Maximum Vibration Displacement Research Articles

Novel small-size seismic metamaterial with ultra-low frequency bandgap for Lamb waves

Seismic metamaterials (SMs) possess bandgap characteristics, enabling effective attenuation of seismic waves within a specific frequency range. However, small-sized SMs typically struggle to achieve a wide low-frequency bandgap. This paper proposes four types of SMs. The dispersion curves of these models were analyzed, and their vibration modes were studied to elucidate the bandgap mechanism. To investigate the influence of structural parameters on the bandgap, geometric variables are analyzed. Subsequently, the spectrum and acceleration time history curves of Lamb waves in a finite SM system are analyzed to verify the bandgap's authenticity. The designed structure exhibits a bandgap ranging from 1.24 Hz to 16.86 Hz, with a relative bandwidth as high as 172.6% and over 96% maximum vibration displacement attenuation of the El Centro seismic wave. The designed SMs effectively cover the 2 Hz seismic peak spectrum that leads to structural damage. They possess ideal relative bandwidth and excellent isolation performance, further advancing the engineering application of SMs.

Study on the effect of bearing position and stiffness on the dynamic behavior of output stage of CHT system based on the cylindrical gear meshing

The internal and external rotor shafts are important components to transfer power in coaxial helicopters, and bearing supports could affect the dynamic behavior of the transmission system. In order to explore the influence of bearing support structure, bearing position and support stiffness on the dynamic behavior of the output stage of coaxial helicopter transmission (CHT) system based on the cylindrical gear meshing, a rigid-flexible coupled dynamic model is established under cantilever-cantilever support structure and cantilever-simple support structure considering the flexibility of rotor shaft based on Timoshenko beam theory, and time-varying mesh stiffness (TVMS), comprehensive meshing error are also considered. Newmark-beta numerical method was applied to calculate the dynamic response. The result indicates that the load sharing performance of gear pair using cantilever-simple support structure is better than that of cantilever-cantilever structure, but the maximum vibration displacement of bull gears is reduced apparently. Simultaneously, the bearing positions and stiffness can be adjusted to achieve better performance in load distribution and maximum vibration displacement of bull gears.

Improved non-contact vibration measurement via acceleration-based blade tip timing

The conventional displacement-blade tip timing (D-BTT) measurements often rely on Once-Per-Revolution (OPR) sensors to compute expected or theoretical time of arrival (TOA) based on rotational speed. However, integrating OPR sensors within the confined space of aero-engines presents challenges, and estimating theoretical TOA introduces computational errors, particularly for low-amplitude, high-frequency blade vibrations. This paper presents the Acceleration-based Blade Tip Timing (A-BTT) method as a solution. Building upon A-BTT, the acquisition of blade tip vibration acceleration serves not only to capture rapid changes in vibration but also to offer richer data for precise measurement of high-frequency blade vibrations. With only three blade tip timing sensors recording actual TOA without an OPR sensor, A-BTT eliminates the need for estimating expected TOA, thus mitigating calculation errors. Furthermore, by analyzing the relationship between maximum blade tip vibration acceleration and displacement during synchronous blade vibration, vibration parameters, such as natural frequency, can be directly identified without prior information such as engine orders. Simulation and experimental results validate the efficacy of the A-BTT method, demonstrating its successful application to specific aero-engine compressor rotor blades.

Vibration characteristics and safety analysis of production string in high temperature, high pressure gas wells

During the production of high-temperature, high-pressure (HPHT) gas wells, the gas entering the production tubing column induces vibration, which in turn leads to changes in the mechanical properties and safety of the tubing column. A dynamic model of the production string in an HPHT gas well was established to study the dynamic characteristics of its production string. The additional axial force caused by the transient temperature change and the nonlinear contact collision between the production string and the casing were considered. The Newmark-β method was used to solve the problem by analyzing and comparing the flow-induced vibration characteristics of the production pipe string. In this study, a gas well in the southwest Sichuan Basin was used as the research object to study the effects of gas production, packer setting position, and string wall thickness on the dynamic characteristics of the string. The results show that in the gas production process, intense vibrations are generated in the transverse and longitudinal directions of the tubular column. After high-velocity gas flows through the production tubing column, the vibrations at the wellbore inclination and the top of the tubing column are more intense. With the rise of production and the downward movement of the packer setting position, the vibration displacement and frequency of the tubing column increase. In addition, as the column's wall thickness increases, the column's stiffness rises, which, in turn, reduces the vibration of the column. When the gas production increases from 60 × 104 m3/d to 150 × 104 m3/d, the maximum transverse vibration displacement of the production string will increase by 22.2%–39.3%, while the frequency will increase by 15.3%–54.3%. When the wall thickness of the pipe column reaches 9.53 mm and 10.92 mm, it can be employed to enhance the safety factor of the string and extend the fatigue life of the string. This study provides a theoretical framework for field string protection and production guidance.

Robust design optimization of spin algorithm to reduce spinning time and vibration in washing machine

This study focuses on optimizing the spin algorithm of washing machines to reduce spin time and vibration, two crucial performance metrics often in a trade-off relationship due to structural limitations. We developed a simulator for the spin process that accounts for the uncertainty associated with the clothes’ position in the drum. Using this simulator, we designed a robust optimization algorithm to minimize spin time while maintaining acceptable vibration levels. The variation in the mass and position of laundry within the drum primarily affects vibration performance during the spin process. We formulated the unknown unbalance caused by the laundry as test-implementable unbalance parameters (UBP), represented as random variables. The uncertainties in the laundry’s unbalance for repeated experiments were estimated by the distribution of these UBPs. Experiments were conducted at parametrically designed points to measure vibrations and internal sensor values for control in specific revolutions per minute (RPM)ranges. These data were used to create approximate models. Monte Carlo simulation was then applied with UBP distributions obtained from the clothing experiments to meta-models, and the simulator was equipped with the spin algorithm. This process allowed us to predict the distribution of the maximum tub vibration displacement and spin time. A robust optimization algorithm was subsequently applied to the simulation model to derive the optimal spin algorithm. The proposed methodology yielded substantial improvements: a 25% reduction in the mean value of maximum displacement and a 90% reduction in the mean value of spin time compared to initial values.

Enhancing heat transfer from a circular cylinder undergoing vortex induced vibration based on reinforcement learning

Machine learning approaches have been proven to be effective and efficient in mediating flow dynamics so as to realize drag reduction, vibration suppression, etc. In this article, an intelligent active flow control approach is proposed to enhance heat transfer of a heated circular cylinder at Re=100 undergoing vortex induced vibration in the lock-in condition. A high-fidelity solver based on the generalized interpolation-supplemented lattice Boltzmann method (GILBM) with moving reference frame (MRF) is used to establish the real-time numerical environment with structural motion, momentum transport, and heat transport. A reinforcement learning (RL) agent realized by proximal policy optimization (PPO) is adopted to establish the model-free controller, which receives sensorymotor cues as feedback signals and determines the real-time velocity issued from the jet as actuation. Through a group of trainings, each of whom involves 200 independent cases, the RL agent eventually learns an effective and efficient control strategy that improves the average heat transfer rate by 76.7%, quantified by the dimensionless Nusselt number. Through analyzing the spatiotemporal variations of vorticity and temperature fields, local Nusselt number and pressure coefficient along the cylinder surface, as well as the statistical flow quantities, it is proved that that the enhanced heat transfer is contributed by both the mediated vortex formation and shedding in vicinity of the blowing jet, as well as the augmented vibration. Extra tests also confirm that the synthetic jets play a much more significant role than the augmented vibration. Furthermore, the success of the control strategy is attributed mainly by the phase lag between the maximum vibration displacement and the moment when the synthetic jets oppose their directions. Moreover, the more realistic but more complicated case with the non-Oberbeck-Boussinesq (NOB) approximation is also tested, confirming good self-adaptivity of the learnt strategy. Through this study, it is verified that the RL to be a powerful tool for mediating flows involving complicated momentum and heat transport.

Damage Analysis of Box Girder Based on a Vehicle–Bridge Interaction System

This study proposes a stress analysis method of reinforced concrete (RC) box girder based on damage to reveal the dynamic mechanical response and damage mechanisms of a bridge under moving vehicle load. The effect of different vehicle mass, speed, concrete strength, and longitudinal reinforcement ratio on the stress of a single box girder is investigated using solid finite element vehicle–bridge interaction dynamic elastic–plastic analysis (a total of 13 kinds of loading schemes) that is based on the Newmark algorithms of a numerical analysis model of a five-axle vehicle and road roughness. The results reveal that the damage status of the RC box girder strongly depends on the vehicle mass and speed. The damage region of the box girder gradually increases, and changes from flexural damage to flexural-shear damage, which fails rapidly as the vehicle mass increases from 10 t to 60 t. With an increase in vehicle speed, the maximum vertical vibration displacement and the maximum longitudinal stress of the steel bar increase nonlinearly and the damage of the box girder first increases and then decreases. The most severe damage occurs at the vehicle speed of 25 m/s for all vehicle masses. As a result, limiting speed below 25 m/s under the vehicle mass (10 t to 60 t) and increasing concrete strength and reinforcement ratio in a certain range could reduce the damage status of a bridge effectively.

Model and Method of Fault Signal Diagnosis for Blockage and Slippage of Rice Threshing Drum

Rice threshing drum of combine harvester is difficult to monitor and repair the abnormal state in time. When slippage or blockage occurs in the threshing drum, the working efficiency of the threshing drum will reduce seriously, such as the threshing efficiency will decline seriously, and then cleaning performance of combine harvester will decline. In order to reveal the vibration characteristics of rice threshing drum under different working conditions and the vibration response state of the drum bearing undergoing different faults occur, the vibration system model of the threshing drum is established in this paper. With the help of the vibration test bench of the multi-stage threshing drum, the vibration signal test of the slippage and blockage of the threshing drum under the belt drive mode is carried out. The results show that the Z direction signal has a vibration peak at the low frequency (25 Hz) when the threshing drum is blocked, the maximum vibration displacement is about 0.55 mm; the Z direction signal signal peak is concentrated at 50 Hz when a slip fault occurs, and the maximum vibration displacement is about 0.184 mm, the fitting effect between frequency and mathematical model is good. The results of this paper reveal the vibration characteristics of the threshing drum under different abnormal working conditions, at the same time provide a theoretical basis for the fault diagnosis of the threshing drum of the combine harvester.

Transverse forced vibration of a diamond wire under support excitations

Diamond wire sawing is a key technology for wafer processing in the semiconductor industry. Transverse wire vibration decreases the wire web gap to below the critical adhesion spacing between the wires, which is an important factor that limits the development of diamond wire slicing technology toward narrower kerf losses and thinner as-cut wafers. In fact, the external excitation source that causes the diamond wire vibration comes primarily from the supports at both ends of the wire. Therefore, an analytic model for transverse forced vibration of a diamond wire under support excitations was developed in this study based on the transverse vibration theory of an axially-moving string fixed at both ends. This partial differential equation with non-homogeneous boundary conditions was solved using the superposition principle and the finite element method. To verify the theoretical model, experimental equipment to text the transverse vibration of a diamond wire with support excitations was developed. The support excitation signal and the wire vibration response were obtained using accelerometer measurements and machine vision detection, respectively. The theoretical results agree well with the experimental results, indicating the correctness of this proposed model. The effects of the vibration source and the installation parameters on the transverse vibration displacement of a diamond wire are discussed. The results show that hysteresis in the movement of the center of the wire causes a certain additional high-frequency vibration, which can make this maximum transverse displacement to be greater than the excitation amplitude, thus making the wire transverse vibration change non-linearly with some parameters. The maximum transverse vibration displacement at the center of the diamond wire increases with increases in the guide wheel machining error amplitude and the wire diameter as well as the wire span, while it decreases with increases in the wire groove diameter and the wire tension. This maximum transverse vibration displacement decreases by approximately 100.22 % and 6.17 % when the guide wheel manufacturing error amplitude and the wire groove diameter are reduced by half and doubled, respectively. Improving the manufacturing accuracy of the guide wheel is still the most effective way of reducing the transverse vibration displacement of the wire. In addition, appropriate increases in the groove diameter and the wire tension and decreases in the wire span are also beneficial for suppressing the wire vibration.

Dynamic characteristics analysis of a dual-rotor system with bolted-disk joint

This article presents a nonlinear vibration characteristics study of a bolted joint dual-rotor system. The motion equations are derived through the lumped mass modeling method and a two-node bolted joint element. Nonlinear time-varying bending stiffness at the joint interface is considered in the numerical integration. Qualitative analysis of the effect of preload on system responses is conducted through changing the value of the transition point of bending stiffness of the bolted joint. Moreover, the transfer path of vibration in the dual-rotor system through inner-shaft bearing was discussed in the present work. The nonlinear differential equations are solved using the Newmark integration method to predict the dynamic characteristics of the dual-rotor system. The results show that the maximum vibration displacement of LP rotor is positively correlated with that of HP rotor as preload changes. Moreover, the maximum amplitude of the time-domain responses of the HP rotor will decrease and the minimum amplitude will increase with the increase of preload. The difference between the maximum and minimum values of the time-domain response will decrease with the increase of preload. This can be explained by the “stiffness hardening” phenomenon of the bolted joint. The research results can help understanding the dynamic properties of the bolted joint dual-rotor system and the vibration transfer path of the rotor system through inner-shaft bearing.

Method for Identifying and Forecasting Mining-Induced Earthquakes Based on Spatiotemporal Characteristics of Microseismic Activities in Fankou Lead/Zinc Mine

The risks associated with underground mining at Fankou Lead/Zinc Mine in South China are growing due to the large-scale mining activities there. To recognize mining-induced earthquakes and assess the risk per mining level, a microseismic monitoring system, which is used to record microseismic events, is installed at multiple mining levels in Fankou Lead/Zinc Mine. The purpose of this study is to identify mining-induced earthquakes and to evaluate the risk per mining level by analyzing the spatiotemporal characteristics of microseismic activities in the Fankou Lead/Zinc Mine. In this study, the Gutenberg-Richter (G-R) relationship is applied to compute the b-value, which is used to obtain the maximum magnitude (M (max)) of microseismic event that probably occurs at each mining level. Then, the evaluation of the recurrence period for M (max) and the probability of the microseismic event with the magnitude M (max) is carried out and the M (max) at each mining level is determined based on the recording period of microseismic events. The results show that factors such as the maximum rock vibration velocity, source parameters, displacement, microseismic waveform and energy ratio (ES/EP) can be used to distinguish whether a recorded microseismic event is mining-induced earthquake. Additionally, we propose a method to assess the possibility of mining-induced earthquake at each mining level based on M (max) and predict the recurrence time of microseismic event with the magnitude M (max). The of two years results of microseismic events monitoring demonstrate that the current study is promising for identifying mining-induced earthquakes, assessing the risk of mining-induced earthquakes, predicting the potential maximum microseismic event in a region and estimating its recurrence period and its probability in the Fankou Lead/Zinc Mine.

Exploring the potential benefits of using metasurface for galloping energy harvesting

Inspired by the successful applications of metasurfaces in many other fields, this paper aims to explore the potential application of metasurfaces in designing aerodynamic systems. Bluff bodies are proposed to be wrapped in metasurfaces for improving galloping energy harvesting. Three different metasurfaces with convex cylinder, tri-prim, and wedge ornaments are designed. A general aeroelastic model for a galloping energy harvester is developed. The aerodynamic force is represented by a polynomial function with its coefficients being determined from three-dimensional CFD simulations. Subsequently, physical prototypes of the proposed galloping piezoelectric energy harvesters are fabricated, and experimental tests are conducted. The theoretical model is validated by the experimental results. The analytical method and three-dimensional CFD simulation are combined to predict the dynamic responses of the metasurface-wrapped GPEHs. Besides, the results show that the metasurface can significantly change the aerodynamic characteristics of the bluff body, and it is learned that a bluff body wrapped in convex cylinder metasurface could bring benefits for promoting galloping energy harvesting performance. Further experimental studies are conducted to reveal the effects of convex ornament parameters on the galloping energy harvesting performance. It is found that using the metasurface distributed with convex cylinder ornaments of diameter 6 mm and height 9 mm leads to the largest vibration displacement and largest voltage output. Compared to the typical GPEH, the maximum vibration displacement and maximum output voltage of the proposed galloping piezoelectric energy harvester can be increased by 26.81% and 26.14%, respectively. The vortex shedding processes around the wind flow fields near the bluff bodies wrapped in metasurfaces are simulated. The underlying aerodynamic mechanism of the influence of the metasurfaces is unveiled. Finally, based on the validated theoretical model, a parametric study is carried out to investigate the effects of the load resistance and electromechanical coupling strength on the galloping energy harvesting performance. It is concluded that increasing the coupling strength to a certain level and tuning the load resistance to the optimal value could further improve the power output. However, when the electromechanical coupling strength increases to a certain extent, the power output will reach the saturation state, and the coupling strength is extremely large. Therefore, a piezoelectric element with a moderate coupling coefficient is recommended for practical applications from the perspective of economic benefit.

Vibration Response Testing and Evaluation of A Hydropower Station’s Gate

We use standard vibration source to verify the method that vibration displacement was obtained by filter and integral in frequency domain. The feasibility and reliability of this method was confirmed. A gate’s vibration response such as acceleration, dynamic stress and displacement was tested. The vibration acceleration is less than 3 m/s2, the vibration displacement is less than 0.25 mm, and the dynamic stress is less than 153.2 MPa. In the initial stage of the gate lifting, the maximum vibration displacement over the standard requirements. Vibration evaluation of the gate was given by the acceleration, displacement and dynamic stress.

Experimental Investigation on Vibration Responses of Fiberglass Reinforced Plastic

The purpose of this study is to analyze the vibration displacement on fiberglass reinforced plastic beams with variations a number of fibers in the resin matrix. Composite beams was made of fiberglass and polyester resin matrix with a number of fiberglass: 0, 24, and 48. Composite beams was manufactured by hand lay-up method with the unidirectional fiber orientation. The composite beams used have the dimension of length: 500 mm, height: 20 mm, and width: 20 mm. During the experimental test, the beam was vibrated using an exciter motor which was placed at the end of the cantilever support then using a vibration meter, the vibration displacement data (mm) was measured by placing the vibration transducer postions : 50 mm, 250 mm, and 450 mm from the cantilever support. During the vibration test, the vibration displacement data on the vibration meter screen were recorded using a camera recorder and the data was taken 6 times at each of measurement points. The experimental and analysis results show that the value of vibration displacement (mm) decreases when the fiberglass is added to the composite beam, or in other words, the addition of fiberglass provides an increase in the ability of the beam to withstand vibrations. The maximum vibration displacement value on composites with 0 fiberglass: 0.641 mm, then the vibration displacement decreased in composites with 24 fiberglass: 0.506 mm and the lowest displacement value for the composites with 48 fiberglass: 0.395 mm. Whereas for 3 measurement points at positions 5 cm, 25 cm, and 45 cm along the beam for three kind of the composites, the maximum value of vibration displacement value was obtained at the end of beam composites or at 45 cm from cantilever support: 0.735 mm on composite beam with 0 fiberglass and minimum at position 5 cm near the cantilever support with the value of vibration displacement: 0.323 mm on composite beam with 48 fiberglass.

Transverse nonlinear vibration modeling and response of eccentric rotor in a switched reluctance motor

In order to investigate the transverse vibration of eccentric rotor in a 12/8 switched reluctance motor (SRM), a whole nonlinear coupled vibration equation of eccentric rotor is built with finite element method (FEM). Based on single tooth radial force and the key parameters variation with rotor position, an analytical formula of magnetic resultant taking into account of the rotor’s vibration displacement is deduced in detail, which is applied onto the intermediate node of eccentric rotor in form of concentrated force. Once the windings currents obtained either by experiments or numerical simulations is input, the vibration response can be solved numerically by Newmark-[Formula: see text] method. Six phase windings currents under angle position control (APC) strategy are chosen as an example and the vibration response are discussed to reflect intrinsic vibration characteristics. From radical resultant vector and its amplitude spectrum, it is proved that the magnetic resultant vector presents multi-petals star shape. The frequency components in magnetic resultant are [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], related to rotational speed, current waveform and minimum common multiple of stator and rotor teeth. However, from displacement locus and its amplitude spectrum, the frequency component of the rotor vibration displacement is also related to the critical whirl speed of the rotor. Transverse superharmonic resonance of eccentric rotor appears at some particular rotational speed and result in a larger rotor vibration. If the rotor runs at the superharmonic speed of 1/19 of first-order critical whirl speed, the maximum vibration displacement radius of the eccentric rotor reaches almost four times that of the rated speed. The vibration locus at these particular speed show rich diversity.

A Novel High-Symmetry Cobweb-Like Disk Resonator Gyroscope

A novel cobweb-like disk resonator gyroscope (CDRG) with a very small frequency split between two degenerate modes has been designed and implemented. In comparison with the ring-like DRG (RDRG), the CDRG has fewer fabrication imperfections owing to its all-linear structure. In addition, the CDRG displays a superior nonlinear effect compared with the RDRG, and internal differential electrode excitation and detection were used to further reduce the nonlinear effect. The CDRGs and RDRGs were placed side by side on the same wafer, and the characteristics of these as-fabricated resonators were then tested. The results showed that the resonant frequencies and Q-factors of the CDRGs and RDRGs were approximately 18 kHz and nearly 100k, respectively. The smallest as-fabricated relative frequency split (29.9 ppm) of the CDRGs was about 10.8 times smaller than that (322.5 ppm) of an RDRG built side by side on the same wafer, which had the lowest relative frequency split among all current disk resonator gyros. Finally, the preliminary results for the performance of the CDRG and RDRG in the force-to-rebalance mode and mode matching are given. Under the same conditions, the maximum vibration displacement, scale factor, angular random walk, and bias instability of the CDRG were improved by 62.8%, 112%, 700%, and 314%, respectively, compared with the RDRG.

Analysis and prediction on the cutting process of constrained damping boring bars based on PSO-BP neural network model

Firstly, this paper computed the static and dynamic characteristics of common boring bars and constrained damping boring bars respectively, and the correctness of the computational model in time-frequency domain was also validated by experiments. Modal frequencies of constrained damping boring bars were obviously more than those of common boring bars, which could effectively avoid structural resonance in low frequency and had an obvious advantage in improving anti-vibration performance of boring bars. The absolute value of the maximum vibration acceleration of common boring bars was 13.1 m/s2, while the absolute value of the maximum vibration acceleration of constrained damping boring bars was 9.1 m/s2. The maximum vibration acceleration decreased by 30.5 %. The maximum vibration displacement of common boring bars was 5.2 mm and corresponding frequency was 201 Hz. The maximum vibration displacement of constrained damping boring bars was 2.3 mm and corresponding frequency was 235 Hz. When the analyzed frequency was lower than the frequency with the maximum vibration displacement, the displacement spectrum of common boring bars had more peak values. Thus, it was clear that constrained damping boring bars had an obvious advantage in improving vibration characteristics. The impact of cutting speed, feed rate and back cutting depth on vibration characteristics was studied respectively. Results showed that the vibration of constrained damping boring bars gradually decreased with the increase of cutting speed and gradually increased with the increase of feed rate and back cutting depth. In addition, the amplitude and frequency of vibration displacement spectrum of boring bars were basically unchanged no matter how cutting parameters changed. In order to quickly predict the vibration characteristic, BP neural network and PSO-BP neural network were respectively used to predict the cutting process of boring bars. When the iteration number of BP neural network was 300, iterative error was 0.00015 which was far more than the set target error. When the iteration number of PSO-BP neural network was 215, iterative error was converged to the set target error. Therefore, PSO-BP neural network had an obvious advantage in predicting the cutting process of boring bars. In addition, the predicted result of PSO-BP neural network was consistent with the experimental result, which showed that the neural network model in this paper was effective.

Experimental Study on Interfacial Area Transport of Two-Phase Flow under Vibration Conditions

An experimental study on air-water two-phase flow under vibration condition has been conducted using double-sensor conductivity probe. The test section is an annular geometry with hydraulic diameter of 19.1 mm. The vibration frequency ranges from 0.47 Hz to 2.47 Hz. Local measurements of void fraction, interfacial area concentration (IAC), and Sauter mean diameter have been performed along one radius in the vibration direction. The result shows that local parameters fluctuate continuously around the base values in the vibration cycle. Additional bubble force due to inertia is used to explain lateral bubble motions. The fluctuation amplitudes of local void fraction and IAC increase significantly with vibration frequency. The radial distribution of local parameters at the maximum vibration displacement is specifically analyzed. In the void fraction and IAC profiles, the peak near the inner wall is weakened or even disappearing and a strong peak skewed to outer wall is gradually observed with the increase of vibration frequency. The nondimensional peak void fraction can reach a maximum of 49% and the mean relative variation of local void fraction can increase to more than 29% as the vibration frequency increases to 2.47 Hz. But the increase of vibration frequency does not bring significant change to bubble diameter.

High‐frequency vibration characteristic of Pb 0.97 La 0.02 (Zr 0.95 Ti 0.05 )O 3 anti‐ferroelectric thick films cantilever

A Pb0.97La0.02(Zr0.95Ti0.05)O3 anti-ferroelectric thick-film micro-cantilever applying micro-machining technology based silicon was designed and fabricated to meet the requirements of high-frequency vibration energy application. The anti-ferroelectric cantilevers showed the high-frequency vibration characteristics with the strain generated due to the anti-ferroelectric–ferroelectric transformation. The maximum vibration velocity and displacement of the cantilever tip of 600 μm (L) × 60 μm (W) × 10 μm (H) were 4.22 m/s and 23.5 μm. The first response frequency was up to 28.6 kHz at 42 V transitions voltage induced when the anti-ferroelectric material layer was strained, significantly larger than the typical piezoelectric cantilevers. The five-size different cantilevers fabricated in one chip had mostly the same sharp voltage, owing to the same thickness of anti-ferroelectric material layer. The vibration frequency increased with the decrease of the cantilever length, while the vibration velocity and displacement had the opposite trends. It can be seen that the silicon-based anti-ferroelectric cantilever with a high vibration frequency shows a more incomparable vibration than other cantilevers of other materials, which can be regarded as a new direction for micro-electro-mechanical system vibration devices.

Nonlinear dynamic analysis for coupled vehicle-bridge vibration system on nonlinear foundation

In this paper, the nonlinear dynamics of a parametrically excited coupled vehicle-bridge vibration system (CVBVS) is investigated, and the coupled system is subjected to a time-dependent transverse load including a constant value together with a harmonic time-variant component. The dynamic equations of the CVBVS are established by using the generalized Lagrange's equation. With the Galerkin truncation method, a set of nonlinear ordinary differential equations are derived by discretizing the continuous governing equation. The influences of parametric excitation with nonlinear support stiffness, mass ratio, excitation amplitude and position relation on the dynamic behaviors are studied for the interaction between vehicle and the bridge. The analysis results indicate that the nonlinear dynamic characteristics are strongly attributed to the interaction of the coupled system. Nonlinear support stiffness of foundation and mass ratio can lead to complex dynamic behaviors such as jump discontinuous phenomenon, periodic, quasi-periodic and chaotic motions. Vibration amplitude increases depending on the position, where the maximum vibration displacement does not occur at the center of the bridge. The excitation amplitude has an obvious influence on the nonlinear dynamic behaviors and the increase of the excitation amplitude makes the vibration strengthen. The bifurcation diagram and 3-D frequency spectrum are used to analyze the complex nonlinear dynamic behaviors of the CVBVS. The presented results can provide an insight to the understanding of the vibration characteristics of the coupled vehicle-bridge vibration system in engineering.