Bending Resonance Research Articles

Resonant-type inertia linear piezoelectric motor based on a synchronized switching stimulated by harmonic synthesized mechanical square wave.

A novel resonant linear piezoelectric motor based on a synchronized switching stimulated by harmonic synthesized mechanical square wave was designed in this study. The driving mechanism of the motor was also investigated. The periodic square wave motions of the clutch and the vibrator were generated by composing two sinusoidal resonant bending vibrations with a frequency ratio of 1:3. The linear motion of the motor output shaft can be realized through the cooperation between the clutch and the vibrator. An experimental device was established to validate the working principle and evaluate the performance of the motor. The prototype motor reached the maximum no-load velocity of 16.35 mm/s with a clutch driving voltage of 200 Vp-p and a vibrator driving voltage of 240 Vp-p for a base frequency of 809 Hz. The maximum traction force of 5.64 N was obtained under the clutch driving voltage of 200 Vp-p and the vibrator driving voltage of 160 Vp-p for a base frequency of 809 Hz. The motor achieved a net efficiency of 21.43% with a load of 2.25 N.

Electronic phase shift measurement for the determination of acoustic wave DOA using single MEMS biomimetic sensor

MEMS acoustic sensors have been developed to mimic the highly-accurate sound-locating system of the Ormia ochracea fly, which detects sound wavelengths much larger than its hearing organ. A typical ormia-based MEMS directional sound sensor possesses two coupled wings that vibrate in response to sound according to a superposition of its two main resonant modes, rocking and bending. Vibrations are transduced into electronic signals by interdigitated comb finger capacitors at each wing’s end along with a capacitance measuring circuitry. A sensor designed to exhibit resonant modes closely placed in frequency, enhancing their coupling, was operated with a closed cavity behind the wings. Simultaneous and independent measurements of electronic signals generated at each of the single sensor wings were used to determine incident sound direction of arrival (DOA). DOA was found proportional to the phase shift between them and to the difference over the sum of their amplitudes as well. Single sensor phase shift DOA measurement presented a resolution better than 3° for sound pressure levels of 25 mPa or greater. These results indicate that a single sensor operating in closed-cavity configuration can provide hemispherical unambiguous direction of arrival of sound waves which wavelength is much larger than the sensor size.

Fiber cladding SPR bending sensor characterized by two parameters* *Project supported by the National Natural Science Foundation of China (Grant No. 61705025), the Natural Science Foundation of Heilongjiang Province, China (Grant No. F2018027), the Fund from Chongqing Municipal Key Laboratory of Institutions of Higher Education (Grant No. [2017]3), the Program of Chongqing Development and Reform Commission (Grant No. 2017[1007]), the

A fiber cladding surface plasmon resonance (SPR) bending sensor is realized by the cladding of the fiber structure. By employing coating film, the sensing zone is protected and the toughness of the sensor increases. Three different sensing probes are tested, the experiment results indicate that the two parameters (wavelength sensitivity and light intensity sensitivity) sensing performances of the eccentric butt joint structures are superior to that of hetero-core structure, and the SPR bending sensor based on hetero-core structure is stable and uneasy to damage. By employing hetero-core fiber and silver film, a fiber cladding SPR bending sensor with better stabilization and sensing performance is realized. The proposed fabricating method of sensing probe with coating film provides a new approach for fiber SPR-distributed bending sensor.

Tunable Fano-like resonances in bent single-mode waveguide-based Fabry-Perot resonator: erratum.

In this erratum, we correct an error in the numerical simulation results published in Opt. Lett.44, 231 (2019)OPLEDP0146-959210.1364/OL.44.000231. The error arose from disregarding cladding modes in the straight input and output waveguide sections [Fig. 2(a) in the original paper]. Although these modes do not contribute directly to the calculated power in the reflected and transmitted fundamental modes in those sections, they do, nevertheless, play a significant role in shaping the reflection and transmission spectra of the bent resonator, as was found after the paper had been published. While the main findings of the original paper remain largely intact, quantitatively the spectra in Figs. 3-6 are inaccurate and must be replaced with the correct ones given in this erratum. Some minor modifications to the conclusions of the original paper that are required in view of the corrected results are also discussed.

Nonlinear dynamic behavior of a flexible asymmetric aero-engine rotor system in maneuvering flight

Aero-engine rotor systems installed in aircraft are considered to have a base motion. In this paper, a flexible asymmetric rotor system is modeled considering the nonlinear supports of ball bearings and Squeeze Film Dampers (SFDs), and the dynamic characteristics of the rotor system under maneuvering flight are systematically studied. Effects of the translational accelerative motions, the angular motions and the pitching flight with combined translational and angular motions on nonlinear dynamic behavior of the rotor system are investigated. The results show that, due to the nonlinear coupled effects among the rotor, ball bearings and SFDs, within the first bending resonance region, responses of the rotor show obvious nonlinear characteristics such as bistable phenomenon, amplitude jumping phenomenon and non-synchronous vibration. Translational acceleration motion of the aircraft leads to axis offset of the rotor system and thus results in the reduction and the final disappearance of the bistable rotating speed region. The pitching angular motion mainly affects rotational vibration of the rotor system, and thus further induces their transverse vibrations. For the pitching flight with combined translational and angular motions, a critical flight parameter is found to correspond to the conversion of two steady responses of the rotor system, in which one response displays small amplitude and synchronous vibration, and the other shows large amplitude and non-synchronous vibration.

Effects of Flexoelectricity and Surface Elasticity on the Nonlinear Magnetoelectric Coupling in Unsymmetric Composites

Flexoelectricity is the development of an electric field under an applied strain gradient. This effect is highly size-dependent and is significant at nanoscales. Unsymmetric magnetoelectric (ME) composites undergo bending deformations under a magnetic field that results in non-zero strain gradients. Hence, it is important to give due consideration to flexoelectricity, along with direct piezoelectricity in these composites. This article presents a finite-element model that predicts the static and dynamic behavior of ME nanobeams subjected to magnetic fields. The effect of material nonlinearity of the ferromagnetic phase and flexoelectricity in the ferroelectric phase on the ME coupling are determined, and the obtained results show agreement with the literature. It is found that flexoelectricity results in substantially higher static ME coefficients. However, the resonant ME response is weakened by flexoelectricity. The effect of surface elasticity on the ME coupling coefficient is also investigated by making use of the Gurtin–Murdoch theory. The surface effects are found to improve the ME coefficient at bending resonance, while its effect is trivial at static and axial resonant conditions. Furthermore, the effect of load resistance on the ME voltage and charge coefficients is determined. The results indicate clear changes in the trend between short-circuit and open-circuit conditions.

Influence of the temperature- and frequency-dependent dynamic properties of rail pads on the vibration characteristics of rails at low temperature

The dynamic properties of railway tracks and rail pads are significant for accurately predicting both the wheel–rail system vibration and rolling noise. The effect that the dynamic properties of rail pads have on the dynamic characteristics of railway tracks at extremely low temperatures was not adequately studied in previous research. In order to better predict the attenuation of the rail vibration, the viscoelastic dynamic properties of rail pads varying nonlinearly with temperature and frequency were first tested, in a wide temperature range (−60 ℃ to 20 ℃), and represented by the fractional derivative Zener model. Then, rail vibration and its attenuation characteristics were investigated by accounting for the frequency-dependent, temperature-dependent and frequency- and temperature-dependent properties, respectively. To be more specific, the frequency and amplitude of the rail first-order bending resonance and pinned–pinned resonance, as well as the rail decay rate were analyzed for the three cases. In conclusion, the study shows that the temperature/frequency-dependent properties of the rail pad have a significant effect on the first-order bending resonance of the rail, but no influence on the pinned–pinned resonance frequency. The rail decay rate indicates a clear increasing trend in the entire frequency domain with the decrease of temperature (especially below about −20 ℃). The frequency dependence mainly affects the vibration and its attenuation characteristics of the rail below about 400 Hz, which should not be ignored in the track dynamics modelling. Therefore, when the analyzed environmental temperature is below −20 ℃, the temperature dependence of rail pads should be considered.

Locomotive wheel polygonisation due to discrete irregularities: simulation and mechanism

Discrete irregularities are a common issue occurring on locomotive wheels. The wheel roughness measured in the field sites indicates that some wheels suffer from discrete wheel irregularities, such as wheel flats or local defect. Meanwhile, the wheels exhibit obvious polygonisation. A wheel wear model is present to study the influence of discrete wheel irregularities on locomotive wheel polygonisation, which consists of a flexible-rigid locomotive-track coupled dynamics model and a wear calculation model based on the frictional work of wheel–rail contact patch. A series of discrete irregularities with different wavelengths are taken as initial input of irregularities. The wheel–rail interaction and wheel polygonisation evolution process induced by discrete wheel irregularities are analysed. The simulation results indicate that discrete wheel irregularities can excite the structural elastic vibration of the wheelset, especially the wheel lateral vibration, which leads to oscillations of the lateral creepage and creep force in a certain frequency. Wheel polygonisation is formed finally resulting from the fluctuation of wheel–rail creepages and creep forces. The frequency-fixing mechanism of wheel polygonisation with wavelengths of 630 and 200 mm in 1/3 octave band are the coupling of parameter excitation of discrete sleeper support with P2 resonance and lower bending resonance of the wheelset, respectively.

Resonant-type piezoelectric linear motor driven by harmonic synthesized mechanical square wave.

In this study, a novel resonant piezoelectric linear motor driven by harmonic synthesized mechanical square waves was designed, fabricated, and tested. The motor consists of a stator, a mover, and auxiliary parts. Periodic square wave motions of the stator and the mover were generated by composing two sinusoidal resonant bending vibrations with a frequency ratio of 1:3. Piezoelectric plates were deformed with a certain regularity to drive the piezoelectric motor. The finite element method software COMSOL was used to design the structure of the motor. An experimental device was established to validate the working principle and evaluate the performance of the motor. The prototype motor reached the maximum no-load velocity of 22.5 mm/s with the stator driven voltage of 140 Vp-p and the mover driven voltage of 180 Vp-p for a base frequency. The maximum traction force of 3.8 N was obtained under a stator driving voltage of 140 Vp-p and a mover driving voltage of 100 Vp-p for the base frequency. The motor achieved a net efficiency of 12.2% with a load of 0.3 N.

Modal analysis of magnetic vibration of induction motor used in household appliances

The paper deals with analysis of vibrational behavior of induction motor using the combined approach linking the finite elements method (FEM) applied to modelling of magnetic and mechanical phenomena in the motor with its modal description in spectral domain. Results of investigations presented in this paper proved that relatively small rotor axis misalignment against stator leads to visible vibration if forces resulted from this effect have frequency close to rotor bending resonance. Paper contains a rigorous description of all steps in analysis with a special attention paid to details of numerical approach both in FEM and in spectral consideration. Results of theoretical investigations were confirmed by measurements.

Giant Self-biased Magnetoelectric Effect in Pre-biased Magnetostrictive–Piezoelectric Laminate Composites

In this study, it is demonstrated that the giant self-biased magnetoelectric (SME) response can be achieved from a center-clamped magnetostrictive–piezoelectric laminate composite by employing magnetic tip masses. An asymmetric laminate structure consisting of two different magnetostrictive layers (Metglas and nickel) with opposite signs of piezomagnetic coefficient is introduced to promote structural bending resonance, and the effect of layout change of attaching the magnetic tip masses on SME responses is systematically investigated. The highest SME effect is observed when all magnetic tip masses are loaded on the Metglas layer and their magnetization directions are normal to the Metglas surface. It is proposed that not only the parallel magnetic domains to external magnetic field but also the non-parallel magnetic domains effectively contribute to the total magnetostriction. The fabricated SME laminates exhibit giant SME voltage coefficients ranging from 14.11 to 52.35 V cm−1 Oe−1, depending on the direction of the fields of the tip magnets. These high SME voltage output values and their controllability are promising for precision field sensors, magnetic energy harvesters and field-tunable devices.

Designing ferroelectric/ferromagnetic composite with giant self-biased magnetoelectric effect

We report a simple and effective method to obtain the magnetoelectric (ME) effect at zero magnetic bias field (HDC = 0), i.e., the self-biased ME (SME) effect, using an ME laminate composite clamped at its center with its free ends loaded with magnetic tip masses. The method exploits the shifting of the magnetic hysteresis loop of the ferromagnetic (FM) layer of the laminate induced by a preapplied magnetic field (Hp) along the longitudinal direction. The optimum magnetic-field strength corresponding to the maximum of the ME voltage coefficient (αME) vs HDC curve was calculated using equations derived from correlations of magnetic coefficients. In experiments involving the laminate with an FM/ferroelectric/FM symmetrical structure, the strength of Hp was tuned to the optimum value, shifting the αME vs HDC curve along the HDC axis enough to obtain the maximum αME at HDC = 0 (αSME). To further enhance αSME, an asymmetric configuration of the laminate was designed using two different FM materials having piezomagnetic coefficients with opposite signs. The ME laminate with the asymmetrical structure exhibited a large αSME of 55.7 V cm−1 Oe−1 at its bending resonance frequency.

Resonance magnetoelectric characteristics of Terfenol-D/Pb(Zr0.52Ti0.48)O3/Ni asymmetric three layered composites

Three resonance modes, a first-order bending resonance mode and nonlinear and first-order longitudinal resonance modes, were observed in Terfenol-D/lead zirconate titanate(PZT)/Ni asymmetric magnetoelectric(ME) laminated composites. The ME outputs and resonance modes were tuned by the ratio of the thickness of the Ni negative magnetostrictive layer to the Terfenol-D positive magnetostrictive layer that of the(tNi/tT). As (tNi/tT) increased from 0.4 to 2.0, the strength of the first-order longitudinal resonance mode was decreased, while the first-order bending resonance was enhanced. The asymmetric threelayered composites exhibited a large ME coefficient of 250mV/(cm Oe) under a bias magnetic field of 400 Oe at quasi-static frequency (1 kHz). This work sheds some light on the design of ME composites with tunable ME resonance modes and multifrequency operation.

Experimental and numerical analysis of the polygonal wear of high-speed trains

High-order wheel polygonal wear results in many problems in track and vehicle systems. To gain insight into its formation mechanism, the relationship between dominating order and vehicle speed and wheel diameter is first analyzed based on the polygonal wear measured at field sites. The measurement data proves that high-order polygonal wear serves as the “fixed-frequency” mechanism. Moreover, the test results of the vibration characteristic of an axlebox show that resonance at 550–650 Hz exists in the vehicle/track systems, which is associated with the formation of high-order polygonalization. Then, a coupled vehicle/track dynamic model is established. By sweeping the frequency excitation, the harmonic behavior of wheel/rail normal forces is evaluated considering a single wheelset model and a bogie model. The results of the two models are compared and indicate that the rail vertical bending modes between the front and rear wheels of the bogie play an important role in the dynamic response of the wheel/rail forces. Particularly, the natural frequency of the third-order rail local bending mode is near the excitation frequency of the high-order polygonal wear. Subsequently, the development of the ideal polygonalization is investigated by introducing the Archard wear model. The results suggest that both the amplitude of the wear depth and the phase difference between the wear depth variation and original polygonalization play vital roles in the enlargement of polygonalization. Using a long-term wear iteration, the growth progress of the typical 20th order polygonal wear on China’s high-speed trains is reproduced. The simulation results indicate that the third-order rail local bending resonance greatly contributes to the periodic fluctuation in the wheel/rail normal forces and further leads to the large periodic wear at approximately 550–650 Hz (19th–23rd orders), the 20th order (577 Hz) among them has the fastest growth rate in each wheel revolution because of the smaller phase difference between the wear depth and the original polygonalization.. In addition, parametric studies show that the dominant order of the polygonal wear largely depends on the vehicle speed and wheelbase. The continuous increase in the stiffness of the railpad shifts the polygonal wear from a high order to a lower order because of the significant P2 resonance. Large railpad damping reduces the growth rate of the high-order wheel polygonal wear.

Adapted measuring sequence for the determination of directional-dependent dynamic material properties using a bending resonance method

Abstract Within this work, an adapted bending resonance method is presented, which is especially suitable to determine the elastic and damping material properties of composite materials. Since the properties of these material group depend among others on frequency and reinforcement direction, a large number of individual tests are required for a sufficient characterisation. Therefore, a new approach for an automatic data acquisition and analysis is developed and presented in this paper. The presented approach bases on a measurement sequence combining different methods like decaying free oscillations and frequency response functions and thus minimises the uncertainties of the damping measurement and enables a test stand automation. The directional-dependent material properties of carbon fibre-reinforced epoxy were determined to demonstrate the proposed resonance bending method with adapted measuring sequence.

A 5 mg micro-bristle-bot fabricated by two-photon lithography

A bristle-bot or vibrobot is a multi-legged robot made of bristles and an oscillating actuator that generates vibrations. This work presents the first demonstration of a micro-bristle-bot, with 3D-printed legs, fabricated by two-photon polymerization (TPP) lithography. The presented miniaturized bristle-bot has a weight of only 5 mg, in the size of 2 mm × 1.87 mm × 0.8 mm, and can achieve a speed up to 4 times the body length per second. A base structure with six legs is fabricated by TPP direct laser writing in a single fabrication step, allowing for rapid prototyping of various leg designs. The base is attached to a 0.3 mm thick lead zirconate titanite (PZT) actuator block. The vibrational energy is provided by an external piezoelectric shaker in this work, which mimics the ocillatory behavior of the on-board PZT block. This work demonstrates the locomotion of micro-bristle-bots with various leg designs that utilizes the resonant bending mode shape at small excitation voltages applied to the external piezoelectric shaker. The presented micro-bristle-bots show a resonant frequency around 6.3 kHz, which can be tailored based on their geometry. This feature allows for addressing individual micro-bristle-bots with various geometries based on their unique resonance frequency.

Influence of the Cyclic Hardening Model on the Results of the Numerical Analysis of Fatigue Life on Example of the Compressor Blade

Abstract The main goal of the presented work is to determine the impact of the cyclic hardening model on the numerical results of the ε-N fatigue test. As an object of study, compressor blade (from PZL-10W helicopter engine) was used. The examined blade was made of EI-961 alloy. In numerical analysis, a geometrical model of the blade with a preliminary defect was created. Geometrical defect – V-notch was created on the leading edge. This defect was introduced in order to weaken the structure of the element and the possibility of observing the crack initiation process (in experimental tests). Material data to ε-N analysis, based on Manson-Coffin-Basquin equation, were estimated for Mitchell’s model. This model was built based on strength data provided by the steel producer. Based on three different models of cyclic hardening (Manson, Fatemi, and Xianxin), a number of load cycles were calculated. Load cycle during numerical analysis was represented as resonance bending with an amplitude of displacement equal to A = 1.8 mm. Obtained results were compared with experimental data. Additionally, the analytical model of ε-N fatigue (depending on the cyclic hardening) was prepared. All the work carried out has been summarized by a comprehensive comparative analysis of the results. Obtained results and dependencies can be used in the selection of an appropriate model of cyclic hardening in further fatigue tests of many aerospace elements.

Energy harvesting performance of unimorph piezoelectric cantilever generator using interdigitated electrode lead zirconate titanate laminate

An unimorph piezoelectric cantilever generator with an interdigitated electrode (IDE) was developed for application to vibration energy harvesters driven in longitudinal mode. Lead zirconate titanate (PZT) thick film was fabricated by lamination of 10 sheets printed with Ag IDE; the laminated film was subsequently cofired at 850 °C for 2 h. Compared with a conventional IDE PZT thick film, the approximately 270 ㎛-thick cofired IDE PZT laminate revealed a significantly increased capacitance due to reduction of transition area. The use of multilayered IDE could result in the enhancement of energy harvesting performance for unimorph piezoelectric cantilever generator using PZT laminate. Optimized bending resonance frequency was obtained at 78 Hz for the unimorph piezoelectric cantilever generator with tip mass of 2.3 g driven in longitudinal vibration mode. Its energy harvesting performance was characterized as having a high power density of 26.7 mW/cm3 across the resistive load of 80 kΩ, corresponding to a normalized power factor of 6.7 mW/G2·cm3.

Magnetoelectric direct and converse resonance effects in a flexible ferromagnetic-piezoelectric polymer structure

Abstract The direct and converse magnetoelectric (ME) effects in a flexible structure containing a mechanically coupled layers of amorphous ferromagnet FeBSiC and a piezo-copolymer poly(viniledene fluoride trifluoroethylen) (P(VDF-TrFE)) are investigated. The mutual transformation of magnetic and electric fields in the structure arises due to a combination of magnetostriction and piezoelectric effects in the ferromagnetic and piezoelectric layer, respectively. The ME effects were induced by exciting the structure with alternating magnetic fields of 0–100 kHz frequency and 1–5 Oe amplitude, or alternating electric fields of amplitudes up to 500 V/cm in the presence of a constant H field. For the direct ME effect the conversion coefficient reached 7.2 V/(cm·Oe) at a bending resonance frequency of 412 Hz and 44 V/(cm·Oe) at a planar resonance frequency of 25.15 kHz. Increasing the excitation magnetic field at the bending resonance frequency, the nonlinear second harmonic generation with an efficiency of 0.24 V/(cm·Oe2) was observed. For the converse ME effect, the conversion coefficient at the planar resonance frequency was 0.09 G·cm/V. The dependences of the efficiencies for the direct and converse ME transformations on the constant field and the amplitudes of the excitation fields are well explained by theory. These results could be used to develop magnetic and electric field sensors, as well as autonomous energy harvesting sources.

Low-Frequency Vibration Energy Harvesting With Bidomain LiNbO3 Single Crystals.

Low-frequency vibration energy harvesting is becoming increasingly important for environmentally friendly and biomedical applications in order to power various wearable and implanted devices. In this paper, we propose the use of piezoelectric congruent LiNbO3 (LN) single crystals, with an engineered bidomain structure, as an alternative to the widely employed lead-based PZT. We thus compared experimentally the pure vibration energy scavenging performance of square-shaped bidomain and single-domain Y+128°-cut LN crystals and a conventional bimorph soft PZT ceramic bonded to long spring-steel cantilevers as a function of the frequency, load resistance, and tip proof mass. At a low bending resonance frequency of ca. 32.2 Hz, the bidomain LN yielded an open-circuit voltage of 1.54 kV/g, almost one order of magnitude larger than that observed in PZT. The maximum extractable average power was found to be of 9.2 mW/g2 in the bidomain LN, 6.2 mW/g2 in the single-domain LN, and 1.8 mW/g2 in the PZT piezo-elastic cantilevers. With five times higher output power density of up to 11.0 mW/(cm [Formula: see text]) under resonance conditions, bidomain LN was thus shown to be a reliable lead-free and high-temperature alternative to PZT, thanks to its considerably larger quality factor and electromechanical conversion efficiency.