Transient bending waves in plates studied by hologram interferometry

Propagating bending waves are studied in plates made of aluminum and wood. The waves are generated by the impact of a ballistic pendulum. Hologram interferometry, with a double pulsed ruby laser as the light source, is used to record the out of plane motion of the waves. Elliptic-like fringes visualize differences in wave speed for different directions in the anisotropic plate and circular ones are obtained for the isotropic plate. The experimental data for the isotropic plate compare favorably with analytical results derived from the Kirchhoff-plate equation with a point impact of finite duration. A similarity variable is found when starting conditions are modeled as a Dirac pulse in space and time, that brings new understanding to the importance of specific parameters for wave propagation in plates. A formal solution is obtained for a point force with an arbitrary time dependence. For times much larger than the contact time, the plate deflection is shown to be identical to that from a Dirac pulse applied at the mean contact time. A method for determining material parameters, and the mean contact time, from the interferograms is hence developed.     

Development, modeling and deflection analysis of hybrid micro actuator with integrated thermal and piezoelectric actuation

Micro actuators are irreplaceable part of motion control in minimized systems. The current study presents an analytical model for a new Hybrid Thermo Piezoelectric micro actuator based on the combination of piezoelectric and thermal actuation mechanisms. The micro actuator structure is a double PZT cantilever beam consisting of two arms with different lengths. The presented micro actuator uses the structure of electrothermal micro actuator in which polysilicon material is replaced by PZT. Also the voltage and poling directions are considered in the lengthwise of PZT beams. As a result, the piezoelectric actuation mechanism is based on d ₃₃ strain coefficient. The tip deflection of micro actuator is obtained using Timoshenko beam theory. Analytical results are compared with FEM results along with other reported results in the literature. The effects of geometrical parameters and PZT material constants on actuator tip deflection are studied to provide an efficient optimization of HTP micro actuator.     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

Determining the contact force during the transverse impact of plates

The contact force during the transverse impact of a plate is determined from dynamic strain-gage measurements made on the plate. Experimental results for the impact of an aluminum plate are presented, and comparisons are made with finite-element predictions and measurements from a force transducer. Paper was presented at the 1986 Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

Modeling and simulation of a novel vertical actuator based on electrowetting on dielectric

A novel vertical actuator based on electrowetting on dielectric （EWOD） was designed, analyzed and simulated. Modeling results indicated that the vertical driving force of the actuator obeyed a second order polynomial of applied voltage, which was verified by Covent_ware 2006. As a resuit, the vertical driving force of the EWOD actuator with a 1.1 nL droplet and a 1.75 μm thick polymer was about 0.5 μN under an applied voltage 100V which was comparable to that of the electrostatic actuators. Moreover, the noise from plane forces we analyzed and simulated was very low. Therefore, we made a conclusion that the EWOD actuator can be used in MEMS transducer.     

FINITE ELEMENT MODELING AND ROBUST VIBRATION CONTROL OF TWO-HINGED PLATE USING BONDED PIEZOELECTRIC SENSORS AND ACTUATORS

Active vibration control for a kind of two-hinged plate is developed in this paper. A finite element model for the hinged plate integrated with distributed piezoelectric sensors and actuators is derived, including bending and torsional modes of vibration. In this model, the hinges are simplified as regular plate elements to facilitate operation. The state space representations for bending and torsional vibrations are obtained. Based on two low-order models of the bending and torsional motion, two H ∞ robust controllers are designed for suppressing the vibrations of the bending and torsional modes, respectively. The simulation results indicate the effectiveness and feasibility of the designed H ∞ controllers. The vibration magnitudes of the low-order modes can be reduced without affecting the high frequency modes.     

Bending and vibration of two-dimensional decagonal quasicrystal nanoplates via modified couple-stress theory

Based on the modified couple-stress theory, the three-dimensional(3D)bending deformation and vibration responses of simply-supported and multilayered twodimensional(2D) decagonal quasicrystal(QC) nanoplates are investigated. The surface loading is assumed to be applied on the top surface in the bending analysis, the tractionfree boundary conditions on both the top and bottom surfaces of the nanoplates are used in the free vibration analysis, and a harmonic concentrated point loading is applied o...     

滑移爆轰驱动下飞板运动姿态的连续电阻测试法

飞板运动姿态的测定是爆炸焊接机理研究的基础,针对传统电测方法存在干扰因素多、易产生弯曲波等缺陷,设计了一种适用于野外大当量下爆炸焊接飞板姿态实验的连续电阻测试方法。研制了3种不同结构的梯形支架型连续电阻探针元件,利用有限元程序分析了探针的导通压力和响应时间,在此基础上,对3种探针实施了爆炸焊接实验,实验结果表明:金属丝网型探针元件具有最优的导通效果,各段测试曲线光滑无毛刺。以该探针数据计算获得了待测飞板的运动姿态曲线,并与Richter简化模型下的近似计算公式结果进行了对比,两者基本一致。所述测试方法实现了炸药爆速和飞板变形曲线的连续、可靠和快速测量,为滑移爆轰驱动问题、爆轰产物状态方程等的研究提供了测试方法补充。     

Experimental and numerical investigations of the responses of a cantilever beam possibly contacting a deformable and dissipative obstacle under harmonic excitation

In this paper, the dynamics of a cantilever beam subjected to harmonic excitations and to the contact of an obstacle is studied with the help of experimental and numerical investigations. The steel flexible structure is excited close to the free end with a shaker and may come into contact with a deformable and dissipative obstacle. A technique for modeling contact phenomena using piece-wise linear dynamics is applied. A finite-dimensional modal model is developed through a Galerkin projection. Concentrated masses, dampers and forces are considered in the equations of motion in such a way that the boundary conditions are those of a cantilever beam. Numerical studies are conducted by assuming finite-time contact duration to investigate the frequency response of the impacted beam for different driving frequencies. Experimental results have been extrapolated through a displacement laser sensor and a load cell. The comparison between numerical and experimental results show many qualitative and quantitative similarities.The novelty of this paper can be synthetized in (a) the development of experimental results that are in good agreement with the numerical implementation of the introduced model; (b) the development of a comprehensive contact model of the beam with an unilateral, deformable and dissipative obstacle located close to the tip; (c) the possibility of accounting for higher modes for the cantilever beam problem, and hence of analyzing how the response varies when moving the excitation (and/or the obstacle) along the beam, and of investigating the effect of the linearly elastic deformability of the built‐in end of the beam; (d) an easy and intuitive solution to the problem of accounting for spatially singular masses, dampers, springs and forces in the motion equations; (e) the possibility of accounting for finite gap and duration of the contact between beam and obstacle.     

A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.     

滑轨导向式静/动态双轴拉伸实验技术

基于液压伺服高速加载系统,发展了一种材料双轴拉伸力学性能测试技术。利用锥面接触导向驱动方法,把加载锤竖直方向的驱动力转化为水平方向的双轴驱动力,从而实现对十字形试样平面双轴加载。借助有限元数值模拟手段优化了锥面接触角和十字形试样尺寸。当接触锥角为45°时,既有较好的水平驱动转化效率,同时又保持较小的接触力,确保水平驱动加载各组件在弹性变形范围内,可多次重复使用。确定了加载臂狭缝个数、狭缝与减薄区边缘长度和标距段厚度等试样设计关键参数,在十字形试样测试标距段内实现了均匀变形。设计了测力夹持一体化导杆和非接触光学全场应变测试系统,准确获得了试样的应力和应变。利用此平面双轴拉伸加载装置,开展2024-T351铝合金板单轴拉伸实验和激光探测同步性验证实验,验证装置设计的可行性;开展铝合金板材在不同加载速率下的双轴拉伸实验,得到在双轴加载下铝合金板材应力应变曲线,并与单轴加载下实验结果进行了对比分析。     

Measuring the Elastic Properties of Freestanding Thick Films Using a Nanoindenter-Based Bending Test

Films with thickness ranging from 10 to 100 μm are increasingly being used as the structural components of microelectromechanical systems (MEMS). Measuring the mechanical properties of these thick films is essential for enabling the design of MEMS with high performance and sufficient reliability. In this paper, we present a simple and convenient method for measuring the elastic modulus of thick films by loading a clamped circular film using a spherical tip. The test is implemented using a commercial nanoindenter so that the load and displacement can be measured with resolution of micronewtons and nanometers, respectively. Robust protocols have been developed for implementing the test within the constraints imposed by the nanoindenter. A crucial component of these protocols is a method for selecting loads to ensure deformation in the elastic bending regime and to minimize the relative contribution of contact indentation. The accuracy and utility of the nanoindenter-based bending test are discussed using measurements on thick films of aluminum and a standard epoxy.     

Practical method of reducing turning motion resistance of tracked vehicles

A practical method of reducing the resistance of a tracked vehicle to turning or steering motion is discussed. The torque of the sprocket shaft for driving the crawler was measured and used to evaluate how the resistance varied compared with the existing method to turning. There are two ways of reducing the turning resistance by decreasing the contact area of track; one is to decrease the width of the braked track and the other is to shorten its contact length during turning or steering motion. The former is practically impossible to control, but the latter is comparatively easy to do, even under that condition. Applying this mechanism, the resistant force (evaluated by measuring the driving torque of the sprocket shaft) could be reduced about 20% when the contact length of the braked track was shortened to form a small pivot area at its center. It was also reduced more than 50% when the contact length of both tracks was shortened to a pivot during turning motion.     

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip, and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage is covered by a compliant material that is periodically impacted by the cantilever’s tip. Building on their earlier work, wherein the authors showed that period-doubling bifurcations associated with near-grazing impacts occur during off-resonance base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces are modeled as Derjaguin–Muller–Toporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change observed with the addition of noise is associated with near-grazing impacts between the tip and the sample. The numerical and experimental results further motivate the formulation of a general analytical framework, in which the Fokker–Planck equation is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived from the Fokker–Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate that noise can be added to the input to facilitate contact between the cantilever’s tip and the surface, when there was previously no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM application, and it is shown that contact between the tip and the sample can be realized by adding noise of an appropriate level to a harmonic excitation.     

扁壳结构弯曲与扭转振动控制试验研究

扁壳结构的弯曲与扭转振动控制对该类结构的应用具有重要意义。本文采用不影响壳体结构的粗压电纤维复合材料(MFC)作动器对其弯曲与扭转振动进行主动控制。建立局部表面粘贴MFC作动器的开口圆柱扁壳的动力学解析模型,得到了作动力和作动力矩的解析表达式,分析了扁壳结构上MFC作动器在弯曲与扭转振动控制中的作动机理。针对一开口碳纤维圆柱扁壳,设计了模糊PD控制器,开展了定频与随机激励下壳体弯曲与扭转振动控制试验,并与传统PD控制试验效果进行了对比。结果表明:MFC作动器在壳体弯曲和扭转振动控制方面作动能力突出;模糊PD控制器的控制效果优于传统PD控制器的控制效果。     

Validation of actuator disc circulation distribution for unsteady virtual blades model

The actuator disc method is an engineering approach to reduce computer resources in computational fluid dynamics (CFD) simulations of helicopter rotors or aeroplane propellers. Implementation of an actuator disc based on rotor circulation distribution allows for approximations to be made while reproducing the blade tip vortices. Radial circulation distributions can be formulated according to the nonuniform Heyson-Katzoff “typical load” in hover. In forward flight, the nonuniform disk models include “azimuthal” sin and cos terms to reproduce the blade cyclic motion. The azimuthal circulation distribution for a forward flight mode corresponds to trimmed conditions for the disk rolling and pitching moments. The amplitude of the cos harmonic is analysed and compared here with presented in references data and CFD simulations results.     

Scattering coefficient reconstruction in plates using focused acoustic beams

A method has been developed and proven using highly focused acoustic beams that allows for the rapid reconstruction of scattering coefficients of a thin anisotropic plate immersed in liquid. In a single bistatic coordinate scan, nearly the entire range of wave number within the spatial and temporal frequency bandwidth of the transducer can be reconstructed. This paper also reports the development of a multiple-source complex transducer point model that includes all extrinsic factors and permits prediction of the wave number-frequency (k–f) domain result obtained from a scan of focused transducers in a pitch-catch reflection or transmission arrangement. Extensive experiments have been performed to test the method and the model and to demonstrate transducer beam effects on the k–f domain results, leading to a very efficient method for mapping major portions of the guided wave dispersion spectrum in thin-plate media. As a demonstration of the technique, an estimate of material elastic properties in an isotropic and a transversely-isotropic plate is reported, making only minimal use of the highly redundant dispersion data. Acoustic velocities inferred from these experiments show a disparity of less than 3% from contact acoustic estimates of the same parameters in either plate.     

Crack propagation in wedged double cantilevered beam specimens

A closed form analytical solution of crack propagation in double cantilevered beam specimens opened at a constant rate has been found. Hamilton's principle for non-conservative systems was applied to describe the crack motion, under the assumption of a Bernoulli-Euler beam. The criterion of crack propagation is a critical bending moment at the crack tip. The calculations of beam motion take into account wave effects in the Bernoulli-Euler theory of elastic beams. The beam shape during the crack motion is found with a similarity transformation and expressed by Fresnel integrals. The boundary conditions satisfied are the fixed ones of zero bending moment and constant beam opening rate at the load end of the specimen and the moving ones of zero deflection and zero slope of the deflected beam at the tip of the moving crack. The fracture represents a moving critical bending moment. The analytical results show that the specific fracture surface energy is a unique function of the ratio of the crack length squared to the time subsequent to loading and this is computed from the recorded time-dependence of the crack length.     

Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrödinger equation

Modern methods of nonlinear dynamics including time histories, phase portraits, power spectra, and Poincaré sections are used to characterize the stability and bifurcation regions of a cantilevered pipe conveying fluid with symmetric constraints at the point of contact. In this study, efforts are made to demonstrate the importance of characterizing the system at the arbitrarily positioned symmetric constraints rather than at the tip of the cantilevered pipe. Using the full nonlinear equations of motion and the Galerkin discretization, a nonlinear analysis is performed. After validating the model with previous results using the bifurcation diagrams and achieving full agreement, the bifurcation diagram at the point of contact is further investigated to select key flow velocities of interest. In addition to demonstrating the progression of the selected regions using primarily phase portraits, a detailed comparison is made between the tip and the point of contact at the key flow velocities. In doing so, period doubling, pitchfork bifurcations, grazing bifurcations, sticking, and chaos that occur at the point of contact are found to not always occur at the tip for the same flow speed. Thus, it is shown that in the case of cantilevered pipes with constraints, more accurate characterization of the system is obtained in a specified range of flow velocities by characterizing the system at the point of contact rather than at the tip.     

Experimental investigation of a single-degree-of-freedom system with Coulomb friction

This paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.