In this paper, a new prototype is proposed for accelerated orthodontic tooth treatment. In contrast to conventional methods, where heavy vibration generators are used, the proposed design is light and small and may remain into patient’s mouth without obstructing his daily activities. To do that, a PVDF Piezoelectric actuator layer is incorporated into a bio-compatible flexible structure which is to be excited by an external electric source. Generally, application of cyclic loading (vibration) reverses bone loss, stimulates bone mass, induces cranial growth, and accelerates tooth movement. This reduce the pain experience and discomfort associated with the treatment and also enhances the patient compliance with the treatment. Vibration has the advantage of minimal side effects in comparison to medicinal treatments. This configuration enables the operator to adjust the vibration frequency as well as the orthodontic force exerted on the tooth.

One major problem of implantable biomedical devices is the source of their power. Batteries, as the main source of current implantable devices, deplete after a few years and either the battery or the whole device needs to be replaced. Usually, this procedure involves a new surgery which is costly and could cause some risks for the patient. In this paper, we study the energy harvesting at small scale for powering implantable biomedical devices. The device consists of a layer of cultured cardiac muscle cells (cardiomyocytes) and a layer of piezoelectric polymer polyvinylidene fluoride (PVDF). The cardiac muscle cells with the desired thickness are grown over the PVDF layer and as the cardiac cells contract the piezoelectric layer deforms and produces electricity. The proposed device uses both piezoelectric and flexoelectric effects of the PVDF layer. At the smaller thicknesses the flexoelectric effect becomes dominant. The amount of power is on the order of multiple microwatts and is sufficient to power variety of sensors and implantable devices in the body. Unlike the battery technology, the proposed energy harvester is autonomous and lasts for the lifetime of patients. In this article, we explain the configuration of the proposed energy harvester, the natural frequency of the device is calculated, the power output is optimized with respect to the thickness of the PVDF, and a resistance sweep is performed to find the optimized resistive load.

Variable stiffness mechanisms have a wide range of applications in the field of human-robot interactions such as rehabilitation robotics, prosthesis and industrial robotics due to their ability to comply with the human limb stiffness in an unstructured environment. This paper presents the analysis of a single degree of freedom variable stiffness actuator based on nonlinear force interactions between permanent magnets and its effect on the natural frequency of the system. In the proposed mechanism, variable stiffness is achieved by modifying the separation between magnets. The main goal here is to achieve a desired cutoff frequency by varying the stiffness of the system to filter out the involuntary movement of upper limb during physical human-robot interactions. Moreover, due to the spring-like non-contact force interactions between magnets, this mechanism can prevent the exchange of high impact forces between the robot and human.

This manuscript investigates energy harvesting from arterial blood pressure via the piezoelectric effect for the purpose of powering embedded micro-sensors in the human brain. One of the major hurdles in recording and measuring electrical data in the human nervous system is the lack of implantable and long term interfaces that record neural activity for extended periods of time. Recently, some authors have proposed micro sensors implanted deep in the brain that measure local electrical and physiological data which is then communicated to an external interrogator. This paper proposes a way of powering such interfaces. The geometry of the proposed harvester consists of a piezoelectric, circular, curved bimorph that fits into the blood vessel (specifically, the Carotid artery) and undergoes bending motion because of blood pressure variation. In addition, the harvester thickness is constrained such that it does not modify arterial wall dynamics. This transforms the problem into a known strain problem and the integral form of Gauss’s law is used to obtain an equation relating arterial wall motion to the induced voltage. The theoretical model is validated by means of a Multiphysics 3D-FEA simulation comparing the harvested power at different load resistances. The peak harvested power achieved for the Carotid artery (proximal to Brain), with PZT-5H, was 11.7 μ W. The peak power for the Aorta was 203.4 μ W. Further, the variation of harvested power with variation in harvester width and thickness, arterial contractility and the pulse rate is investigated. Moreover, potential application of the harvester as a chronic, implantable and real-time Blood pressure sensor is considered. Energy harvested via this mechanism will also have applications in long-term, implantable Brain Micro-stimulation.

This manuscript investigates the flexural wave propagation behavior of a foldable metamaterial structure. Origami-inspired foldable structures are making inroads into many engineering applications — deployable solar cell arrays, foldable telescope lenses, foldable automotive airbags, to name a few; driven primarily by some of the remarkable mechanical properties (high stiffness, negative Poisson’s ratio, bistability etc.) of these structures. The chief motivation of this research is a comprehensive analysis of flexural wave propagation in such foldable structures. The repeating unit cell of the structure consists of an Euler-Bernoulli beam and a torsion spring. Transfer Matrix (TM) method is used to analyze the vibration attenuation properties of the structure and it is shown that the structure exhibits bandgap behavior. The obtained bandgaps are validated using Finite Element Analysis (FEA). Using the characteristic equation of the transfer matrix, we derive a transcendental equation for the bandgap edge frequencies. We show that for the n th band gap, the second band edge frequency is always equal to the natural frequency of the n th modeshape of the constituent beam under the simply supported condition. This frequency, therefore, is independent of the torsion spring constant. In addition, a detailed parametric study of the variation in band edge frequencies when the geometric and material parameters of the structure (Young’s modulus of beam, torsional spring constant, width and thickness of beam etc.) are varied is conducted. It is concluded that the ratio of flexural rigidity of the beam to the torsion spring constant (EI/k t ) is an important parameter affecting the width of the bandgap. For low values of the ratio, i.e., low beam flexural rigidity and high torsional stiffness, the first band edge frequency is almost equal to the second band edge and, effectively, no bandgap exists. As the stiffness ratio increases, i.e. high flexural rigidity (EI of the beam) and low torsional stiffness k t , the first band edge frequency assumes progressively lower values relative to the second band edge and we obtain a relatively large bandgap over which no flexural waves propagate. This has important ramifications for the design of foldable metamaterial structures.

This manuscript investigates one way sound propagation in Magnetorheological fluids (MRF) using spatio-temporal modulation of the applied magnetic field. One-way propagation of waves in a structure can have potential technological applications such as sound isolation, filtering and echo suppression. Several experimental works in the literature have shown that elastic properties of MRF’s (local speed of sound, in particular) are dependent on the applied magnetic field. Therefore, several fascinating possibilities regarding the manipulation of sound waves in MRF, by tailoring the applied magnetic field, exist. A effective medium approximation (previously used in literature) is used to analyze sound propagation in a MRF composed of hydrogen-reduced Iron particles suspended in pure glycerine. Floquet-Bloch theory is used to obtain a quadratic eigenvalue problem that gives the band structure as a function of the material and modulation parameters. When the applied magnetic field is allowed to vary only in space, regular bandgaps are obtained as a result of Bragg scattering. In contrast, the temporal variation of the magnetic field to induce a traveling wave like variation of the modulated parameters, breaks the symmetry of the Brilloouin zones and we obtain directional bandgaps. The theoretical band structure is validated by numerical band diagrams obtained using a Finite Element code. This research has important applications in active sound manipulation.

This paper investigates energy harvesting from arterial blood pressure via the piezoelectric effect for the purpose of powering embedded micro-sensors in the brain. Blood flow is highly dynamic and arterial blood pressure varies, in the average human blood vessel, from 120 mm of Hg to 80 mm of Hg and we look at transduction of this pressure variation to electric energy via the piezoelectric effect. We propose two different geometries for this purpose. Initially, we look at the energy harvested by a cylinder, coated with PVDF (Polyvinylidene fluoride) patches, placed inside an artery acted upon by blood pressure. The arrangement is similar to that of a stent which is a cylinder placed in veins and arteries to prevent obstruction in blood flow. The governing equations of the harvester are obtained using Hamilton’s principle. Pressure acting in arteries is radially directed and this is used to simplify the governing equations. Specifically, radial pressure directed on the inner wall of the cylinder is assumed to excite only the radial breathing mode of vibration. Using this, the transfer function relating pressure to the induced voltage across the surface of the harvester is derived and the power harvested by the cylindrical harvester is obtained for different shunt resistances. However, the natural frequency of the radial breathing mode (RBM) is found to be very high and the harvested power at the frequencies of interest (3 Hz – 20 Hz) is very low. To decrease the natural frequency, we propose a novel streaked cylinder design that involves cutting the cylinder along the length, transforming it to a curved beam with an opening angle of 360 deg.. The governing equations corresponding to a circular curved beam, with PVDF patches on top and bottom surfaces, are derived using Hamilton’s principle and modal analysis is used to obtain the transfer function relating radial pressure to induced voltage. We validate the derived transfer function by evaluating the harvested power for a beam with very large radius of curvature; in which case, the curved beam becomes a straight beam and the harvested power is compared with the same for a straight beam (which exists in the literature). Further, we conduct design analyses and obtain the power as the geometric parameters of the harvester are varied for the purpose of optimizing the dimensions of harvester for maximal power generation. The power harvested by the harvester, at lower frequencies is deemed to be satisfactory.

The batteries of the current pacing devices are relatively large and occupy over 60 percent of the size of pulse generators. Therefore, they cannot be placed in the subtle areas of human body. In this paper, the mastication force and the resulting tooth pressure are converted to electricity. The pressure energy can be converted to electricity by using the piezoelectric effect. The tooth crown is used as a power autonomous pulse generator. We refer to this envisioned pulse generator as the smart tooth. The smart tooth is in the form of a dental implant. A piezoelectric vibration energy harvester is designed and modeled for this purpose. The Piezoelectric based energy harvesters investigated and analyzed in this paper initially includes a single degree of freedom piezoelectric based stack energy harvester which utilizes a harvesting circuit employing the case of a purely resistive circuit. The next step is utilizing and investigating a bimorph piezoelectric beam which is integrated/embedded in the smart tooth implant. Mastication process causes the bimorph beam to buckle or return to unbuckled condition. The transitions result in vibration of the piezoelectric beam and thus generate energy. The power estimated by the two mechanisms is in the order of hundreds of microwatts. Both scenarios of the energy harvesters are analytically modeled. The exact analytical solution of the piezoelectric beam energy harvester with Euler-Bernoulli beam assumptions is presented. The electro-mechanical coupling and the geometric nonlinearities have been included in the model for the piezoelectric beam.

A thermally buckled piezoelectric energy harvester is designed to power biomedical devices inside the body. The energy harvester (EN) uses the vibrations inside the body to generate the electricity needed for powering biomedical sensors and devices. The piezoelectric beam consists of a brass substrate and two piezoelectric patches attached to the top and the bottom of the substrate. The bimorph beam is inside a rigid frame. The bimorph beam is buckled due to the difference in the coefficient of the thermal expansion of the beam and the frame. Inside the body, most of the energy content come from the low-frequency vibrations (less than 50 Hz ). Having high natural frequency is a major problem in Microelectromechanical systems (MEMS) energy harvesters. Considering the small size of the EN, 1 cm 3 , the natural frequency is expected to be high. In our design, the natural frequency is lowered significantly by using a buckled beam. A mass is also used in the middle of the beam to decrease the natural frequency even more. Since the beam is buckled, the design is bistable and nonlinear which increases the output power. In this paper, the natural frequencies and mode shapes of the EN are analytically derived. The geometric nonlinearities are included in the electromechanical coupled governing equations. The governing equations are solved and it is shown that the device generates sufficient electricity to power biomedical sensors and devices inside the human body.

Embedded piezoelectric energy harvesting (PEH) systems in medical pacemakers have been an attractive and well visited research area. These systems typically utilize different configurations of beam structures with forcing originating from heart beat oscillations. The goal of these systems is to remove the pacemaker battery, which makes up 60–80% of the device volume, and replace it with a self-reliant power option. With emerging technologies encouraging a push towards leadless pacemakers typical energy harvesting beam structures are becoming inherently coupled with the heart system. The introduction of the nonlinearity resulting from the bistable magnetic interaction of two magnets is known to enhance energy harvesting performance due to its double-well potential behavior. Introducing the elastic magnifier enables large tip oscillations and high energy orbits for the bistable system. A continuous nonlinear model is derived for the bistable system (BPEH) and a one-degree-of-freedom linear mass-spring-damper model is derived for the elastic magnifier. The elastic magnifier (EM) will not consider the damping negligible due to the viscous nature of the heart, unlike most models. For experimental testing a physical model was created for the bistable structure and fashioned to an elastic magnifier. A hydrogel was chosen as the physical model for the EM. Experimental results have shown that the bistable piezoelectric energy harvester coupled with a linear elastic magnifier (BPEH+LEM) produces more power at certain input frequencies and operates a larger bandwidth than a PEH, BPEH, and a standard piezoelectric energy harvester with the elastic magnifier (PEH+LEM). Numerical simulations were validated by these results showing that this system enters high-energy and high orbit oscillations. It has been shown that BPEH systems implemented in medical pacemakers can have enhanced performance if positioned over the myocardial heart wall.

When there is a two to one internal resonance ratio between the natural frequencies of the pitch motion and the roll motion of a ship, a nonlinear energy transfer occurs between the modes. If the ship is excited near the pitch natural frequency and at a large enough excitation amplitude, the pitch mode transfers energy to the roll mode. We use this interesting phenomenon to develop a wave power device for off-shore purposes. In this paper, we experimentally show that we can use a horizontal pendulum and use the quadratic nonlinear coupling between the pitch and the roll mode to get full rotation of the pendulum inside the ship. A rotating pendulum will generate orders of magnitude more power than a locally oscillating one when connected to a DC generator. This article measures the angle of the pendulum at the pitch frequency excitation of the ship to experimentally confirm the expected theoretical results on this phenomenon.

This paper presents a method to utilize the pitch-roll nonlinear energy transfer phenomenon in vessels for off-shore wave power generation. This paper builds on an existing design where the power generator is a horizontal pendulum on board a vessel. The surface waves result in rocking of the ship, which in turn results in rotation of the pendulum. The pendulum is connected to a DC generator to produce power. The coupled electro-mechanical system is modeled using energy methods. The design in this paper utilizes the nonlinear coupling between the roll and pitch motions of the generator vessel. The natural frequency of the roll motion of the vessel is tuned to be twice the fundamental frequency of the pitch motion. In this specific condition when the vessel is excited in the pitch direction, the energy is nonlinearly transferred to the roll mode and the vessel oscillates in the roll direction. It is shown that the combination of the pitch as well as roll motion is far superior to the pitch motion since the combination results in full rotations of pendulum. A pendulum in full rotations generates orders of magnitude more power compared to a locally oscillating pendulum.

This paper investigates the spin resonance of a rattleback subjected to base oscillations. The phenomenon of Spin resonance can transduce vibrations to rotations. The rattleback is an ellipsoidal top with a preferred direction of spin. If rotated anti to it, longitudinal vibrations are set up and spin direction is reversed. Simulations and results are presented which show that the rattleback has a mono-peak spin resonance with respect to base vibrations. Two frequencies that appear in the response are identified — the Coupled and Uncoupled frequencies. Spin resonance, it is deduced, occurs when the base frequency is twice the coupled frequency of the rattleback. A linearized model is developed and a closed form expression for the Resonant frequency in terms of the inertia parameters of the rattleback is derived. Novel ideas for applications in Energy harvesting and Vibration sensing that utilize the phenomenon of spin resonance are also included.

A three dimensional piezoelectric vibration energy harvester is designed to generate electricity from heartbeat vibrations. The device consists of several bimorph piezoelectric beams stacked on top of each other. These horizontal bimorph beams are connected to each other by rigid vertical beams making a fan-folded geometry. One end of the design is clamped and the other end is free. One major problem in micro-scale piezoelectric energy harvesters is their high natural frequency. The same challenge is faced in development of a compact vibration energy harvester for the low frequency heartbeat vibrations. One way to decrease the natural frequency is to increase the length of the bimorph beam. This approach is not usually practical due to size limitations. By utilizing the fan-folded geometry, the natural frequency is decreased while the size constraints are observed. The required size limit of the energy harvester is 1 cm by 1 cm by 1 cm. In this paper, the natural frequencies and mode shapes of fan-folded energy harvesters are analytically derived. The electro-mechanical coupling has been included in the model for the piezoelectric beam. The design criteria for the device are discussed.

This paper presents vibration analysis and structural optimization of a self-assembled structure for swimming. The third mode shape of the structure in the longitudinal direction resembles the body waveform of a swimming eel fish. At the final destination, the box self-assembles using shape memory alloys. MFCs (Piezoelectric Micro Fiber Composites) are actuated at the fundamental natural frequency of the structure. This excites the primary mode of resonance. We optimize the thickness of the panels and the stiffness of the joints to most efficiently generate the swimming waveforms that resembles the body waveform of eel. Traveling wave is generated using two piezoelectric batches actuators bonded on the first and fourth segments of the beams in the longitudinal direction. Excitation of the piezoelectrics results in coupled system dynamics equations that can be translated into generation of waves. Theoretical analysis based on the distributed parameter model was conducted in this paper. A scalar measure of the traveling to standing wave ratio was created using 2-dimensional Fourier Transform of the wave form. The results then were compared to common method in the literature for assessment of standing to traveling wave ratio.

This paper uses the method of Quadratures in conjunction with the Maximum Entropy principle to investigate the effect of parametric uncertainties on the mean power output and root mean square deflection of piezoelectric vibrational energy harvesting systems. Uncertainty in parameters of harvesters could arise from insufficient manufacturing controls or change in material properties over time. We investigate bimorph based harvesters that transduce ambient vibrations to electricity via the piezoelectric effect. Three varieties of energy harvesters — Linear, Nonlinear monostable and Nonlinear bistable are considered in this research. This analysis quantitatively shows the probability density function for the mean power and root mean square deflection as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the bimorph and magnet gap of the energy harvester. The method of Quadratures is used for numerically integrating functions by propagating weighted points from the domain and evaluating the integral as a weighted sum of the function values. In this paper, the method of Quadratures is used for evaluating central moments of the distributions of rms deflection and mean harvested power and, then, in conjunction with the principle of Maximum Entropy (MaxEnt) an optimal density function is obtained which maximizes the entropy and satisfies the moment constraints. The The computed nonlinear density functions are validated against Monte Carlo simulations thereby demonstrating the efficiency of the approach. Further, the Maximum Entropy principle is widely applicable to uncertainty quantification of a wide range of dynamic systems.

A fan-folded piezoelectric energy harvester is designed to generate electricity using heartbeat vibrations. This energy harvester consists of several bimorph beams stacked on top of each other making a fan-folded shape. Each beam has a brass substrate and two piezoelectric patches attached on both sides of it. These beams are connected to each other by rigid beams. One end of the device is clamped to the wall and the other end is free to vibrate. A tip mass is placed at the free end to enhance the output power of the device and reduce the natural frequency of the system. High natural frequency is one major concern about the microscaled energy harvesters. The size for this energy harvester is 1 cm by 1 cm by 1 cm, which makes the natural frequency very high. By utilizing the fan-folded geometry and adding tip mass and link mass to the configuration, this natural frequency is reduced to the desired range. The generated electricity can be used to power up a pacemaker. If enough electricity is generated, the pacemaker operates without having a battery and the patient does not need to have a surgery every seven to ten years to have the battery replaced. The power needed for a pacemaker to operate is about 1 microwatt. In this paper, the natural frequencies and mode shapes of fan-folded energy harvesters with added tip mass and link mass are analytically derived. The electro-mechanical coupling has been included in the model and the expression for the multi-mode power frequency response function is calculated.

This paper presents the relation between uncertainty in the excitation and parameters of vibrational energy harvesting systems and their power output. Nonlinear vibrational energy harvesters are very sensitive to the frequency of the base excitation. If the excitation frequency does not match with the resonance frequency of the energy harvester, the power output significantly deteriorates. The mismatch can be due to the inherent changes of the ambient oscillations. The fabrication errors or gradual changes of material properties also result in the mismatch. This paper quantitatively shows the probability density function for the power as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the energy harvester, and design parameters. Recently developed the conjugated unscented transformation methodology is used in conjunction with the principle of maximum entropy to compute the probability distribution for the base response and power. The computed nonlinear density functions are validated against Monte Carlo simulations.

This work presents a model for energy harvesting characterization of a simply supported beam with a mass in the middle to be used for powering pacemakers from heartbeat vibrations. The required power for a typical pacemaker is about 1.0 microwatts. A uniform cross-section beam, bimorph structures, employing double piezoelectric layers is used. PSI-5H4E piezoelectric and brass substrate is used in this study. Different configurations are utilized to identify the optimal design for lightweight energy harvesting devices with low-power applications to tune the natural frequencies of the energy harvester towards the operating ambient vibration source. In this paper, the exact analytical solution of the piezoelectric beam energy harvester with Euler–Bernoulli beam assumptions is presented. The energy harvester is intended to generate power from heartbeat induced vibrations to power implantable cardiac devices. The base excitations are thus heartbeat induced tissue vibrations. The proposed configuration harvests energy from the reverberation of heartbeats and converts it to electricity and could generate about 0.22 microwatts of power. Using the Fourier transform, the frequency response function for the voltage; current and power of the harvester are obtained. The power output for a range of values for the resistive load connected to the bimorph PZT layers is investigated to determine the optimized value of the resistive load that gives the maximum power output for the corresponding configuration of the beam. Stress analysis is performed for the substrate and PZT layer to make sure that the stress are within the permissible values to avoid breaking or failing of the beam. Results show that the use of mid mass is capable of harvesting a significant power with the proposed configurations.