Active boundary control of vibrating marine riser with constrained input in three-dimensional space

In this paper, the effects of initial deflection on the static and dynamic behaviors of circular capacitive transducers are experimentally investigated. The obtained results are in good agreement with numerical simulations. It is shown that the initial deflection has a major impact on the static response of the resonator by shifting the pull-in voltage, and on its dynamic response by increasing the resonance frequency and modifying the bifurcation topology from softening to hardening behavior. Moreover, the dynamic behavior of the microplate may display nonlinear periodic and quasiperiodic responses due to geometric and electrostatic nonlinearities.

     

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvature-dominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.     

Free and forced nonlinear oscillations of a two-layer composite beam with interface slip

Free and forced flexural nonlinear vibrations of a two-layer beam are investigated. Each beam is assumed to have Euler?CBernoulli kinematics and free-free boundary conditions. The interface allows only nonlinear elastic slip between adjacent sides of the beams, so that the transversal displacement is unique. Free vibrations are considered first by the multiple time scale method, which allows to determine the amplitude dependent nonlinear natural frequencies of the system. It is shown that the nonlinear coefficient of the backbone curve is positive, so that hardening/softening behavior of the interface generates hardening/softening behavior of the whole structure. The modifications of the linear normal modes for moderate excitation amplitudes have been computed. Forced and damped nonlinear oscillations are then considered by the same mathematical method, and the nonlinear frequency response curves are obtained.     

Thermomechanical transitions in doubly-clamped micro-oscillators

The small size and low damping of MEMS oscillators give rise to phenomena that are not observed routinely at the macroscopic scale. In this work we document and explain an experimentally observed transition in the response of a doubly clamped micromechanical oscillator with pretension. The transition from softening to hardening is repeatedly observed upon increasing the power of an incident sensing laser beam, a procedure routinely used to improve signal strength during optical detection of resonant motion of microstructures. At intermediate laser power, a novel resonant response that displays characteristics of both softening and hardening in the same sweep, is observed experimentally. Increased laser heating of a structure in tension may be expected to increase softening behavior. Using tools from non-linear dynamics and continuum mechanics, we show that the observed counter-intuitive behavior can be explained by a competition between the opposing responses of linear and non-linear stiffnesses to a change in temperature.     

Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect

The nonlinear modal coupling in a T-shaped piezoelectric resonator, when the former two natural frequencies are away from 1:2, is studied. Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior. The first primary resonance of the vertical beam, owing to modal coupling, exhibits an abrupt amplitude increase, namely the Hopf bifurcation. The frequency comb phenomenon induced by modal coupling is measured experimentally. A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon. The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.

     

Analysis of the localization of deformation and the complete stress–strain relation for mesoscopic heterogeneous brittle rock under dynamic uniaxial tensile loading

Stress redistribution induced by excavation results in the tensile zone in parts of the surrounding rock mass. It is significant to analyze the localization of deformation and damage, and to study the complete stress–strain relation for mesoscopic heterogeneous rock under dynamic uniaxial tensile loading. On the basis of micromechanics, the complete stress–strain relation including linear elasticity, nonlinear hardening, rapid stress drop and strain softening is obtained. The behaviors of rapid stress drop and strain softening are due to localization of deformation and damage. The constitutive model, which analyze localization of deformation and damage, is distinct from the conventional model. Theoretical predictions have shown to consistent with the experimental results.     

Dynamic limit analysis formulation for impact simulation of structural members

This paper introduces an extended concept of limit analysis to deal with the dynamic equilibrium condition considering the inertia and strain-rate effect for dynamic behavior of structures. The conventional limit analysis method has been applied to only static collapse analysis of structures without consideration of dynamic effects in the structural behavior. A dynamic formulation for the limit analysis has been derived for incremental analysis dealing with time integration, strain and stress evaluation, strain hardening, strain-rate hardening and thermal softening. The time dependent term in the governing equation is integrated with the WBZ-α method. The dynamic material behavior is described by the Johnson–Cook model in order to consider strain-rate hardening and thermal softening as well as strain hardening. Simulations have been carried out for impact analysis of a Taylor bar and an S-rail and their numerical results are compared with elasto-plastic explicit analysis results by LS-DYNA3D. Comparison demonstrates that the dynamic finite element limit analysis can predict the crashworthiness of structural members effectively with less effort and computing time than the commercial code compared. The crashworthiness of a structure with the rate-dependent constitutive model is also compared to that with the quasi-static constitutive relation in order to investigate the dynamic effect on deformation of structures.     

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.     

旋转内接功能梯度材料梁刚柔热耦合动力学特性研究

对具有旋转内接功能梯度材料(functionally graded material,FGM) 梁系统的刚柔热耦合动力学特性进行研究。假定梁为Euler–Bernoulli 型,由双组分材料制成,其力学性能参数沿厚度方向呈幂律变化。考虑柔性梁的横向弯曲变形和轴向拉伸变形,并计入横向弯曲引起的纵向缩短,即非线性耦合项。采用假设模态法离散柔性梁的变形场,运用第二类 Lagrange 方程推导出系统的一次近似刚柔热耦合动力学方程,并编制旋转内接FGM梁动力学仿真软件。然后通过仿真算例详细研究了各种无量纲参数及温度变化对系统固有频率、临界转速以及动力学特性的影响。研究表明：内接FGM梁的径长比、功能梯度系数以及温度变化对系统的动力学特性均有较大影响。

     

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler–Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.     

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator(QCR)in thickness-shear vibrations with the upper surface covered by an array of micro-beams(MBs)under large deflection.Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator,dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations.It is found that the frequency shift produces a little right(left)translation for increasing elastic modulus(length/radius ratio)of MBs.Moreover,the frequency right(left)translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one.     

匀速转动内悬臂梁稳定性研究

本文采用了凯恩简化模型并提出大范围平动和转动共同作用下的连续体梁模型;通过两种模型分析了匀速转动内悬臂梁的稳定性;指出了匀速转动内悬臂梁存在动力柔化现象,动力柔化的原因在于梁的大范围平动;提出了匀速转动内悬臂梁的内转半径和外转半径的概念,指出匀速转动内臂梁的内转半径和外转半径比值存在一定关系时,系统为一阶稳定,研究表明,同时作大范围平动和转动的柔性梁存在柔化和刚化的分界点,需要在实际应用中予以注意。     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

Q345钢和H62黄铜声发射信号及力学行为的关系研究

本文利用声发射装置采集了Q345钢和H62黄铜两种材料拉伸过程中的动态声信号。结果发现两种材料在线弹性阶段末端都会产生大量声发射信号,但有明显屈服流动的Q345钢在硬化阶段的开始时段也会产生信号峰值。为了研究两种材料在拉伸变形过程中声发射的微观机制,本文采用扫描电镜下原位拉伸实验方式观察了两种材料在不同拉应力下晶粒内部滑移线的产生和演变过程。在此基础上总结出了两种材料声发射信号与力学行为的关系,指出应以第一次声发射信号的峰值对应的工作应力作为材料屈服应力及其合理性,并按此标准给出H62黄铜的屈服应力为193MPa。     

Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The model takes into account geometric, inertia, and piezoelectric nonlinearities. A combination of the Galerkin technique, the extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple scales is used to determine analytical expressions for the tip deflection, output voltage, and harvested power near the first global natural frequency. The results show that one- or two-mode approximations are not sufficient to produce accurate estimates of the voltage and harvested power. A parametric study is performed to investigate the effects of the nonlinear piezoelectric coefficients and the excitation amplitude on the system response. The effective nonlinearity may be of the hardening or softening type, depending on the relative magnitudes of the different nonlinearities.     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

On the secondary resonance of a MEMS resonator: A conceptual study based on shooting and perturbation methods

Nonlinear dynamics of a clamped–clamped capacitive micro-beam resonator subjected to subharmonic excitation of order one-half is studied. The micro-beam resonator is sandwiched with two piezoelectric layers throughout the length, and as a result of piezoelectric actuation a tensile/compressive axial load is induced along the length which is used as a frequency tuning tool. The resonator is subjected to a combination of a bias DC and harmonic AC electrostatic actuations. In order to determine the frequency response subharmonic resonance condition, both perturbation and shooting methods are applied. The stability of the periodic solutions and the bifurcations types are also studied. It is shown that the application of perturbation method imposes some limitations on the order of magnitudes of the terms in the differential equation of the motion; as a result out of the domain where the ordering assumption of the perturbation solution does not hold, some periodic solutions as well as some vital bifurcation points are missed. It is shown that on the frequency domain, the resonator exhibits both softening and hardening behaviors whereas this is not predicted by the perturbation scheme. The effect of DC and AC actuation voltages on the qualitative response of the system is determined. It is shown that based on the polarity of the piezoelectric actuation, the frequency response curves can be shifted both in forward and backward directions which can be used in the design of novel RF MEMS filters/sensors.     

Benchmark experiments and characteristic cyclic plasticity deformation

Key issues in cyclic plasticity modeling are discussed based upon representative experimental observations on several commonly used engineering materials. Cyclic plasticity is characterized by the Bauschinger effect, cyclic hardening/softening, strain range effect, nonproporitonal hardening, and strain ratcheting. Additional hardening is identified to associate with ratcheting rate decay. Proper modeling requires a clear distinction among different types of cyclic plasticity behavior. Cyclic hardening/softening sustains dependent on the loading amplitude and loading history. Strain range effect is common for most engineering metallic materials. Often, nonproportional hardening is accompanied by cyclic hardening, as being observed on stainless steels and pure copper. A clarification of the two types of material behavior can be made through benchmark experiments and modeling technique. Ratcheting rate decay is a common observation on a number of materials and it often follows a power law relationship with the number of loading cycles under the constant amplitude stress controlled condition. Benchmark experiments can be used to explore the different cyclic plasticity properties of the materials. Discussions about proper modeling are based on the typical cyclic plasticity phenomena obtained from testing several engineering materials under various uniaxial and multiaxial cyclic loading conditions. Sufficient experimental evidence points to the unambiguous conclusion that none of the hardening phenomena (cyclic hardening/softening, strain range effect, nonproportional hardening, and strain hardening associated with ratcheting rate decay) is isotropic in nature. None of the hardening behavior can be properly modeled with a change in the yield stress.     

含裂纹梁非线性静动力特性及简化动力学建模Static and dynamic behaviour of cracked beam and simplified dynamic model

主要研究裂纹对梁结构动力特性的影响规律,进而为含裂纹梁结构状态监测提供理论依据。首先,对裂纹影响区域进行分析,建立含裂纹梁二维接触非线性有限元模型,阐明含裂纹梁具有拉压不同刚度的静力特性;其次,通过对机理模型的分析,指出拉压不同刚度会引起轴向与弯曲的耦合振动;然后,通过非线性动力学分析方法研究其动力特性,观察到含裂纹梁在冲击荷载下会产生轴向与弯曲的耦合振动现象,并指出这种轴向与弯曲耦合振动的一个重要特征是轴向振动频谱图中含有弯曲振动基频的两倍频成分;最后,通过引入非线性弹簧建立一种新颖的含裂纹梁简化动力学模型,通过与精细有限元分析对比,验证了模型的合理性。该简化动力学模型将接触非线性问题转换为材料非线性问题,避免了费时的接触非线性动力学求解过程。