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Mechanical vibrations in large structures such as buildings, bridges, dams and critical frequencies in large machinery generally have low frequencies (100Hz-1000Hz). To monitor large areas of such structures we need huge network of low cost, easily manufacturable, self-powered and stand-alone vibration spectrum sensors. The sensors should also consume very little power during their overall operation cycle and have moderately high frequency resoultion. The thesis provides mathematical analysis, design and development of stand-alone, low frequency vibration spectrum analyzer .A mechanically stretched polymer piezoelectric membrane, which has a fixed length and tension, can act as a single frequency detector due to its unique resonant frequency. Stretching multiple ribbons of diffferent lengths and tensions, a vibration spectrum analyzer, which gives the Fourier frequency components present in an arbitrary mechanical input vibration, can be designed. The thesis presents a detailed description of experiments to evaluate a low frequency vibration spectrum analyzer system that accepts an incoming input vibration and directly provides the spectrum as output. Polymer piezoelectric materials being easily manufacturable these sensors can be deployed in wide area sensor networks that monitor large structures. The thesis also shows design of a vibration energy harvesting system based on the concept of harvesting energy at low frequencies. The need for developing such an energy harvesting system arises from the necessity of making the vibration sensor, self-powered. Multiple experimental tests were performed before developing a prototype vibration energy harvesting circuit.

Piezoelectric-based energy harvesting devices provide an attractive approach to powering remote devices as ambient mechanical energy from vibrations is converted to electrical energy. These devices have numerous potential applications, including actuation, sensing, structural health monitoring, and vibration control -- the latter of which is of particular interest here. This work seeks to develop an understanding of energy harvesting behavior within the framework of a semi-active technique for reducing turbomachinery blade vibrations, namely resonance frequency detuning. In contrast with the bulk of energy harvesting research, this effort is not focused on maximizing the power output of the system, but rather providing the low power levels required by resonance frequency detuning. The demands of this technique dictate that harvesting conditions will be far from optimal, requiring that many common assumptions in conventional energy harvesting research be relaxed. Resonance frequency detuning has been proposed as a result of recent advances in turbomachinery blade design that have, while improving their overall efficiency, led to significantly reduced damping and thus large vibratory stresses. This technique uses piezoelectric materials to control the stiffness, and thus resonance frequency, of a blade as the excitation frequency sweeps through resonance. By detuning a structure*s resonance frequency from that of the excitation, the overall peak response can be reduced, delaying high cycle fatigue and extending the lifetime of a blade. Additional benefits include reduced weight, drag, and noise levels as reduced vibratory stresses allow for increasingly light blade construction. As resonance frequency detuning is most effective when the stiffness states are well separated, it is necessary to harvested at nominally open- and short-circuit states, corresponding to the largest separation in stiffness states. This presents a problem from a harvesting standpoint however, as open- and short-circuit correspond to zero charge displacement and zero voltage, respectively, and thus there is no energy flow. It is, then, desirable to operate as near these conditions as possible while still harvesting sufficient energy to provide the power for state-switching. In this research a metric is developed to study the relationship between harvested power and structural stiffness, and a key result is that appreciable energy can be harvested far from the usual optimal conditions in a typical energy harvesting approach. Indeed, sufficient energy is available to power the on-blade control while essentially maintaining the desired stiffness states for detuning. Furthermore, it is shown that the optimal switch in the control law for resonance frequency detuning may be triggered by a threshold harvested power, requiring minimal on-blade processing. This is an attractive idea for implementing a vibration control system on-blade, as size limitations encourage removing the need for additional sensing and signal processing hardware.

data_05_d_000.csv - Curve of the RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions δ = 0.0, κ = 0.5. data_05_d_015.csv - Curve of the RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions δ = 0.15, κ = 0.5. data_05_d_030.csv - Curve of the RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions δ = 0.3, κ = 0.5. data_05_d_060.csv - Curve of the RMS values of voltage induced on piezoelectric electrodes for p = 0.183 and randomly selected initial conditions δ = 0.6, κ = 0.5. data_06r_o_19.csv - The orbits of the periodic solutions presented in Fig. 6(a) ω = 1.9, Poincaré points = 2. data_06b_o_19.csv - The orbits of the periodic solutions presented in Fig. 6(a) ω = 1.9, Poincaré points = 3. data_06r_o_21.csv - The orbits of the periodic solutions presented in Fig. 6(b) ω = 2.1, Poincaré points = 2. data_06g_o_21.csv - The orbits of the periodic solutions presented in Fig. 6(b) ω = 2.1, Poincaré points = 3. data_06b_o_21.csv - The orbits of the periodic solutions presented in Fig. 6(b) ω = 2.1, Poincaré points = 9. data_06r_o_26.csv - The orbits of the periodic solutions presented in Fig. 6(c) ω = 2.6, Poincaré points = 2. data_06b_o_26.csv - The orbits of the periodic solutions presented in Fig. 6(c) ω = 2.6, Poincaré points = 3. data_06g_o_26.csv - The orbits of the periodic solutions presented in Fig. 6(c) ω = 2.6, Poincaré points = 6. data_06r_o_38.csv - The orbits of the periodic solutions presented in Fig. 6(d) ω = 3.8, Poincaré points = 3. data_06b_o_38.csv - The orbits of the periodic solutions presented in Fig. 6(d) ω = 3.8, Poincaré points = 4. data_06g_o_38.csv - The orbits of the periodic solutions presented in Fig. 6(d) ω = 3.8, Poincaré points = 5. data_06lb_o_38.csv - The orbits of the periodic solutions presented in Fig. 6(d) ω = 3.8, Poincaré points = 7. data_06p_o_38.csv - The orbits of the periodic solutions presented in Fig. 6(d) ω = 3.8, Poincaré points = 9. data_07b_d_015.csv - Numerical results showing the influence of potential asymmetry on the probability of occurrence of particular solutions for δ = 0.15. data_07g_d_030.csv - Numerical results showing the influence of potential asymmetry on the probability of occurrence of particular solutions for δ = 0.30. data_07lb_d_06.csv - Numerical results showing the influence of potential asymmetry on the probability of occurrence of particular solutions for δ = 0.60. data_07r_d_000.csv - Numerical results showing the influence of potential asymmetry on the probability of occurrence of particular solutions for δ = 0.0. This repository contains the results of numerical simulations of a nonlinear bistable system for harvesting energy from ambient vibrating mechanical sources. Detailed model tests were carried out on an inertial energy harvesting system consisting of a piezoelectric beam with additional springs attached. The mathematical model was derived using the bond graph approach. Depending on the spring selection, the shape of the bistable potential wells was modified including the removal of wells’ degeneration. Consequently, the broken mirror symmetry between the potential wells led to additional solutions with corresponding voltage responses. The probability of occurrence for different high voltage/large orbit solutions with changes in potential symmetry was investigated. In particular, the periodicity of different solutions with respect to the harmonic excitation period were studied and compared in terms of the voltage output. The results showed that a large orbit period-6 subharmonic solution could be stabilized while some higher subharmonic solutions disappeared with the increasing asymmetry of potential wells. Changes in frequency ranges were also observed for chaotic solutions.

The subject of the research contained in this repository is a new design solution for an energy harvesting system resulting from the combination of a quasi-zero-stiffness energy harvester and a two-stage flexible cantilever beam. Numerical tests were divided into two main parts-analysis of the dynamics of the system due to periodic, quasiperiodic, and chaotic solutions and the efficiency of energy generation. The results of numerical simulations were limited to zero initial conditions, as they are the natural position of the static equilibrium. The repository compares graphically the energy efficiency for the selected range of the dimensionless excitation frequency. For this purpose, three cases of piezoelectric mounting were presented on figures - only on the first stage of the beam, on the second and both stages. The analysis has been carried out with the use of diagrams showing difference of the effective values of the voltage induced on the piezoelectric electrodes. The results indicate that for effective energy harvesting, it is advisable to attach piezoelectric energy transducers to each step of the beam despite possible asynchronous vibrations.

Vibration control is a large branch in control research, because all moving systems may induce desired or undesired vibration. Due to the limitation of passive system's adaptability and changing excitation input, vibration control brings the solution to change system dynamic with desired behavior to fulfill control targets. According to preference, vibration control can be separated into two categories: vibration reduction and vibration amplification. Lots of research papers only examine one aspect in vibration control. The thesis investigates the control development for both control targets with two different control applications: vehicle suspension and ocean wave energy converter. It develops control methods for both systems with simplified modeling setup, then followed by the application of a novel mechanical motion rectifier (MMR) gearbox that uses mechanical one-way clutches in both systems. The flow is from the control for common system to the control design for a specifically designed system. In the thesis, active (model predictive control: MPC), semi-active (Skyhook, skyhook-power driven damper: SH-PDD, hybrid model predictive control: HMPC), and passive control (Latching Control) methods are developed for different applications or control performance comparison on single system. The thesis also studies about new type of system with switching mechanism, in which other papers do not talk too much and possible control research direction to deal with such complicated system in vibration control. The state-space modeling for both systems are provided in the thesis with detailed model of the MMR gearbox. From the simulation, it can be shown that in the vehicle suspension application, the controlled MMR gearbox can be effective in improving vehicle ride comfort by 29.2% compared to that of the traditional hydraulic suspension. In the ocean wave energy converter, the controlled MMR WEC with simple latching control can improve the power generation by 57% compared to the passive MMR WEC. Besides, the passive MMR WEC also shows its advantage on the passive direct drive WEC in power generation improvement. From the control development flow for the MMR system, the limitation of the MMR gearbox is also identified, which introduces the future work in developing active-MMR gearbox by using an electromagnetic clutch. Some possible control development directions on the active-MMR is also mentioned at the end of the thesis to provide reference for future works. Master of Science Vibration happens in our daily life in almost all cases. It is a regular or irregular back and forth motion of particles. For example, when we start a vehicle, the engine will do circular motion to drive the wheel, which causes vibration and we feel wave pulses on our body when we sit in the car. However, this kind of vibration is undesirable, since it makes us uncomfortable. The car manufacture designs cushion seats to absorb vibration. This is a way to use hardware to control vibration. However, this is not enough. When vehicle goes through bumps, we do have suspension to absorb vibration transferred from road to our body. The car still experiences a big shock that makes us feel dizzy. On the opposite direction, in some cases when vibration becomes the motion source for energy harvesting, we would like to enhance it. Hardware can be helpful, since by tuning some parameters of an energy harvesting device, it can match with the vibration source to maximize vibration. However, it is still not enough due to low adaptability of a fixed parameter system. To overcome the limitation of hardware, researches begin to think about the way to control vibration, which is the method to change system behavior by using real-time adjustable hardware. By introducing vibration control, the theory behind that started to be investigated. This thesis investigates the vibration control theory application in both cases: vibration reduction and vibration enhancement, which are mentioned above due to opposite application preferences. There are two major applications of vibration control: vehicle suspension control and ocean wave energy converter (WEC) control. The thesis starts from the control development for both fields with general modeling criteria, then followed by control development with specific hardware design-mechanical motion rectifier (MMR) gearbox-applied on both systems. The MMR gearbox is the researcher designed hardware that targets on vibration adjustment with hardware capability, which is similar as the cushion seats mentioned at the beginning of the abstract. However, the MMR cannot have capability to furtherly optimize system vibration, which introduces the necessity of control development based on the existing hardware. In the suspension control application, the control strategy introduced successfully improve the vehicle ride comfort by 29.2%, which means the vehicle body acceleration has been reduced furtherly to let passenger feel less vibration. In the WEC application, the power absorbed from wave has been improved by 57% by applying suitable control strategy. The performance of improvement on vibration control has proved the effect on further vibration optimization beyond hardware limitation.

thesis ; A standard lumped parameter model for an inertial vibration energy harvester consists of a proof mass, spring, and damper(s). This model can also be described with a proof mass, viscous damping element for parasitic mechanical losses, and a generalized transducer that applies some force to the mass damper system. The transducer may contain restorative spring elements and energy extraction elements to harvest power. Currently the framework to relate vibration input to an optimal transducer architecture does not exist. Previous work has shown that for some inputs nonlinear transducer architectures can result in an increased power output. This paper outlines a mathematical framework needed in order to find the optimal transducer architecture for a given vibration input. This framework defines the theoretical upper limit that any inertial transducer can harvest from a given vibration input in the presence of viscous mechanical damping. This framework is then applied to three cases of standard input types. The first application is a single sinusoid input. The transducer architecture found is the expected result, a linear spring with matched resonance to the input, and an energy extraction element, that behaves as a linear viscous damper, with matched impedance to the mechanical damping. The second application of this framework is an input of two sinusoids both having equal magnitude but different frequencies. The resulting optimal transducer is dependent on the difference in the frequencies of the two signals. This optimal transducer is often not realizable with a passive system, as it is inherently time dependent. For all cases of frequency separation between the two sinusoidal inputs, the upper limit for the energy generated is found to be twice that of a linear harvester tuned to the lower of the two frequencies. The third application is for an input whose frequency changes linearly in time (i.e. a swept sinusoid). The optimal transducer architecture for this input is found to be completely time ...

peer-reviewed Vibration energy harvesters (VEHs) scavenge ambient vibrational energy, offering an alternative to batteries for the autonomous operation of low power electronics. VEHs are typically spring-mass-dampers that extract mechanical energy from a vibrating source, converting it into useful electrical energy. A number of transduction mechanisms can be utilised, with electromagnetic induction of interest herein. Velocity amplification, a technique used to increase velocity through impacts, is employed in this thesis to improve the power output and operational bandwidth of multiple-degree-of-freedom (multi-DoF) piecewise linear (PWL) VEHs, compared to linear resonators. Such a harvester is referred to as a velocity ampli ed electromagnetic generator (VAEG), with a gain in power achieved by increasing the relative velocity between the magnet and coil in the transducer. In this thesis, VAEGs were investigated numerically and experimentally under sinusoidal excitation, for a range of parameters. An analysis of the in uence of mass con guration on multi-DoF VAEGs was undertaken. It was determined that under forced excitation, contrary to velocity ampli cation theory, 2-DoF con gurations achieve higher RMS velocities and, hence, voltages than systems with greater numbers of DoFs. With increasing mass ratio, despite the RMS velocity increasing, the RMS voltage actually decreases, as the increase in velocity does not compensate for the reduction in transducer size. A 2-DoF VAEG with a mass ratio of R = 3 was selected for in-depth investigation. The harvester was characterised with frequency sweeps for a range of base acceleration levels and gap lengths|a key geometric parameter. A shift in peak output power towards lower frequencies is observed with increasing gap, due to the decreasing e ective sti ness, while RMS velocity also increases. The acceleration level required to achieve large amplitude oscillations increases with gap, however. An optimisation of the 2-DoF VAEG is presented, resulting in the prediction of a relatively high volume gure of merit (FoMV = 2:83%) at high accelerations (10 m=s2) and low frequencies (16.4 Hz). It is demonstrated that the hysteresis behaviour and dependence of RMS response on initial conditions associated with non-linear VEHs is not present in the VAEGs herein. Consequently, the frequency responses presented are independent of initial conditions, which is signi cant for the applicability of VAEGs. To determine the in uence of scale on the harvester response, the 2-DoF VAEG was fabricated at three length scales (s = V olume1=3), with the electrical and mechanical systems considered separately|a number of deviations from linear scaling methodologies were required to achieve this. It was determined that the gap does not scale, while the load power is predicted to scale as PL x s5:51, suggesting that achieving high power densities in a VAEG at low device volumes is extremely challenging. VAEG con gurations with 2-DoFs and low mass ratios demonstrate the highest power densities, while the optimal gap is dependent on the excitation conditions and increases with increasing acceleration amplitude, at the optimal frequency. VAEGs are found to be most suitable for applications with high acceleration levels and low frequencies, where high power densities can be achieved.

Vibration control is aimed to suppress or eliminate unwanted vibration to ensure proper operation of machines. On the other hand, energy harvesting intends to scavenge energy from ambient vibrations to power electronical devices such as wireless sensors. It is much desired to achieve simultaneous vibration control and energy harvesting. A great amount of effort has been focused on the use of a linear vibration absorber for this purpose. The shortcoming of such an approach is that its effectiveness is limited to a narrow bandwidth of frequency. The goal of this research is to develop a device in order to achieve simultaneous vibration suppression and energy harvesting in a broad frequency band. Instead of using a linear vibration absorber, a nonlinear energy sink (NES) is considered. Since it is very challenging to realize a true NES as it requires a zero linear stiffness, this study focus on developing a variant NES that possesses a low linear stiffness but high nonlinear stiffness. Three designs and their corresponding apparatus are introduced. A base excitation is conducted to determine the spring restoring force in order to character the stiffness of each design. The apparatus that best emulates the NES is chosen. A stiff primary system and a flexible primary system are also developed by changing the primary spring’s stiffness. The behaviors of the chosen variant NES are further investigated in two combined system: weakly coupled one (a stiff primary system plus the variant NES) and the strongly coupled one (a flexible primary system plus the variant NES). The transient responses of the two combined systems are investigated numerically and experimentally. The steady state responses of the two combined systems to a harmonic base excitation are investigated in numerically and experimentally. The results from both the weakly coupled and the strongly coupled systems show some typical features of the NES: 1:1 resonance, targeted energy transfer (TET), initial energy or excitation level dependence, jumping phenomena, and strongly modulated response (SMR), etc.

A standard lumped parameter model for an inertial vibration energy harvester consists of a proof mass, spring, and damper(s). This model can also be described with a proof mass, viscous damping element for parasitic mechanical losses, and a generalized transducer that applies some force to the mass damper system. The transducer may contain restorative spring elements and energy extraction elements to harvest power. Currently the framework to relate vibration input to an optimal transducer architecture does not exist. Previous work has shown that for some inputs nonlinear transducer architectures can result in an increased power output. This paper outlines a mathematical framework needed in order to find the optimal transducer architecture for a given vibration input. This framework defines the theoretical upper limit that any inertial transducer can harvest from a given vibration input in the presence of viscous mechanical damping. This framework is then applied to three cases of standard input types. The first application is a single sinusoid input. The transducer architecture found is the expected result, a linear spring with matched resonance to the input, and an energy extraction element, that behaves as a linear viscous damper, with matched impedance to the mechanical damping. The second application of this framework is an input of two sinusoids both having equal magnitude but different frequencies. The resulting optimal transducer is dependent on the difference in the frequencies of the two signals. This optimal transducer is often not realizable with a passive system, as it is inherently time dependent. For all cases of frequency separation between the two sinusoidal inputs, the upper limit for the energy generated is found to be twice that of a linear harvester tuned to the lower of the two frequencies. The third application is for an input whose frequency changes linearly in time (i.e. a swept sinusoid). The optimal transducer architecture for this input is found to be completely time dependent. However for the case when the change in the input frequency is much slower than the period of the system, the transducer can be approximated by a linear spring whose stiffness changes in time.