Bending Resonance Frequency Research Articles

Strength, elasticity and the limits of energy dissipation in two related sea urchin spines with biomimetic potential

The calcitic spines of the sea urchins Heterocentrotus mamillatus and H. trigonarius are promising role models for lightweight applications, bone tissue scaffolds and energy dissipating processes due to their highly porous and organized structure. Therefore, mechanical properties including Young’s Modulus, strength, failure behaviour and energy dissipation efficiency have been investigated in depth with uniaxial compression experiments, 3-point bending tests and resonance frequency damping analysis. It was found that despite a very similar structure, H. trigonarius has a significantly lower porosity than H. mamillatus leading to a higher strength and Young’s Moduli, but limited ability to dissipate energy. In order to show reliable energy dissipation during failure in uniaxial compression, a transition porosity of 0.55–0.6 needs to be exceeded. The most effective structure for this purpose is a homogeneous, foam-like structure confined by a thin and dense shell that increases initial strength and was found in numerous spines of H. mamillatus. Sharp porosity changes induced by dense growth layers or prominent wedges of the spines’ radiating building principle act as structural weaknesses, along which large flakes can be spalled, reducing the energy dissipation efficiency considerably.The high strength and Young’s Modulus at the biologically necessary high porosity levels of the spines is useful for Heterocentrotus and their construction therefore remains to be a good example of biomimetics. However, the energy dissipative failure behaviour may be regarded as a mere side effect of the structure.

Nonlinear magnetoelectric effect in unsymmetric laminated composites

This work is aimed at the development of a finite element formulation for the analysis of unsymmetric magneto-electric (ME) laminated structures. While analytical solutions are readily available for symmetric structures, the coupling between axial and bending deformations in unsymmetric structures impedes such an analytical solution thus motivating the search for a numerical solution. The proposed finite element model includes this coupling under Euler–Bernoulli assumptions and further includes the material nonlinearity exhibited by the ferromagnetic phase. The enhancement of the ME coefficient under resonant conditions has also been studied under bending and axial resonant regimes. Resonant ME coefficients of magnitude at least 30 times higher than the quasi-static values were estimated. A parametric study has also been performed with the aim of optimizing the ME coefficient with respect to the applied DC bias field, operating frequency, volume fraction and the modulus ratio of the constituents and the different boundary conditions. The boundary conditions yielding a cantilever configuration were found to offer the least bending resonant frequency and the highest axial resonant ME coefficient, thus proving to be the most viable in practice.

Mass detection in nanobeams from bending resonant frequency shifts

Abstract Nanobeams are frequently used as vibration based-sensors to detect mass changes caused, for instance, by attachment of foreign atoms/molecules or chemical/molecular absorption. This paper deals with the bending vibration of a uniform nanobeam carrying a single point mass (direct problem) as well as the identification of the attached mass (inverse problem). The nanobeam is described using the modified strain energy theory adapted to the Euler-Bernoulli beam model, and the natural vibration frequencies have been obtained. Under the assumption of small intensity of the concentrated mass, a solution of the inverse problem based on the measurement of the mass-induced shifts in the first two eigenfrequencies is proposed. Both the cases of simply supported and cantilever end conditions are discussed in detail. The theoretical method is verified by numerical simulation and numerical tests agree well with analytical results.

Magnetoelectric metglas/bidomain y + 140°-cut lithium niobate composite for sensing fT magnetic fields

We investigated the magnetoelectric properties of a new laminate composite material based on y + 140°-cut congruent lithium niobate piezoelectric plates with an antiparallel polarized “head-to-head” bidomain structure and metglas used as a magnetostrictive layer. A series of bidomain lithium niobate crystals were prepared by annealing under conditions of Li2O outdiffusion from LiNbO3 with a resultant growth of an inversion domain. The measured quasi-static magnetoelectric coupling coefficient achieved |αE31| = 1.9 V·(cm Oe)−1. At a bending resonance frequency of 6862 Hz, we found a giant |αE31| value up to 1704 V·(cm Oe)−1. Furthermore, the equivalent magnetic noise spectral density of the investigated composite material was only 92 fT/Hz1/2, a record value for such a low operation frequency. The magnetic-field detection limit of the laminated composite was found to be as low as 200 fT in direct measurements without any additional shielding from external noises.

A Concept of Thermographic Method for Non-Destructive Testing of Polymeric Composite Structures Using Self-Heating Effect.

Traditional techniques of active thermography require an external source of energy used for excitation, usually in the form of high power lamps or ultrasonic devices. In this paper, the author presents an alternative approach based on the self-heating effect observable in polymer-based structures during cyclic loading. The presented approach is based on, firstly, determination of bending resonance frequencies of a tested structure, and then, on excitation of a structure with a multi-harmonic signal constructed from the harmonics with frequencies of determined resonances. Following this, heating-up of a tested structure occurs in the location of stress concentration and mechanical energy dissipation due to the viscoelastic response of a structure. By applying multi-harmonic signal, one ensures coverage of the structure by such heated regions. The concept is verified experimentally on artificially damaged composite specimens. The results demonstrate the presented approach and indicate its potential, especially when traditional methods of excitation with an external structure for thermographic inspection cannot be applied.

Experimental investigation into the mechanism of the polygonal wear of electric locomotive wheels

ABSTRACTExperiments were conducted at field sites to investigate the mechanism of the polygonal wear of electric locomotive wheels. The polygonal wear rule of electric locomotive wheels was obtained. Moreover, two on-track tests have been carried out to investigate the vibration characteristics of the electric locomotive's key components. The measurement results of wheels out-of-round show that most electric locomotive wheels exhibit polygonal wear. The main centre wavelength in the 1/3 octave bands is 200 mm and/or 160 mm. The test results of vibration characteristics indicate that the dominating frequency of the vertical acceleration measured on the axle box is approximately equal to the passing frequency of a polygonal wheel, and does not vary with the locomotive speed during the acceleration course. The wheelset modal analysis using the finite element method (FEM) indicates that the first bending resonant frequency of the wheelset is quite close to the main vibration frequency of the axle box. The FEM results are verified by the experimental modal analysis of the wheelset. Moreover, different plans were designed to verify whether the braking system and the locomotive's adhesion control have significant influence on the wheel polygon or not. The test results indicate that they are not responsible for the initiation of the wheel polygon. The first bending resonance of the wheelset is easy to be excited in the locomotive operation and it is the root cause of wheel polygon with centre wavelength of 200 mm in the 1/3 octave bands.

A novel piezoelectric actuator with two operating modes

A novel piezoelectric actuator with two operating modes is proposed and tested in this work, whose unique feature is that it has different mechanical output performances under two bending resonance frequencies. The proposed actuator is fabricated by bonded eight pieces of lead zirconate titanate ceramic plates on an aluminum alloy beam symmetrically. When the ceramic plates are excited by signals with resonance frequency of the first bending mode of the actuator, two bending vibrations will be superimposed to form elliptical movements on the two driving tips, which is the first operating mode. The other operating mode can be realized easily by changing the working frequency to the second bending mode of the actuator. These two operating modes are calculated and compared in detail. The prototype achieves a maximum no-load speed of 171 mm/s and maximum thrust force of 0.6 N using the first operating mode, whereas these two values are increased to be about 208 mm/s and 0.76 N under the second operating mode. The weight of the proposed piezoelectric actuator is about 17.7 g, and the maximum force weight ratio is tested to be about 42.9 N/kg.

Ride comfort enhancement in railway vehicle by the reduction of the car body structural flexural vibration

The paper approaches the issue of reduction in the vertical bending vibrations of the railway vehicle carbody and the ride comfort enhancement at high velocities, starting from the prospect of isolating the vibrations by the best possible selection of the passive suspension damping in the vehicle. To this purpose, the examination falls on the influence of the vertical suspension damping upon the vibrations regime of the vehicle at the bending resonance frequency and upon the ride comfort. The results of the numerical simulations regarding the frequency response of the carbody acceleration and the comfort index will be therefore used. A value of the secondary suspension damping can be thus identified that will provide the best ride comfort performance. Similarly, the ride comfort can be increased by raising the primary suspension damping ratio.

Multi-Field Analysis and Experimental Verification on Piezoelectric Valve-Less Pumps Actuated by Centrifugal Force

A piezoelectric centrifugal pump was developed previously to overcome the low frequency responses of piezoelectric pumps with check valves and liquid reflux of conventional valveless piezoelectric pumps. However, the electro-mechanical-fluidic analysis on this pump has not been done. Therefore, multi-field analysis and experimental verification on piezoelectrically actuated centrifugal valveless pumps are conducted for liquid transport applications. The valveless pump consists of two piezoelectric sheets and a metal tube with piezoelectric elements pushing the metal tube to swing at the first bending resonant frequency. The centrifugal force generated by the swinging motion will force the liquid out of the metal tube. The governing equations for the solid and fluid domains are established, and the coupling relations of the mechanical, electrical and fluid fields are described. The bending resonant frequency and bending mode in solid domain are discussed, and the liquid flow rate, velocity profile, and gauge pressure are investigated in fluid domain. The working frequency and flow rate concerning different components sizes are analyzed and verified through experiments to guide the pump design. A fabricated prototype with an outer diameter of 2.2 mm and a length of 80 mm produced the largest flow rate of 13.8 mL/min at backpressure of 0.8 kPa with driving voltage of 80 Vpp. By solving the electro-mechanical-fluidic coupling problem, the model developed can provide theoretical guidance on the optimization of centrifugal valveless pump characters.

Thermal-Mechanical Noise in Resonant Thin-Film Magnetoelectric Sensors

Thin-film magnetoelectric sensors, i.e., composites of magnetostrictive and piezoelectric materials, are able to measure very low magnetic flux densities in the picotesla range. In order to further improve the limit of detection it is of high importance to understand and quantify the relevant noise sources. In this paper, a common model for the deflection noise in vibrational structures is applied to the cantilever structure of resonant magnetoelectric sensors. By means of deflection and noise measurements the existence of thermal-mechanical noise even in sensor structures with a size in the centimeter range is proven. Based on these findings a noise equivalent circuit is suggested which allows not only the distinction between the impact of different sensor-intrinsic noise sources and also the involvement of the preamplifier noise. We found that the thermal-mechanical noise is the dominant noise source if direct signal detection is performed at the first bending resonance frequency of the sensor. However, this kind of noise is not the limiting influence when applying magnetic frequency-conversion techniques.

Biomechanical Assessment for Healing Progression of Fractured Long Bones: Numerical Investigations of Bending Stiffness and Resonant Frequency

Though biomechanical methods have been proposed to assess the healing status of fractured bones for more than two decades, the effective stiffnesses obtained theoretically never match the experimentally measured results for the healing progression. This paper proposed a novel numerical model, the simulation results of which are able to reflect the experimental observations. The callus is divided into 10 regions with different material properties and the gap-narrowing process of the fracture is simulated with the variations of the material properties during the healing progression. The variations of the effective bending stiffness and resonant frequency with the healing progression have been obtained. The bending stiffness and resonant frequency squared of the fractured bone show a substantial creeping part during gradual narrowing of the fracture gap. They start to increase rapidly during bridging of the fracture gap by a bony callus. When the Young’s modulus in the callus region calcified last (i.e., Region 10) reaches 5% that of the reference intact bone, the bending stiffness and resonant frequency squared rise up to 90% those of the reference intact bone. After that they increase slowly and get flat; they become less sensitive to bone growth in the late healing stages. It is the first time that the simulation results demonstrate three distinct stages like in the experimentally measured results. These results imply that the variations of the bending stiffness and resonant frequency squared are not linearly correlated with the healing progression; however, their fast growing phase does indicate bony bridging of the callus.

Effects on the torsional vibration behavior in the investigation of dental implant osseointegration using resonance frequency analysis: a numerical approach.

Resonance frequency analysis (RFA) methods are widely used to assess implant stability, particularly the Osstell® device. The potential effects associated with this method have been discussed in the literature. Torsional RFA (T-RFA), mentioned in our previous study, could represent a new measurement method. The purpose of this study was to simulate T-shaped and Osstell® transducer-implant-bone system models; compare their vibration modes and corresponding resonance frequencies; and investigate the effects of their parameters, such as the effective implant length (EIL), bone quality, and osseointegration level, on the torsional resonance frequency (TRF) and bending resonance frequency (BRF) using three-dimensional finite element analysis. Following the finite element model validation, the TRFs and BRFs for three different EILs and four types of bone quality were obtained, and the change rates during 25 degrees of osseointegration were observed. The analysis showed that an increase in the EIL and a decrease in bone quality have less effect on the declination rate of TRFs than on that of BRFs. TRFs are highly sensitive to the stiffness of the implant-bone interface during the healing period. It was concluded that T-RFA has better sensitivity and specificity.

Bio-Inspired Miniature Direction Finding Acoustic Sensor.

A narrowband MEMS direction finding sensor has been developed based on the mechanically coupled ears of the Ormia Ochracea fly. The sensor consists of two wings coupled at the middle and attached to a substrate using two legs. The sensor operates at its bending resonance frequency and has cosine directional characteristics similar to that of a pressure gradient microphone. Thus, the directional response of the sensor is symmetric about the normal axis making the determination of the direction ambiguous. To overcome this shortcoming two sensors were assembled with a canted angle similar to that employed in radar bearing locators. The outputs of two sensors were processed together allowing direction finding with no requirement of knowing the incident sound pressure level. At the bending resonant frequency of the sensors (1.69 kHz) an output voltage of about 25 V/Pa was measured. The angle uncertainty of the bearing of sound ranged from less than 0.3° close to the normal axis (0°) to 3.4° at the limits of coverage (±60°) based on the 30° canted angle used. These findings indicate the great potential to use dual MEMS direction finding sensor assemblies to locate sound sources with high accuracy.

Investigation of a Bending-Mode Magneto(Elasto)electric Sensor Using a Phase Modulation With a PLL

Bending-mode magnetostrictive-piezoelectric sensors clamped at its two extremities show promising results for an enhancement of its magnetic field sensitivity by using a phase modulation (PM) technique. In this operating mode, the sensor is excited by an external carrier at its bending resonant frequency. The results of such a magnetic field sensing by a magneto(elasto)electric bilayer when using a PM technique with a phase locked loop circuitry are presented. The aim of this method is to follow the phase shift at the bending resonant frequency of the sensor, which is proportional to the applied magnetic field for the small-signal regime. We obtained a magnetic sensitivity of ~1.5 kV/T and an equivalent magnetic noise level around 80 nT/$\surd $ Hz at 2 Hz. These performances are presently limited by the noise from our electronics, suggesting that there is room for further improvements.

A magnetoelectric composite based signal generator

Self-oscillations in an active loop consisting of a wide-band amplifier and a magnetoelectric composite in the feedback circuit have been observed. The composite with a ferroelectric lead zirconate titanate bimorph and ferromagnetic Metglas serves as a resonator that determines the frequency of oscillations and provides the feedback voltage. Under amplitude balance and phase matching conditions, the device generated signals at 2.3 kHz, at the bending resonance frequency of the composite. The oscillations were observed over a specific range of magnetic bias H. The shape of the signal generated is dependent on electrical circuit parameters and magnitude and orientation of H.

A Bonded Type Ultrasonic Motor Using the Bending of a Crossbeam

This paper proposed a new crossbeam ultrasonic motor, which was made of a cross-shaped metal frame and eight pieces of lead zirconate titanate ceramic plates with a size of $10~\text {mm}\times 3~\text {mm}\times 1$ mm. Two cross-cone-shaped horns were machined at two ends of the crossbeam, and the tips of the horns served as the driving feet. Ellipse trajectories of the two driving feet were generated by superimposing two orthogonal first bending vibrations with the same resonance frequency but a temporal shift of 90°. A Symmetric structure of the proposed ultrasonic motor solved the problem of mode frequencies degeneracy. A new method to excite these two bending vibrations was proposed. Finite-element method simulation was developed to obtain the vibration characteristics of the crossbeam motor. The new excitation method was compared with the traditional one, and it was found that the vibration amplitudes of the driving feet under the new excitation method were about three times that of the traditional one. At last, experiments were accomplished on a fabricated prototype. The two tested first bending resonance frequencies agreed well with each other at $\sim 40.5$ kHz. Mechanical output performance of the prototype was tested; the maximum speed was $\sim 64$ r/min, and the maximum output torque was $\sim 10.4\text {mN}\cdot \text {m}$ . This paper provides a new idea for an ultrasonic motor with a miniature structure and also a new excitation method for bending vibration.

An electromechanical coupling model of a bending vibration type piezoelectric ultrasonic transducer

An electromechanical coupling model of a bending vibration type piezoelectric ultrasonic transducer is proposed. The transducer is a Langevin type transducer which is composed of an exponential horn, four groups of PZT ceramics and a back beam. The exponential horn can focus the vibration energy, and can enlarge vibration amplitude and velocity efficiently. A bending vibration model of the transducer is first constructed, and subsequently an electromechanical coupling model is constructed based on the vibration model. In order to obtain the most suitable excitation position of the PZT ceramics, the effective electromechanical coupling coefficient is optimized by means of the quadratic interpolation method. When the effective electromechanical coupling coefficient reaches the peak value of 42.59%, the optimal excitation position (L1=22.52mm) is found. The FEM method and the experimental method are used to validate the developed analytical model. Two groups of the FEM model (the Group A center bolt is not considered, and but the Group B center bolt is considered) are constructed and separately compared with the analytical model and the experimental model. Four prototype transducers around the peak value are fabricated and tested to validate the analytical model. A scanning laser Doppler vibrometer is employed to test the bending vibration shape and resonance frequency. Finally, the electromechanical coupling coefficient is tested indirectly through an impedance analyzer. Comparisons of the analytical results, FEM results and experiment results are presented, and the results show good agreement.

A Novel Rotary Piezoelectric Motor Using First Bending Hybrid Transducers

We report a novel rotary piezoelectric motor using bending transducers in this work. Three transducers are used to drive a disk-shaped rotor together by the elliptical movements of their driving tips; these motions are produced by the hybrid of two first bending vibration modes. The proposed piezoelectric transducer has a simple structure as it only contains an aluminum alloy beam and four pieces of PZT plates. Symmetrical structure is the only necessary condition in the design process as it will ensure the resonance frequencies of the two orthogonal first bending modes are equal. Transducers with first bending resonance frequency of about 53 kHz were fabricated and assembled into a rotary motor. The proposed motor exhibits good performance on speed and torque control. Under a working frequency of 53.2 kHz, the maximum no-load speed and the maximum torque of the prototype are tested to be 53.3 rpm and of 27 mN·m.

Resonance magnetoelectric effect in an asymmetric magnetostrictive/piezoelectric trilayered composite structure

Resonant magnetoelectric(ME) effect in FeNi–PZT–FeCuNiSiB trilayered composite with asymmetric magnetostrictive layers is investigated. The magnetic layers facilitate effective excitation of bending oscillations in the structure due to the flexural deformation caused by the asymmetric stress distribution in the FeNi–PZT–FeCuNiSiB composite. As a result, two remarkable resonance peaks appear at bending resonance frequency f1 = 38.8 kHz and longitudinal resonance frequency f2 = 163.2 kHz, respectively. The magnetic field frequency dependence of ME voltage coefficient of the FeNi–PZT–FeCuNiSiB trilayer is distinct from those of FeNi–PZT–FeNi and FeCuNiSiB–PZT–FeCuNiSiB trilayers. Furthermore, the dual-peak ME effects at bending and longitudinal resonance frequencies are observed. The ME voltage coefficient at bending resonance is 1.18 V/Oe (14.75 V/cm Oe) that is 1.68 times larger than the value measured for a FeNi–PZT bilayer of similar dimensions. These results provide the possibility of implementing FeNi–PZT–FeCuNiSiB trilayered composite in magnetic-sensing devices.

Small-Scale Multiaxial Setup for Damage Detection Into the Very High Cycle Fatigue Regime

Micro electro mechanical systems, coatings, and thin films contain materials that are often subjected to complex loading conditions and high frequencies. Therefore, the implementation of a resonant multiaxial fatigue setup for small-scale samples is of high interest. Finite Element simulations have been used to design small-scale samples which possess very close bending and torsional resonant frequencies. The bending and torsional modes are excited by two piezo actuators working either in or out of phase with one another. The bending and torsional amplitudes are measured independently by a laser and the actuator amplitudes are controlled by a Field Programmable Gate Array. The fatigue setup can be used with a varying range of sample sizes from centimeters down to tens of micrometers. The novel multiaxial resonant micro fatigue setup as well as results (fatigue damage for Ni and lifetime for Cu) from bending small-scale fatigue tests are shown and discussed.