Thin Cantilever Beam Research Articles

An arc-shaped piezoelectric generator for multi-directional wind energy harvesting

In this study, a piezoelectric wind energy harvester was demonstrated, which aimed at addressing the limitations of the existing approaches including single-directional operation and narrow working wind speed range. In the harvester, an arc-shaped elastic beam, instead of conventional thin cantilever beams, was adopted to extract wind energy. Benefiting from the beam’s characteristics of arc-shaped structure and elasticity, the harvester is capable of scavenging wind energy without any extra accessory and responding to multi-directional wind excitations. An analytical model was established to investigate the effects of wind direction and structural parameters on the electrical output. In test, the harvester worked efficiently with wind coming from four directions in a speed range of 2–17m/s and produced a maximum open-circuit voltage up to 34V. When connected to an external load of 15kΩ, the harvester showed a peak output power of 1.73mW at 17m/s. In addition, 18 serial-connected commercial light-emitting diodes (LEDs) were lit up simultaneously at the wind speed of 10.5m/s, which confirmed the practicability of the harvester.

Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations

This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.

3D, wideband vibro-impacting-based piezoelectric energy harvester

An impacting-based piezoelectric energy harvester was developed to address the limitations of the existing approaches in single-dimensional operation as well as a narrow working bandwidth. In the harvester, a spiral cylindrical spring rather than the conventional thin cantilever beam was utilized to extract the external vibration with arbitrary directions, which has the capability to impact the surrounding piezoelectric beams to generate electricity. And the introduced vibro-impacting between the spiral cylindrical spring and multi-piezoelectric-beams resulted in not only a three-dimensional response to external vibration, but also a bandwidth-broadening behavior. The experimental results showed that each piezoelectric beam exhibited a maximum bandwidth of 8 Hz and power of 41 μW with acceleration of 1 g (with g=9.8 ms−2) along the z-axis, and corresponding average values of 5 Hz and 45 μW with acceleration of 0.6 g in the x-y plane.

Energy harvesting prospects in turbulent boundary layers by using piezoelectric transduction

Thin flexible cantilever beams with patches of piezoelectric materials or surrogate beams with attached strain gages have been electromechanically characterized for energy harvesting inside turbulent boundary layers. A turbulent boundary layer carries mechanical energy distributed over a range of temporal and spatial scales and their interaction with the immersed piezoelectric beams results in a strain field which generates the electrical charge. This energy harvesting method can be used for developing self-powered electronic devices such as flow sensors. In the present experimental work, various energy harvesters were placed in the boundary layers of a large scale wind tunnel with Reθ between 2000 and 7500. The orientation of the beam relatively to the incoming flow and the wall was found to be critical parameters affecting the energy output. “Power maps” are presented for various roll and pitch angles as well as external flow velocities. The role of large instantaneous turbulent boundary layer structures in this rather complex fluid–structure interaction is discussed in interpreting the electrical output results. The forces acting on the vibrating beams have been measured dynamically and a theory has been developed which incorporates the effects of mean local velocity, turbulence intensity, the relative size of the beam׳s length to the integral length scale of turbulence, the structural properties of the beam and the electrical properties of the active piezoelectric layer to provide reasonable estimates of the mean electrical power output.

Design and optimization of a bi-axial vibration-driven electromagnetic generator

To scavenge energy from ambient vibrations with arbitrary in-plane motion directions and over a wide frequency range, a novel electromagnetic vibration energy harvester is designed and optimized. In the harvester, a circular cross-section elastic rod, not a traditional thin cantilever beam, is used to extract ambient vibration energy because of its capability to collect vibration from arbitrary in-plane motion directions. The magnetic interaction between magnets and the iron core contributes to a nonlinear oscillation of the rod with increased frequency bandwidth. The influences of the structure configurations on the electrical output and the working bandwidth of the harvester are investigated using Ansoft's Maxwell 3D to achieve optimal performance. The experimental results show that the harvester is sensitive to vibrations from arbitrary in-plane directions and it exhibits a bandwidth of 5.7 Hz and a maximum power of 13.4 mW at an acceleration of 0.6 g (with g = 9.8 ms−2).

On the flexural vibrations of generalized thermo-elasto-diffusive thin cantilever beam

The flexural vibrations in a homogenous isotropic, thermoelastic-diffusive thin cantilever beam have been analyzed in closed form based on the Euler–Bernoulli theory. The analytical expressions for deflection, thermal moment, mass moment, frequency shift and thermoelastic-diffusive damping (inverse quality factor) have been obtained for clamped-free (cantilever) beam. It is found that the thermoelastic-diffusive damping and frequency shift of beam vibrations significantly depend on diffusive properties. The analytical results have been analyzed numerically with the help of MATLAB software. The values of effective flexural rigidity have also been computed and presented in tabular form. The numerical computed results have been presented graphically. This study may be useful in the design and construction of sensors, gyrometers, charge detectors, radio frequency filters, communicators and energy harvesters etc due to mass concentration change in the materials.

Porous LSCF/dense 3YSZ interface fracture toughness measured by single cantilever beam wedge test

Sandwich specimens were prepared by firing a thin inter-layer of porous La0.6Sr0.4Co0.2Fe0.8O3-d (LSCF) to bond a thin tetragonal yttria-stabilised zirconia (YSZ) beam to a thick YSZ substrate. Fracture of the joint was evaluated by introducing a wedge between the two YSZ adherands so that the stored energy in the thin YSZ cantilever beam drives a stable crack in the adhesive bond and allows the critical energy release rate for crack extension (fracture toughness) to be measured. The crack path in most specimens showed a mixture of adhesive failure (at the YSZ-LSCF interface) and cohesive failure (within the LSCF). It was found that the extent of adhesive fracture increased with firing temperature and decreased with LSCF layer thickness. The adhesive failures were mainly at the interface between the LSCF and the thin YSZ beam and FEM modelling revealed that this is due to asymmetric stresses in the LSCF. Within the firing temperature range of 1000-1150C, the bonding fracture toughness appears to have a strong dependence on firing temperature. However, the intrinsic adhesive fracture toughness of the LSCF/YSZ interface was estimated to be 11 Jm2 and was not firing temperature dependent within the temperature range investigated.

Efficiency Enhancement of a Cantilever-Based Vibration Energy Harvester

Extracting energy from ambient vibration to power wireless sensor nodes has been an attractive area of research, particularly in the automotive monitoring field. This article reports the design, analysis and testing of a vibration energy harvesting device based on a miniature asymmetric air-spaced cantilever. The developed design offers high power density, and delivers electric power that is sufficient to support most wireless sensor nodes for structural health monitoring (SHM) applications. The optimized design underwent three evolutionary steps, starting from a simple cantilever design, going through an air-spaced cantilever, and ending up with an optimized air-spaced geometry with boosted power density level. Finite Element Analysis (FEA) was used as an initial tool to compare the three geometries' stiffness (K), output open-circuit voltage (Vave), and average normal strain in the piezoelectric transducer (εave) that directly affect its output voltage. Experimental tests were also carried out in order to examine the energy harvesting level in each of the three designs. The experimental results show how to boost the power output level in a thin air-spaced cantilever beam for energy within the same space envelope. The developed thin air-spaced cantilever (8.37 cm3), has a maximum power output of 2.05 mW (H = 29.29 μJ/cycle).

A two-dimensional broadband vibration energy harvester using magnetoelectric transducer

In this study, a magnetoelectric vibration energy harvester was demonstrated, which aims at addressing the limitations of the existing approaches in single dimensional operation with narrow working bandwidth. A circular cross-section cantilever rod, not a conventional thin cantilever beam, was adopted to extract vibration energy in arbitrary in-plane motion directions. The magnetic interaction not only resulted in a nonlinear motion of the rod with increased frequency bandwidth, but also contributed to a multi-mode motion to exhibit double power peaks. In energy harvesting with in-plane directions, it showed a maximum bandwidth of 4.4 Hz and power of 0.59 mW, with acceleration of 0.6 g (with g = 9.8 m s−2).

Piezoceramic d15shear-induced direct torsion actuation mechanism: a new representative experimental benchmark

A new piezoceramic <TEX>$d_{15}$</TEX> shear-induced torsion actuation mechanism representative benchmark is proposed and its experimentations and corresponding 3D finite element (FE) simulations are conducted. For this purpose, a long and thin smart sandwich cantilever beam is dimensioned and built so that it can be used later for either validating analytical Saint Venant-type solutions or for analyzing arm or blade-based smart structures and systems applications. The sandwich beam core is formed by two adjacent rows of 8 oppositely axially polarized d15 shear piezoceramic patches, and its faces are dimensionally identical and made of the same glass fiber reinforced polymer composite material. Quasi-static and static experimentations were made using a point laser sensor and a scanning laser vibrometer, while the 3D FE simulations were conducted using the commercial software <TEX>$ABAQUS^{(R)}$</TEX>. The measured transverse deflection by both sensors showed strong nonlinear and hysteretic (static only) variation with the actuation voltage, which cannot be caught by the linear 3D FE simulations.

A quasi-modal approach to overcome FBG limitations in vibration control of smart structures

Embedding FBG sensors in carbon fiber structures is a very attractive procedure, due to the small fiber cross section and to the possibility of manufacturing arrays of many gratings into a single optical fiber. This embedding is particularly useful for the manufacturing of smart structures, enabling improvement of their characteristics thanks to the embedded sensors and actuators. However, the low precision of FBG measurements makes the effectiveness of such signals in control applications limited. This paper deals with the possibility of reducing vibrations in structures by using distributed sensors embedded in carbon fiber structures through the so-called sensor-averaging technique. This method provides a properly weighted average of the outputs of a distributed array of sensors generating spatial filters on a broad range of undesired resonance modes without adversely affecting phase and amplitude. This approach combines the positive aspects of decentralized control techniques, because the control forces applied to the system are independent, with, as for centralized controls, the possibility of exploiting the information from all the sensors. Theoretical aspects are supported by experimental applications on a large flexible system composed by a thin cantilever beam with 30 longitudinal FBG sensors and six piezoelectric actuators (PZT).

Effect of the root crack on the lateral buckling loads and natural frequencies of sandwich composite beams

This study aims to examine the effect of interfacial root crack on the lateral buckling and free vibration responses of a sandwich composite beam experimentally and numerically. Lateral buckling loads and natural frequencies in a thin sandwich composite cantilever beam with root crack are determined. The crack with various lengths is opened between the face sheet and foam core, such as 50, 100, 150 and 200mm. Lateral buckling and free vibration tests of these samples are carried out. For the numerical analysis, ANSYS finite element software is used. Results obtained by numerical analyses and experiments are compared and it is seen that there is a good agreement between them.

Effect of the root crack on natural frequencies of sandwich composite beams

This study aims to examine the effect of interface crack on the free vibration response of a sandwich composite beam experimentally and numerically. Natural frequencies in a thin sandwich composite cantilever beam with root crack are determined. The crack with various lengths is opened between the face sheet and foam core, such as 50, 100, 150 and 200 mm. Free vibration tests of these samples are carried out. For the numerical analysis, ANSYS finite element software is used. Results obtained by numerical analyses and experiments are compared and it is seen that there is a good agreement between them.

Effect of interface crack on lateral buckling behavior and free vibration response of a sandwich composite beam

The aim of this study is investigation of the effect of interface crack on lateral buckling load and free vibration response of a sandwich composite beam using experimental methods and finite element solutions. The lateral buckling load and natural frequencies in a thin sandwich composite cantilever beam with crack were considered. The crack was opened between the face sheets and foam core. The length of the crack was selected, such as 100, 150, 200, and 250 mm. Lateral buckling and vibration tests were applied on these samples and then the critical lateral buckling load and natural frequencies were found using experimental and finite element method. In the experimental studies, in-house test mechanisms were used. For the numerical analysis, ANSYS finite element software was used. Close results were obtained between both two methods.

Forced vibrations of a cantilever beam

The theoretical and experimental solutions for vibrations of a vertical-oriented, prismatic, thin cantilever beam are studied. The beam orientation is ‘downwards’, i.e. the clamped end is above the free end, and it is subjected to a transverse movement at a selected frequency. Both the behaviour of the device driver and the beam's weak-damping resonance response are compared for thecase of an elastic beam made from PVC plastic excited over a frequency range from 1 to 30 Hz. The current analysis predicts the presence of ‘pseudo-nodes’ in the normal modes of oscillation. It is important to note that our results were obtained using very simple equipment, present in the teaching laboratory.

Strain microgauge implementation on cylindrical metal substrates

This work mainly focuses on the development of germanium-based thin-film piezoresistive strain gauges on thin NiTi and stainless steel cylinders. These microgauges enable the real-time measurement of the cylinder's strain distribution from which its deflection status can be deduced, based on an analytical mechanical model of thin cantilever beams. The adaptation of thin cylinders to typical micromachining equipment requires several adjustments in preparation works. The fabrication process of germanium microgauges also has to be adjusted according to the particularities of metal substrates. A number of polycrystalline germanium strain microgauges of various dimensions are implemented on thin cylinders. The results of the fabrication process are presented. The existing constraints of the current process and the potential improvement measures are then discussed.

Comparison of Control Laws for Vibration Suppression Based on Energy Consumption

The research study presented here examines four conventional vibration suppression control laws and four hybrid modifications of these laws using a switching method. The motivation is to determine which of these eight controllers results in the least amount of power flow to the actuator to have the same settling time under free vibrations. The reason to look at reduced energy controllers is the idea that in some applications, very little energy is available for control, yet passive and semi-active methods cannot meet performance demands. In particular, the eventual goal is to reduce transient vibrations of smart structures using energy obtained from harvesting and/or low-power storage devices (batteries or super capacitors), as often desirable in aerospace systems. The four conventional active control systems compared in this study are Positive Position Feedback (PPF) control, Proportional Integral Derivative (PID) control, non-linear control, and Linear Quadratic Regulator (LQR) controls. A hybrid version of each controller is obtained by implementing a bang-bang control law (on-off control). The bang-bang control algorithm switches the control voltage between an external voltage supply and the feedback signal provided by the PPF, PID, non-linear, or LQR controllers. The purpose of combining the bang-bang control law with the aforementioned controllers is to reduce the power requirement for vibration suppression by providing an active controller with limited voltage input. Free vibrations of a thin cantilevered beam with a piezoceramic transducer are controlled by these eight controllers with a focus on the fundamental transverse vibration mode. Experimental results exhibit that the system with hybrid bang-bang-non-linear controller requires 67.3% less power than its conventional version. The hybrid versions require significantly less power flow compared to their conventional counterparts for the PPF, PID, and LQR controllers as well. Experiments also reveal the presence of substantial piezoelectric non-linearities in the transducer. The voltage-dependent behavior of the electromechanical coupling coefficient is identified empirically and represented by a curve-fit expression. A real-time adaptive control algorithm is developed to account for the voltage-dependent behavior of the coupling coefficient, enabling good agreement between the simulation and experimental results.

조합공진 영역에서 감쇠의 영향을 고려한 비선형 진동 응답 특성

Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.

Shape Memory Alloy-Piezoelectric Active Structures for Reversible Actuation of Bistable Composites

A study was conducted to introduce an actuation mechanism, called shape memory alloy-piezoelectric active structures (SMAPAS) that combined the advantages of the piezoelectric shape memory alloy (SMA) materials to achieve self-resetting bistable composites. The approach used piezoelectric actuation to provide a rapid snap-through with significant degree of control and a relatively slow, but high-strain SMA actuation to reverse the state change. A thin cantilever beam of carbon-fiber or epoxy material was used to demonstrate the two-way actuation. The composite lay-up procedure was a standard method for the manufacturing of carbon laminates through a standard cure cycle to a maximum cure temperature of 125°C and a pressure of 85 psi. A macrofiber composite piezoelectric actuator was used to conduct the investigations and it consisted of aligned piezoelectric fibers with an interdigitated electrode to direct the applied electric field along the fiber length.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 ≪ H ≪ E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.