Fundamentals of Vibrations

Environmental and operational conditions effects on Lamb wave based structural health monitoring systems: A review

Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction.

http://iopscience.iop.org/article/10.1088/0964-1726/24/4/045042/pdf

Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction

This paper focuses on the transient nonlinear dynamics and targeted energy transfer (TET) of a Bernoulli–Euler beam coupled to a continuous bistable nonlinear energy sink (NES). This NES comprises a cantilever beam with the partial constrained layer damping (PCLD) and an end mass controlled by a nonlinear magnetostatic interaction force. The theoretical model of the nonlinear system is built based on the Lagrange equations and assumed-modes expansion method. A new parameter system damping ratio is proposed to evaluate the TET efficiencies. Impact experiments are carried out to verify the theoretical model and mechanisms. The results show that the bistable NES can achieve high and strongly robust TET efficiencies under broad-range impacts. The shear modulus of the viscoelastic layer, the length of the PCLD and the end mass have significant influences on TET efficiencies. Analyses of the TET mechanisms in the bistable NES show the following: steady transition of the stable state is an important reason for maintaining high TET efficiencies; nonlinear beatings can occur in high-frequency, fundamental and long-period subharmonic branches; and resonance captures featuring fundamental and subharmonic also help achieve rapid energy dissipation.

Highly efficient continuous bistable nonlinear energy sink composed of a cantilever beam with partial constrained layer damping

Fatigue in piezoelectric ceramic vibrational energy harvesting: A review

Piezoelectric energy harvesting has attracted extensive research in the advancement of new designs and techniques over the last decade. The cantilever shaped piezoelectric energy harvesting beam is one of the most employed designs, due to its simplicity and flexibility for further performance enhancement. The strain distribution along the cantilever piezoelectric energy harvesting beam is nonuniform, which would induce fatigue damage at the root of the cantilever on the long run. This particular issue has seldom been addressed in the literature. This article presents an experimental investigation on the fatigue behavior of a cantilever piezoelectric energy harvesting beam at different base excitation levels. The experimental study is augmented with analytical formulation to examine the strain levels and with finite element analysis formulation to model the piezoelectric energy harvesting beam with a macro fiber composite piezoelectric transducer. A two-dimensional model is developed based on the three-dim...

Long-term fatigue behavior of a cantilever piezoelectric energy harvester

The need for long-term solutions to power various wireless sensor systems has been driving the research in the area of energy harvesting for the past decade. The present paper brings forth an investigation into the realm of piezoelectric energy harvesting (PEH) using nonlinear vibrations. A piezoelectric cantilever beam with a magnetic tip mass interacting with additional magnets around it forms a multi-stable nonlinear PEH configuration. The study indicates that the multistable configuration provides a widened bandwidth as compared to the conventional linear PEH devices and an increased voltage output as compared to many other PEH devices. An experimental parametric study is conducted to arrive at an optimal configuration for the performance enhancement of the harvester along with a glimpse into the enhanced magnetostatic interactions equations and various possible magnetic nonlinear configurations for the given conditions.

/pdf/enhancement-of-piezoelectric-energy-harvesting-with-multi-7q7r1i40wa.pdf

Enhancement of piezoelectric energy harvesting with multi-stable nonlinear vibrations

Lamb wave based Structural Health Monitoring (SHM) has received much attention during the past decades for its broad coverage and high sensitivity to damage. Lamb waves can be used to locate and quantify damage in static structures successfully. Nonetheless, structures are usually subjected to various external vibrations or oscillations. Not many studies are reported in the literature concerning the damage detecting ability of Lamb wave in oscillating structures which turns out to be a pivotal issue in the practical application of the SHM technique. For this reason in this study, the propagating capability of Lamb waves in a vibrating thin aluminum plate is examined experimentally. Two circular shaped piezoelectric wafer active transducers are surface-bonded on the aluminum plate where one acted as an actuator and another as a sensor. An arbitrary waveform generator is connected to the actuator for the generation of a windowed tone burst on the aluminum plate. An oscilloscope is connected to the sensor for receiving the traveled waves. An external shaker is used to generate out-of-plane external vibration on the plate structure. Time of flight (TOF) is a crucial parameter in most Lamb wave based SHM studies, which measures wave traveling time from the actuator to sensor. In the present study the influence of the external vibrations on the TOF is investigated. Experiments are performed under different boundary conditions of the plate, such as free-free and fixed by gluing. The effects of external vibrations in the frequency range between 10 Hz to 1000 Hz are analyzed. Comparisons are carried out between the resulting Lamb wave signals from the vibrating plate for different boundary conditions. Experimental results show that the external vibrations in relatively low frequency range do not change the TOF during the application of Lamb wave based SHM.

https://dr.ntu.edu.sg/bitstream/10356/88759/1/Lamb%20wave%20propagation%20in%20vibrating%20structures%20for%20effective%20health%20monitoring.pdf

Lamb wave propagation in vibrating structures for effective health monitoring

Vibration energy harvesting using piezoelectric material has received great research interest in the recent years. To enhance the performance of piezoelectric energy harvesters, one important concern is to increase their operating bandwidth. Various techniques have been proposed for broadband energy harvesting, such as the resonance tuning approach, the frequency up-conversion technique, the multi-modal harvesting and the nonlinear technique. Usually, a nonlinear piezoelectric energy harvester can be easily developed by introducing a magnetic field. Either mono-stable or bi-stable response can be achieved using different magnetic configurations. However, most of the research work for nonlinear piezoelectric energy harvesting has focused on the SDOF cantilever beam. A recently reported linear 2-DOF harvester can achieve two close resonant frequencies with significant power outputs. However, for this linear configuration, although a broader bandwidth can be achieved, there exists a deep valley in-between the two response peaks. The presence of the valley will greatly deteriorate the performance of the energy harvester. To overcome this limitation, a nonlinear 2-DOF piezoelectric energy harvester is proposed in this article. This nonlinear harvester is developed from its linear counterpart by incorporating a magnetic field using a pair of magnets. Experimental parametric study is carried out to investigate the behavior of such harvester. With different configurations, both mono-stable and bi-stable behaviors are observed and studied. An optimal configuration of the nonlinear harvester is thus obtained, which can achieve significantly wider bandwidth than the linear 2-DOF harvester and at the same time overcome its limitation.

/pdf/broadband-energy-harvesting-using-nonlinear-2-dof-4d053fl524.pdf

Broadband energy harvesting using nonlinear 2-DOF configuration

Over the last decade, cantilever energy harvesters gained immense popularity owing to the simplicity of the design and piezoelectric energy harvesting (PEH) using the cantilever design has undergone considerable evolution. The major drawback of a vibrating cantilever beam is its vulnerability to fatigue over a period of time. This article brings forth an experimental investigation into the phenomenon of fatigue of a PEH cantilever beam. As there has been very little literature reported in this area, an effort has been made to scrutinize the damage due to fatigue in a linear vibrating cantilever PEH beam consisting of an aluminum substrate with a piezoelectric macro-fiber composite (MFC) patch attached near the root of the beam and a tip mass attached to the beam. The beam was subjected to transverse vibrations and the behavior of the open circuit voltage was recorded with passing time. Moreover, electro-mechanical admittance readings were obtained periodically using the same MFC patch as a Structural health monitoring (SHM) sensor to assess the health of the PEH beam. The results show that with passing time the PEH beam underwent fatigue in both the substrate and MFC, which is observed in a complimentary trend in the voltage and admittance readings. The claim is further supported using the variation of root mean square deviation (RMSD) of the real part of admittance (conductance) readings. Thus, this study concludes that the fatigue issue should be addressed in the design of PEH for long term vibration energy harvesting.

https://dr.ntu.edu.sg/bitstream/10356/88618/1/Experimental%20investigation%20of%20fatigue%20in%20a%20cantilever%20energy%20harvesting%20beam.pdf

Panduranga Vittal Avvari

Papers

Long-term fatigue behavior of a cantilever piezoelectric energy harvester

Enhancement of piezoelectric energy harvesting with multi-stable nonlinear vibrations

Lamb wave propagation in vibrating structures for effective health monitoring

Broadband energy harvesting using nonlinear 2-DOF configuration

Experimental investigation of fatigue in a cantilever energy harvesting beam