoretical dynamic model of the coupled system is proposed. Utilizing the Galliakin decomposition method and Runge–Kutta method, the harvested power of the external load resistance, and tip vibration displacements of the Galfenol energy harvesting model are analyzed. The influences of the external excitation, external resistance, and NES parameters on the output characteristic of the proposed coupling system have been investigated. Results reveal that introducing NES can reduce the cantilever beam’s vibration while considering the geometric nonlinearity of the cantilever beam can induce a nonlinear softening phenomenon for the output behaviors. Compared to the linear system without NES, the coupling model proposed in this work can achieve dual efficacy goals over a wide range of excitation frequencies when selecting appropriate parameters. In general, large excitation amplitude and NES stiffness, small external resistance, and small or large NES damping values can achieve the effect of broadband energy harvesting.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

Flow-induced vibration attenuation of a viscoelastic pipe conveying fluid under sinusoidal flow using a nonlinear absorber

In this paper, the dynamics of a viscoelastic pipe conveying fluid attached to a nonlinear energy sink (NES) subjected to a sinusoidal flow is studied, aiming at performance improvement of such fluid-interaction systems. The NES has an essentially nonlinear cubic stiffness and a nonlinear cubic damping. Complexification-averaging and fourth-order Runge-Kutta methods are applied to solve the equations of the motion. The conditions of flow-induced instability, the weak modulated response (WMR), and the strongly modulated response (SMR) are investigated. The influence of the internal fluid velocity, the external flow velocity, the viscoelastic damping coefficient, the NES stiffness, location, and damping on the system efficiency is elucidated. The Poincare-Bendixson theorem implies that there are no closed trajectories in the phase diagram of the system response. The results revealed that the occurrence probability of the SMR and jump phenomenon in the system response increases by ascending the internal fluid velocity. Besides, it is shown that at high external fluid velocities or low viscoelastic damping coefficients, the detached resonance curve (DRC) emerges in the frequency-response curves, and simultaneously the unstable regions expand. Furthermore, by approaching the NES installation location to the pipe supports, the occurrence probability of the SMR, DRC, and WMR descends, the divergence regions are enlarged and the transient response lasts longer.

Nonlinear vibration control of a cantilevered fluid-conveying pipe using the idea of nonlinear energy sink

Different from the both-end supported pipe conveying fluid as a conservative system, the cantilevered fluid-transporting pipe is a non-conservative system and its dynamic behavior is more complex with flutter instabilities when the flow velocity is beyond the critical value. Indeed, controlling such a flutter system is always challenging in engineering applications. This study presents nonlinear vibrations of cantilevered pipe conveying fluid passively controlled via a nonlinear energy sink (NES). Based on the Hamilton principle, the nonlinear dynamic equations coupling with the NES are derived and discretized using high-order Galerkin method. It is indicated that increasing the mass and damping of NES results in an increase in critical flow velocity. Importantly, the optimal placed position of NES where the critical flow velocity is highest has a strong relationship with the pipe’s flutter mode. In the following, the nonlinear analysis shows the dynamic controlling effect on vibration amplitude of the pipe can be classified to three suppression regions with increasing the flow velocity. Varying the mass, damping and stiffness of NES is followed by variations of the suppression regions which are associated with controlling effects and dynamic behaviors of the pipe system.