Analysis, Simulation And Experiment Of Vibration-based Nonlinear Energy Harvesting

The problem of energy is one of the hot topics, many researchers have been trying to find and develop new energy to solve the shortage of energy and the problem of use traditional energy. Vibration energy is widespread in our ambient, grow at rapid pace. Vibratory energy harvester is a mechanism which converts mechanical energy to electrical energy. Due to vibration-based energy have characterized structural simple, green and sustainable, so won widely concerned.The modeling, analysis, simulation and experiment of vibration-based nonlinear energy harvesting are investigated in this dissertation. Four different types of energy harvesters are designed, the output voltage and the output power response are considered. The statistical moments of the output voltage and the power response for six different types of energy harvesters are proposed under random excitations. The electromechanical coupling governing equation are derived based on Hamilitonian principle. The steady-state response of voltage and power are analyzed via the method of multiple scales. The stochastic averaging method is developed for nonlinear energy harvesters subject to Gaussian white noise external and parametric excitations, the results of analysis were validated thought Monte Caro simulations. The main points of the concrete are as follows:The snap-through mechanism is employed to harvest electricity from random vibration through piezoelectricity. The electromechanical coupling equations was derived via the Newton’s second law and the Kirchhoff voltage laws. The method of the moment differential equations is applied to determine the statistical moments of the displacement response and output voltage. The effects of the system parameters on the output voltage and output power are examined. An electromagnetic device with snapthrough nonlinearity is proposed as an archetype of internal resonance energy harvester. The method of multiple scales is applied to derive the amplitude-frequency response relationships of the displacement and the electric current in the first primary resonances with the one-to-two internal resonance. The amplitude-frequency response curves of the current and the power have two peaks bending to the left and the right respectively. The effects of the system parameters on the output current and output power are examined under harmonic and four different types of random excitations.An L-shaped piezoelectric cantilevered harvester augmented with frequency tuning magnets is considered. The electromechanical coupling equations was derived via the energy method, the linear constitutive equations of piezoelectricity and the Gauss’ s law. The method of multiple scales is applied to derive the amplitude-frequency response relationships of the displacement and the electric voltage in the first primary resonances with the one-to-two internal resonance. The amplitude-frequency response curves of the voltage have two peaks bending to the left and the right respectively. The effects of the system parameters on the output voltage are examined. Results clearly illustrate an improved bandwidth and output voltage over a case which does not involve an internal resonance. A lumped-parameters nonlinear model of the harvester is developed and validated against experimental findings.An axially loaded energy harvester with an oscillator is considered. The electromechanical coupling equations was derived via the Hamilton principle and the Gauss’ s law. The method of multiple scales is applied to derive the amplitude-frequency response relationships of the voltage and the power in the first primary resonances with a one-to-two internal resonance. Maximum power is delivered to a load resistance. The amplitude-frequency response curves of the voltage and the power under the optimal load resistance have two peaks bending to the left and the right respectively. The results demonstrate that the internal resonance design can improve bandwidth and produces more electricity than the conventional linear energy harvester.Stochastic averaging method is proposed for nonlinear energy harvesters subject to Gaussian white noise external and parametric excitations. The averaged Ito equations are derived via the standard stochastic averaging method, the exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. A new stochastic averaging method is proposed for nonlinear vibration energy harvesters subject to Gaussian white noise excitation. The generalized harmonic transformation scheme is applied to decouple the electromechanical equations, then obtained an equivalent nonlinear system which is uncoupled to an electric circuit. The stochastic averaging method is developed by using the generalized harmonic functions. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the amplitude and the power of the stationary response. The procedure is applied to three different type Duffing vibration energy harvesters under Gaussian white excitations. The effects of the system parameters on the mean-square voltage and the output power are examined.The main innovation of this dissertation are as follows:1. the snap-through piezoelectric energy harvester, the snap-through magnetoelectric energy harvester, L-shaped piezoelectric cantilevered harvester augmented with magnets and axially loaded energy harvester with an oscillator are designed.2. the double-jumping phenomenon on the frequency–amplitude curves are discovered for vibration-based energy harvester under one-to-two internal resonance. The results demonstrate that the internal resonance design can improve bandwidth and produces more electricity than the conventional linear energy harvester.3. the method of decoupling was proposed for enerergy harvesting via generalized harmonic functions, and validated by introducing the Monte Carlo simulations.