Static Load Deflection Research Articles

Additive Manufacturing of Microcantilevers of Varying Stiffness for Sensing Applications

Introduction Microcantilevers have numerous applications in physical, biological and chemical sensing. They have been employed for determination of the fluid viscosity and density [1], detection of biomolecular interaction [2], and part per billion (ppb) level of ammonia in ambient atmosphere [3]. The silicon-based microcantilevers are the most common type of these microdevices, however the biological and physical applications of the polymeric and polymer-composite microcantilevers have been reported in the literature [4], [5]. The polymeric cantilevers have lower Young’s modulus compared to the ones made of silicon and are more sensitive for static deflection measurement [6]. The polydimethylsiloxane (PDMS) and SU-8 are examples of polymers used for fabricating cantilevers through the soft-lithography process. Although the soft-lithography is a matured process for fabrication of the micro-electromechanical systems (MEMS), it is time consuming and costly in comparison with the additive manufacturing process. This may justify further investigations on employing Additive Manufacturing (AM) technologies in fabrication of the MEMS devices. In this study, we report additive manufacturing of the polymeric microcantilevers with different dimensions using SLA 3D printing technology for employing in micro-sensing applications. Method Four 300 μm width microcantilevers with different lengths and thicknesses, were 3D printed using the Form 2 SLA 3D printer. Table 1 presents the dimensions of the cantilevers. Figure 1 shows the images of the green parts on the building platform and the final parts after post processing. 50 μm was chosen as a thickness of each layer for printing. The building material was Flexible resin (Formlabs, USA). Table 2 presents the characteristics of the printing material. The printing process of all cantilevers took 2.5 hours. To investigate the mechanical property of printed cantilevers, the linear stiffness of each part was determined by the static load-deflection tests. The tests were performed by imposing the deflection to the tip of cantilever and recording the corresponding load. The maximum deflection applied to cantilevers was 300 μm. The FemtoTools FT-RS1002 Microrobotic Measurement System was employed to perform the measurements using the mounted sensing probe with the needle tip section size of (50 × 50 μm), force range of ±100000 μN, and resolution of 5 μN. Figure 2 illustrates the front and side views of the sensing probe in contact with the one of cantilevers at the beginning of the measurement test. Results and Conclusions The length and thickness of the microcantilever affect its sensitivity. Figure 3 displays the force-deflection graphs of microcantilevers with different length-thickness ratios obtained from the tests explained in methodology. Due to the small deflection imposed to all plastic microcantilevers with respect to their dimensions, the results show the bilinear response of the cantilevers. The linear relation between the force and the deflection can be observed when the samples deflects beyond the 80 μm. Despite various dimensions of the fabricated microcantilevers, the graph confirms that the length-thickness ratio affects the stiffness of the beams which is determined by the slope of each graphs. Table 3 presents the stiffness of fabricated samples. The graphs show increasing the length-ratio of the microbeams results in increasing the stiffness of the beam. The mechanical stiffnesses of the low length-thickness ratio microcantilevers, samples 1 and 2, are comparable with the PDMS cantilever’s stiffness reported in reference [7] . This reveals the possibility of employing the SLA 3D printing method in fabrication of the operational microcantilevers. This manufacturing method offers the simplicity, time and cost reduction in fabrication of the microcantilevers. References Kim, Deokman, et. al. "Determination of fluid density and viscosity by analyzing flexural wave propagations on the vibrating micro-cantilever." Sensors 17, no. 11 (2017): 2466.Amritsar, Jeetender, et. al. "Conformational detection of heat shock protein through bio-interactions with microstructures." Research on Biomedical Engineering 36, no. 1 (2020): 89-98.Liu, Manyi, et. al. "Revealing humidity-enhanced NH3 sensing effect by using resonant microcantilever." Sensors and Actuators B: Chemical 257 (2018): 488-495.Seena, V., et. al. "Polymer microcantilever biochemical sensors with integrated polymer composites for electrical detection." Solid State Sciences 11, no. 9 (2009): 1606-1611.Sadabadi, Hamid, and Muthukumaran Packirisamy. "Nano-integrated suspended polymeric microfluidics (SPMF) platform for ultra-sensitive bio-molecular recognition of bovine growth hormones." Scientific reports 7, no. 1 (2017): 1-10.Chaudhary, Monika, and Amita Gupta. "Microcantilever-based sensors." Defence Science Journal 59, no. 6 (2009): 634-641.Nezhad, Amir Sanati, et. al. "PDMS microcantilever-based flow sensor integration for lab-on-a-chip." IEEE Sensors journal 13, no. 2 (2012): 601-609. Figure 1

Deflection test and modal analysis of lightweight timber floors

In order to meet the objective requirements of the safety and comfort of the modern lightweight timber floors, and strengthen the research on the coupling performance of the lightweight timber floors vibration characteristics and the building comfort, this article discusses the floor of a two-story prefabricated lightweight timber building demonstration house. In this paper, the floor structure of a two-story light-weight wooden house has been carried out on structural calculation modal and experimental modal, static uniform load and concentrated load deflection value testing. The evaluation of the deflection value of the floor structure, the mode shape, the coupling of the fundamental frequency mode parameters, and the vibration comfort were also studied. The results show that the fundamental frequency simulation value, one-way modal test value and two-way modal test value of the floor structure all meet the requirements of BS-6472 (BS6472-1:2008). That is, the floor structure is not lower than 8 Hz design requirements, and meets the frequency of BS-6472(BS6472-1:2008). The weighted root mean square acceleration is lower than the requirement of 0.45 m/s2; the first three natural frequencies of the floor structure calculated by the finite element simulation are 16.413, 31.847 and 48.921 Hz, and the fundamental frequency mode is the bending vibration in the length and width directions. The second order is the bending mode in the length direction, and the third order is the bending mode in the width direction. The fundamental frequency of the two-way modal test of the floor structure is the first-order bending mode in the X direction; and the second-order natural frequency is the second-order bending vibration shape in the X direction. when the uniform load is mainly the weight of floor own, the simulated maximum deflection value is 1.0658 mm; the simulation is performed according to the standard value of 0.566 kN/m for the uniform load of the floor design, and the simulation is the largest. The maximum deflection value of the simulated floor is 1.47383 mm at its midpoint, which meets the requirements of National Building Code of Canada-2015 (NBCC). The maximum deflection limit of the light wood structure floor system is lower than 3 m and the maximum deflection limit is 2 mm; the six deflection value test lines simulated under a concentrated load of 1 kN all present a parabolic distribution and are symmetrical. The above results has engineering application value for promoting the research on the vibration characteristics of the fabricated lightweight timber floors structure and its optimization design.

Rotordynamic Analysis of Gas Foil-Polymer Bearings Based on a Structural Elasticity Model of Polymer Layer along with Static-Load Deflection Tests

In this study, rotordynamic analysis is performed using a simple structural model for the polymer layer of gas foil-polymer bearing (GFPB) composed of an accumulated bump foil and a polymer layer with high structural damping. The simple model that considers the elastic behavior of a cylinder-shaped polymer layer is introduced, and the structural stiffness of the layer is estimated based on Hooke’s law for differential elements in the layer. In addition, the simple model is coupled with the structural stiffness of the bump foil in consideration with a series relationship, which represents the structural model of GFPBs. A GFPB with thickness of 2 mm is fabricated, and the structural model is validated via static-load deflection tests for the GFPB. As a result of model validation, the proposed model is found to be effective in predicting the elastic behavior under the lightly loaded condition of GFPB. Next, the static performances of GFPBs, namely, gas-film pressure, thickness, and journal positions with respect to different polymer layer thickness, are analyzed to evaluate rotordynamic stability of GFPBs. The results indicate that high thickness yields an increase in damping and a decrease in cross-coupled effects. Specifically, in this study, 3 mm-thick polymer gives the best stability performance given the predicted effective damping results. As a result, this work provides a reasonable model for structural elasticity of GFPBs and lays a foundation for the widespread use of GFPBs.

Research on static and dynamic behaviors of PC track beam for straddle monorail transit system

In this study, in-situ static and dynamic tests of four pre-stressed concrete (PC) track beams with different span lengths and curvatures in a straddle monorail transit system were reported. In the static load tests, the strain and deflection at critical sections of the PC track beams were measured to determine the load bearing capacity and stiffness. The dynamic responses of strain, deflection, acceleration, and displacement at key positions of the PC track beams were measured under different train speeds and train loads to systematically study the dynamic behaviors of the PC track beams. A three-dimensional finite element model of the track beam-vehicle coupled vibration system was established to help understand the dynamic behavior of the system, and the model was verified using the test results. The research results show that the curvature, span length, train speed, and train loads have significant influence on the dynamic responses of the PC track beams. The dynamic performance of the PC track beams in the curve section is susceptible to dynamic loads. Appropriate train loads can effectively reduce the impact of the train on the PC track beam. The PC track beams allow good riding comfort.

Curvature based DAD-method for damage localisation under consideration of measurement noise minimisation

Several research projects on condition assessment of bridges have proven that structural responses from dynamic excitation or static loading are influenced by local damages and thus, could be used for the detection and localisation of damages. Particularly, the curvature of structures is directly depending on their stiffness. In order to localise the discontinuities in curvature lines resulting from damage, this paper uses the so-called Deformation Area Difference Method (DAD), which is based on static load deflection tests on bridge structures. The DAD-method for damage localisation is presented within the paper using a theoretical example, which is then verified by two laboratory experiments. The first experiment consists of a reinforced concrete beam, which is loaded stepwise until failure of the concrete in the compression zone. Due to the load increase, the tensile zone of the beam starts cracking, leading to a stiffness reduction. The application of the DAD-method allows identifying the cracked area from the measurement of the deflection line. However, a challenge and a prerequisite for the applicability of the DAD-method is the highly accurate measurement of the deflection line. Therefore, one of the most modern measurement techniques such as digital photogrammetry is applied. Nonetheless, the accuracy of each measurement technique is limited. The second laboratory experiment consists of a steel beam, which is locally damaged at three positions. The degree of the damage is stepwise increased in order to identify at which degree of damage the applied DAD-method is still able to identify and localise damage.In this work, the focus lies on the minimisation of the effect of noise resulting from the limited measurement precision. Possible solutions were examined and proposed based on methods such as data smoothing using polynomial regression, consideration of standard deviation and measurement point variation. The reduction of the noise effect leads to an increase in the sensitivity of the damage localisation. The DAD-method has proven its potential for practical application through the successful localisation of cracking in the concrete beam.

Design & Manufacture of a High-Performance Bicycle Crank by Additive Manufacturing

A new practical workflow for the laser Powder Bed Fusion (PBF) process, incorporating topological design, mechanical simulation, manufacture, and validation by computed tomography is presented, uniquely applied to a consumer product (crank for a high-performance racing bicycle), an approach that is tangible and adoptable by industry. The lightweight crank design was realised using topology optimisation software, developing an optimal design iteratively from a simple primitive within a design space and with the addition of load boundary conditions (obtained from prior biomechanical crank force–angle models) and constraints. Parametric design modification was necessary to meet the Design for Additive Manufacturing (DfAM) considerations for PBF to reduce build time, material usage, and post-processing labour. Static testing proved performance close to current market leaders with the PBF manufactured crank found to be stiffer than the benchmark design (static load deflection of 7.0 ± 0.5 mm c.f. 7.67 mm for a Shimano crank at a competitive mass (155 g vs. 175 g). Dynamic mechanical performance proved inadequate, with failure at 2495 ± 125 cycles; the failure mechanism was consistent in both its form and location. This research is valuable and novel as it demonstrates a complete workflow from design, manufacture, post-treatment, and validation of a highly loaded PBF manufactured consumer component, offering practitioners a validated approach to the application of PBF for components with application outside of the accepted sectors (aerospace, biomedical, autosports, space, and power generation).

In-Plane Flexible Ring Tire Model—Part 1: Modeling and Parameter Identification

ABSTRACT The tire model is essential for accurate and efficient vehicle dynamic simulation. In this article, an in-plane flexible ring tire model is proposed, in which the tire is composed of a rigid rim, a number of discretized lumped mass belt points, and numerous massless tread blocks attached on the belt. One set of tire model parameters is identified by approaching the predicted results with ADAMS® FTire virtual test results for one particular cleat test through the particle swarm method using MATLAB®. Based on the identified parameters, the tire model is further validated by comparing the predicted results with FTire for the static load-deflection tests and other cleat tests. Finally, several important aspects regarding the proposed model are discussed.

Influence of steel–concrete bond damage on the dynamic stiffness of cracked reinforced concrete beams

In this article, experiments focusing at the influence of steel–concrete bond damage on the dynamic stiffness of cracked reinforced concrete beams are reported. In these experiments, the bond between concrete and reinforcing bar was damaged using appreciate flexural loads. The static stiffness of cracked reinforced concrete beam was assessed using the measured load–deflection response under cycles of loading and unloading, and the dynamic stiffness was analyzed using the measured natural frequencies with and without sustained loading. Average moment of inertia model (Castel et al. model) for cracked reinforced beams by taking into account the respective effect of bending cracks (primary cracks) and the steel–concrete bond damage (interfacial microcracks) was adopted to calculate the static load–deflection response and the natural frequencies of the tested beams. The experimental results and the comparison between measured and calculated natural frequencies show that localized steel–concrete bond damage does not influence remarkably the dynamic stiffness and the natural frequencies both with and without sustained loading applied. Castel et al. model can be used to calculate the dynamic stiffness of cracked reinforced concrete beam by neglecting the effect of interfacial microcracks.

Performance Measurements of Gas Bearings With High Damping Structures of Polymer and Bump Foil Via Electric Motor Driving Tests and One Degree-of-Freedom Shaker Dynamic Loading Tests

This paper presents comprehensive test measurements for gas journal bearings with damping structures of a bump foil layer and/or a polymer layer. A one-pad top foil forms the bearing surface, under which the bearing structure and a bearing housing are located. Test bearings include gas foil bearings (GFBs), gas polymer bearings (GPBs), and gas foil-polymer bearings (GFPBs). In addition, three metal shims were employed to create wedge effects in the GFPBs. First, static load-deflection tests of test bearings estimate the radial assembly clearance. Second, shake dynamic loading tests identify frequency-dependent dynamic characteristics. An electromagnetic shaker provides flat bearing specimens with one degree-of-freedom (1DOF) vertical dynamic loading. GFPB was measured to exhibit a higher structural damping and lower stiffness than GFB. Lastly, the electric motor driving tests examine the rotordynamic stability performance. A permanent magnet (PM) synchronous motor drives a PM rotor supported on a pair of test journal bearings. As a result, the GFPBs with mechanical preloads enhanced the rotordynamic performance with no subsynchronous motions up to the maximum rotor speed of 88 krpm, and the bearing friction characteristics as well. Furthermore, they showed comparable rotordynamic performance to three-pad GFBs from a past literature, even with larger bearing clearances and small mechanical preloads.

Finite element simulation of carbon fibre-reinforced composite laminates subjected to low velocity impact using damage induced static load-deflection methodology

This work is concerned with the prediction of low velocity impact damage resistance of carbon fibre-reinforced laminated composite laminates. Pre-assumed damage induced laminates were simulated to correlate damage corresponding to impactor nose profiles. Majority of the existing studies conducted on the topic are experimental, based on three-dimensional stresses and failure theories that cannot readily predict ply level impact damage. Hence efficient computational models are required. The present study was conducted to efficiently predict ply level impact response of composite laminates. Static load-deflection based computational model was developed in the commercial software ABAQUSTM. Eight, 16, and 24 ply laminates impacted by point, small, medium, and flat nose impactors were considered with emphasis on flat nose impacts. Loading areas under the impactor nose profiles were partitioned to investigate effects from variations in applied loading. Pre-assumed damage zones consisting of degraded material properties equivalent to the impactor nose profiles were inserted across thickness of the laminates to predict ply-by-ply damage. Impactor nose profiles and pre-assumed damage zones (size, type, and location) were correlated to the simulation produced deflection quantities to predict the ply level damage. Selected results were compared against the data available in the literature and also against the intra-simulation results and found in good agreement.

함정탑재장비용 대용량 마운트의 성능시험평가

Mounts for shipboard equipment in naval ships play an important role for vibration and shock suppression. New large-capacity resilient mounts, SDR-D30 and SDR-D45, have been developed. This paper involves performance tests for the mount which have maximum load of 30 kN and 45 kN, respectively. The performance tests have been carried out for several mounts based on military standards, such as MIL-M-19863D(SH), MIL-M-21693C(SH), MIL-M-17508F(SH), and MIL-S-901D(NAVY). The test items consist of deflection at upper rate load test, dynamic stiffness, uniformity, static load-deflection(axial, transverse and longitudinal), drift test, fatigue test, and shock test. From these performance tests, it is confirmed that the two mounts have good performances based on military standards.

Seismic behaviour of a through-beam connection between concrete-filled steel tubular columns and reinforced concrete beams

Abstract This paper aims to investigate the seismic and post-seismic behaviour of a new and innovative type of through-beam connection between a concrete-filled steel tubular (CFST) column and a reinforced concrete (RC) beam. In this new connection system, the steel tube is completely or partially cut with the cut or openings being at the corresponding beam location, with the longitudinal steel reinforcing bars for the beam remaining continuous through the connection region. A strengthening ring beam is used to enlarge the connection zone in order to compensate for the possible decrease of the axial load carrying capacity as a result of the discontinuity of the steel tube that encases the column. Cyclic loading tests and subsequent axial compressive tests are reported on six beam–column specimens. Based on the experimental results, the hysteretic response, the skeletal and post-cyclic static load–deflection curves, the strain, ductility, strength and the stiffness degradation and energy dissipation are discussed. The favourable seismic performance of the connection is demonstrated in the tests. A finite element model is then developed and validated by a comparison with the experimental results. The relative effects of the reinforcement ratio of the frame beam and the ring beam, and the axial compressive force in the column on the seismic behaviour of the connection are elucidated through parametric studies.

Rotordynamic Performance of Shimmed Gas Foil Bearings for Oil-Free Turbochargers

Oil-free turbochargers (TCs) will increase the power and efficiency of internal combustion engines, both sparking ignition and compression ignition, without engine oil lubricant feeding or scheduled maintenance. Using gas foil bearings (GFBs) in passenger vehicle TCs enables compact, lightweight, oil-free systems, along with accurate shaft motion. This paper presents extensive test measurements on GFBs for oil-free TCs, including static load-deflection measurements of test GFBs, rotordynamic performance measurements of a compressed air driven oil-free TC unit supported on test GFBs, and bench test measurements of the oil-free TC driven by a passenger vehicle diesel engine. Two configurations of GFBs, one original and the other modified with three shims, are subjected to a series of experimental tests. For the shimmed GFB, three metal shims are inserted under the bump-strip layers, in contact with the bearing housing. The installation of shims creates mechanical preloads that enhance a hydrodynamic wedge in the assembly radial clearance to generate more film pressure. Simple static load-deflection tests estimate the assembly radial clearance of the shimmed GFB, which is smaller than that of the original GFB. Model predictions agree well with test data. The discrepancy between the model predictions and test data is attributed to fabrication inaccuracy in the top foil and bump strip layers. Test GFBs are installed into a TC test rig driven by compressed air for rotordynamic performance measurements. The test TC rotor, 335 g in weight and 117 mm long, is coated with a commercially available, wear-resistant solid lubricant, Amorphous M, to prevent severe wear during start-up and shutdown in the absence of an air film. A pair of optical proximity probes positioned orthogonally at the compressor end record lateral rotor motions. Rotordynamic test results show that the shimmed GFB significantly diminishes the large amplitude of subsynchronous rotor motions arising in the unmodified GFB. Predicted synchronous rotor amplitudes and rigid body mode natural frequencies agree reasonably well with recorded test data. Finally, the oil-free TC is installed into a passenger vehicle diesel engine test bench. The TC rotor speed is controlled by the vehicle engine. Speed-up tests show dominant synchronous motion (1X) of the rotor. Whirl frequencies of the relatively small subsynchronous motions are associated with the rigid body natural mode of the TC rotor-GFB system as well as (forced) excitation from the four-cylinder diesel engine. The bench test measurements demonstrate a significant reduction in the amplitude of subsynchronous motions for the shimmed GFB, thus verifying the preliminary test results in the TC test rig driven by compressed air.

Effects of Material Properties on Static Load-Deflection and Vibration of a Non-Pneumatic Tire During High-Speed Rolling

Effects of Material Properties on Static Load-Deflection and Vibration of a Non-Pneumatic Tire During High-Speed Rolling

Static and Cyclic Load-Deflection Characteristics of NiTi Orthodontic Archwires Using Modified Bending Tests

Near-equiatomic nickel-titanium (nitinol) has the ability to return to a former shape when subjected to an appropriate thermomechanical procedure. One of the most successful applications of nitinol is orthodontic archwire. One of the suitable characteristics of these wires is superelasticity, a phenomenon that allows better-tolerated loading conditions during clinical therapy. Superelastic nitinol wires deliver clinically desired light continuous force enabling effective tooth movement with minimal damage for periodontal tissues. In this research, a special three-point bending fixture was invented and designed to determine the superelastic property in simulated clinical conditions, where the wire samples were held in the fixture similar to an oral cavity. In this experimental study, the load-deflection characteristics of superelastic NiTi commercial wires were studied through three-point bending test. The superelastic behavior was investigated by focusing on bending time, temperature, and number of cycles which affects the energy dissipating capacity. Experimental results show that the NiTi archwires are well suited for cyclic load-unload dental applications. Results show reduction in superelastic property for used archwires after long-time static bending.

Design of Bio-inspired Flexible Wings for Flapping-Wing Micro-sized Air Vehicle Applications

The unmatched performance of insect flight is a motivation for bio-inspired designs of synthetic wings that can undergo large deformations in flapping flight. In this paper, we experimentally study the aerodynamic performance of a bio-inspired flexible flapping wing, which has the static load–deformation characteristics of a hawkmoth (Manduca sexta) wing, and compare it with a similar geometry rigid wing. The bio-inspired wing is designed using finite element analysis, coupled with an optimization solver, to match the static load–deflection characteristics of the synthetic wing with that of real hawkmoth wings. A flexible synthetic wing is constructed using a combination of materials (carbon, nylon and rubber) for the veins and a latex membrane. The aerodynamic performance of the synthetic deformable wing is tested on a robotic flapper, using commonly observed kinematic templates of insect flapping (and rotation). Our results show increased thrust by the flexible wing for all kinematic patterns in comparison to the rigid wing. A host of important advantages provided by wing flexibility are mentioned in the context of flapping flight.

Integrated Tracking and Focusing Systems of MEMS Optical Pickup Head

This paper presents a novel bidirectional-driven microelectromechanical systems (MEMS) light manipulation stage. The designed device consists of two actuators integrated with a lens to act as both tracking (in-plane) and focusing (out-of-plane) components for optical pickup head. The actuator is driven by thermal, as well as magnetic, means. According to a static-load deflection test, this device can achieve bidirection actuation with output displacement up to plusmn54.5 mum. In addition, this MEMS device has a very small form factor and provides an excellent response time and size reduction. It can be employed on the portable optical storage system

Micromechanical testing of SU‐8 cantilevers

ABSTRACTSU‐8 is a photoplastic polymer with a wide range of possible applications in microtechnology. Cantilevers designed for atomic force microscopes were fabricated in SU‐8. The mechanical properties of these cantilevers were investigated using two microscale testing techniques: contact surface profilometer beam deflection and static load deflection at a point on the beam using a specially designed test machine. The SU‐8 Young's modulus value from the microscale test methods is approximately 2–3 GPa.

OS06W0411 Micromechanical testing of SU-8 cantilevers

SU-8 is a photoplastic polymer with a wide range of applications in microtechnology. Cantilevers designed for a commercial Atomic Force Microscope (AFM) were fabricated in SU-8. The mechanical properties of these cantilevers were investigated using two microscale mechanical testing techniques: contact surface profilometer deflection, known as MAT-Test, and static load deflection using a specially designed test machine, the MFT2000. The Young's modulus values from the microscale test methods are approximately 2-3 GPa. These results are compared with results from macroscale tests of 4-5 GPa. The test methods and the results are discussed.

A reliable single-layer out-of-plane micromachined thermal actuator

Out-of-plane electrothermal actuators have been applied to a variety of fields with the bimorph effect being the most commonly used driving method, due to simple fabrication process. However, such an actuator experiences a shear force at the interface of different materials, while actuated. Delamination therefore takes place and decreases its lifetime. In this study, a novel bi-directional out-of-plane electrothermal actuator is designed and fabricated. Unlike the bi-metal and hot–cold arm thermal actuator, this actuator can move in two directions. Since this actuator is consisted of only single-layer thin film material, it can prevent from delamination. According to the static load–deflection test, this actuator can achieve bi-directional actuation with amplitude near 6–7 μm when driven at 5 V. According to the vibration test, the dynamics of the actuator is influenced not only by the thermal characteristics but also by the vibration modes. Consequently, the thermal actuator still has a significant output when driven near 40 kHz. The actuator were experienced a fatigue test which shows that its resonant frequency remains unchanged after 109 cycles of continuous operation with driving voltage at 2.25 V.