FORCED VIBRATIONS WITH INTERNAL RESONANCE OF A PIPE CONVEYING FLUID UNDER EXTERNAL PERIODIC EXCITATION

Applying the multidimensional Lindstedt-Poincare （MDLP） method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under ex- ternal periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are de- cided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.

The Anti-Vibrating-Impact Research of the Piezoelectric Resonator Force Sensor

Based on the analysis of one-dimension inertial accelerometer movement model,from which the resolution of the accelerometer inertial mass displacement equation was derived,the response of the sensor sensing element to vibration and impact of various frequencies was studied.The theoretical and experimental results show that a reasonable configuration among the sensing element inherent frequency,environmental exciting frequency and the damp factors of the sensor is the key to prevent the sensor from damage.The sensor has good anti-vibrating impact ability when the relative damp factor is 0.7,and the environmental interferential vibrating frequency is less than 0.35 times of the inherent frequency of the sensing element.

Nonlinear Forced Vibration of Cantilevered Pipes Conveying Fluid

The nonlinear forced vibrations of a cantilevered pipe conveying fluid under base excitations are explored by means of the full nonlinear equation of motion, and the fourth- order Runge-Kutta integration algorithm is used as a numerical tool to solve the discretized equations. The self-excited vibration is briefly discussed first, focusing on the effect of flow velocity on the stability and post-flutter dynamical behavior of the pipe system with parameters close to those in previous experiments. Then, the nonlinear forced vibrations are examined using several concrete examples by means of frequency response diagrams and phase-plane plots. It shows that, at low flow velocity, the resonant amplitude near the first-mode natural frequency is larger than its counterpart near the second-mode natural frequency. The second-mode frequency response curve clearly displays a softening-type behavior with hysteresis phenomenon, while the first-mode frequency response curve almost maintains its neutrality. At moderate flow velocity, interestingly, the first-mode resonance response diminishes and the hysteresis phenomenon of the second-mode response disappears. At high flow velocity beyond the flutter threshold, the frequency response curve would exhibit a quenching-like behavior. When the excitation frequency is increased through the quenching point, the response of the pipe may shift from quasiperiodic to periodic. The results obtained in the present work highlight the dramatic influence of internal fluid flow on the nonlinear forced vibrations of slender Pipes.

Vibrational resonance in a multistable system with position-dependent mass

The occurrence of vibrational resonance(VR)in a dual-frequency-driven multistable system with a spatially varying mass modelling particle with position-dependent mass(PDM)and evolving in a one-dimensional symmetric periodic potential has been investigated and reported in this paper.We numerically compute and analyze the response amplitude,the effects of the PDM parameters(m0,a)on the potential structure,the occurrence of VR and the bifurcation of the equilibrium points.It is shown that the PDM parameters,besides controlling VR,can induce unconventional resonance patterns through the variation of the potential well depth.The resonant states can be influenced through the cooperation of the PDM parameters and the external forcing leading the system from multiresonance state into single and double resonance states.The contributions of the fixed rest mass m0 on the VR and the PDM-induced resonance are determined by threshold conditions imposed by the magnitude of the mass nonlinear strength a.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

A New Type of a Magnetic Plane Motor Coupled Mechanical Vibration with Electromagnetic Force

This paper proposes a new magnetic plane motor capable of rotation by the resonance energy of double-cantilever beam model excited by an electromagnetic force. This magnetic plane motor has two double-cantilever models, and the rotational direction is able to change by changing of the vibration mode. Basic characteristics of a prototype for the magnetic plane motor, such as rotational speed, output torque and efficiency were determined experimentally. Experimental results demonstrated that the rotational speed of 8.1 rpm was obtained with output torque of 0.07 Ncm for the magnetic plane motor having double-cantilever model. The output torque characteristics of the magnetic plane motor with two double-cantilever models improved 200 percent compared with double-cantilever model.

A New Motor of Stick Type with Coupled Mechanical Vibration of Bimorph Beam and Frictional Force

This paper proposes a new non-magnetic motor with a rotor rotated by using the resonance energy of a bimorph cantilever beam excited by electrostatic force. The use of flexible material enables conversion of translational vibration to rotary movement in one direction. Basic characteristics of a prototype motor with two bimorph cantilever beams, such as rotational speed, output torque, and efficiency were determined experimentally. Results show that a maximum rotational speed of 2800 rpm was obtained without a load torque. It is also observed that this motor produces the output torque of 98 μNm when the rotational speed was 980 rpm. The maximum efficiency was 24% when the input power was 0.065 W.

Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

In this study,for the first time,we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator.We undertake two models to capture the nanostructure nonlocal size effects:the strain and the velocity gradient theories.We use a reduced-order model based on the differential quadrature method(DQM)to discretize the goverming nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system.The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model.The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and,most importantly,the critical resonant frequencies of such nanoresonators.Neglcting these effects may impose a considerable source of error,which can be amended using more accurate modeling techniques.

Forced response of quadratic nonlinear oscillator: comparison of various approaches

The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of dif- ferent analytical approximate approaches. The forced vibration of snap-through mecha- nism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincar method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are com- pared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method pre- dicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the Lindstedt- Poincar method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.

3D Characteristic Diagram of Acoustically Induced Surface Vibration with Different Landmines Buried

The 3D characteristic diagram of acoustically induced surface vibration was employed to study the influence of different buried landmines on the acoustic detection signal. By using the vehicular experimental system for acoustic landmine detection and the method of scanning detection, the 3D characteristic diagrams of surface vibration were measured when different objects were buried underground, including big plastic landmine, small plastic landmine, big metal landmine and bricks. The results show that, under the given conditions, the surface vibration amplitudes of big plastic landmine, big metal landmine, small plastic landmine and bricks decrease in turn. The 3D characteristic diagrams of surface vibration can be used to further identify the locations of buried landmines.

Effects of Span Length and Additional Structure on Flow-Induced Transverse Vibration Characteristic of a Cantilevered Rectangular Prism

We consider the effects of the aspect ratio L/H (where L is the length of a prism, and H is the height of a prism normal to the flow direction) and the size of additional structures (which are a plate and a fin on the surface of a prism) on a vibration characteristic of a cantilevered rectangular prism. The present research is intended to support the analysis of energy harvesting research on the flow-induced vibration in water flow using a magnetostrictive phenomenon. The prisms are constructed from stainless steel and mounted elastically to a plate spring attached to the ceiling wall of the water tunnel. The prisms with aspect ratios of L/H ≥ 5 have reasonably identical vibration characteristics. However, the difference in the vibration characteristic appears distinctly on a rectangular prism with an aspect ratio of L/H = 2.5. The rectangular prism with an aspect ratio of L/H = 10 and a side ratio of D/H = 0.2 has a stable and large response amplitude and oscillates with a lower velocity. The length of the added plate and the size of the added fin influence the velocity of vibration onset. If the length of the added plate and fin size on the rectangular prism with D/H = 0.2 becomes large, the curve of the response amplitude shifts to that of the rectangular prism with D/H= 0.5. The response amplitude of the rectangular prism with/without plate or fin is found to be related to the second moment of area of the prism.

弦振动实验的拓展

弦振动实验不仅可以研究弦受迫振动时的振幅变化,还可以研究相位变化,特别是共振时的相位变化.本文对弦振动的简化模型进行了微分方程建模,研究了弦线在受迫振动时幅值与相位的变化规律.采用共振法和相位法测得弦线共振频率,计算得到弦的线密度,2种方法测得的实验值均与理论值符合较好.该实验不仅可以拓展弦振动实验,还可以进一步加深学生对共振现象的理解.

一种椭圆形截面拱的气动特性及共振风速研究

以一个椭圆形截面拱为工程背景,对其气动特性和共振风速进行了研究。首先,分别制作了该结构1∶150和1∶300缩尺比的测压与测力试验模型,研究了典型工况下的平均和脉动风压系数、平均气动力系数及Strouhal数等。其次,采用测力试验得到的三个坐标轴方向脉动基底力对应的峰值频率,对该结构的共振风速进行了估算。结果表明:该椭圆截面拱的气流分离点出现在圆周角112.5°附近,最小平均风压系数在0.9左右波动;脉动风压分布受气动外形影响较大,最大脉动风压系数发生在拱顶靠近观光平台的两侧截面气流分离点处,约为0.23;平均气动力系数在拱轴方向沿圆周关于180°风向角反对称,而在垂直于拱轴的方向呈正对称,最大平均阻力系数为0.42左右,远小于圆形截面值;结构三个坐标轴方向的脉动基底气动力功率谱均出现明显的能量峰值,且各峰值对应的频率不同;结构的第一阶振动以垂直于拱轴方向的振动为主,共振风速为38.8 m/s。

某全回转救助拖船船体结构振动分析

针对全回转救助拖船在螺旋桨最大转速时出现的船体结构振动问题,通过实船振动测试分析,判断引起船体结构振动的激励源来自艉部螺旋桨,而螺旋桨激励引起船体结构强迫振动和共振。在采取船艉结构加强,敷设阻尼减振材料的方法进行振动控制后,实船测试表明,船体结构振动速度最大降低7.23 mm/s。

Oscillator Subject to Periodic and Random Forces

We illustrate the influence of an external periodic force and noise on a physical system by the example of an oscillator. These two forces seem to be the reverse of each other, since the latter leads to disorder while the former works in an orderly fashion. Nevertheless, it is shown that they may influence a system in a similar way, sometime even substituting for one another. These examples serve to illustrate one of the main achievements of twentieth-century physics, which has established that deterministic and random phenomena complement rather than contradict each other.

光电法受迫振动实验的研究与应用

以常见的玻璃杯为对象,研究通过声波使其受迫振动。利用光杠杆放大法及图形分析法测量反射光斑的振动频率及宽度,即玻璃杯受迫振动的频率及振幅,从而取得不同玻璃杯受迫振动的幅频特性曲线、峰值及对应玻璃杯的共振频率,并依据受迫振动理论模型计算出玻璃杯的固有频率,结果表明实测玻璃杯受迫振动的频率与理论模型计算的固有频率二者相符。将不同体积、不同种类的液体加入玻璃杯后会改变玻璃杯的共振频率,测量得到的玻璃杯共振频率与理论计算结果一致;测量加入不同浓度液体玻璃杯的共振频率,将之与浓度进行拟合,根据拟合方程可以计算该溶液的浓度,结果误差较小。

轴向运动形状记忆合金层合梁的参强联合共振

该研究探讨了轴向变速运动形状记忆合金(shape memory alloy,SMA)层合梁在简谐激励下的参强联合共振问题。基于SMA的Falk多项式本构模型,结合Timoshenko梁理论推导了轴向运动SMA层合梁的非线性振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散,用多尺度法以及坐标变换的方法推导系统参强联合共振的幅频响应方程。通过算例分析,得到不同物理参数变化时的幅频响应曲线图和振幅-参数曲线图,分析了轴向速度、温度及强迫激励对系统参强联合共振特性的影响。结果表明,系统呈现典型的非线性振动特征和复杂的动力学行为。

POM圆盘轴对称弯曲振动研究

研究了一种材料为聚甲醛(POM)的薄圆盘声波辐射体,压电换能器在其中心处产生振动激励.采用解析法设计了POM圆盘,用有限元方法对POM圆盘−换能器振动系统进行了建模、计算.在系统谐振频率处,有限元计算和实验测试了圆盘的振动位移与系统的电声效率.结果表明,POM圆盘和钢圆盘半径、厚度相同时,POM圆盘−换能器振动系统在空气中的半功率带宽更宽,而钢圆盘−换能器振动系统的电声效率更高;POM圆盘−换能器振动系统更易施加较高的电压或有功功率;激励电压相同时,POM圆盘的振动位移大于钢圆盘.

十字型微谐振梁多场耦合振动及信号分析

微机电系统(MEMS)又称微系统或微电子机械系统,是在微电子技术基础上发展起来的一种高科技微型器件或系统。MEMS集光刻、腐蚀、LIGA、硅和非硅表面微加工、精密机械加工等技术于一体,其尺寸在微米量级。利用微加工技术生产的微传感器以结构简单、灵敏度高和工作稳定等特点而广泛应用于工程实际中。微传感器通常采用静电激励与电容检测方法检测信号,即利用谐振梁振动时的位移变化导致电极之间的距离变化,从而使电极之间的电容值产生变化,检测到的电容变化频率即为谐振梁振动的频率。为解决微传感器电容检测信号微弱、检测精度较低的问题,提出了一种十字型微谐振梁。为研究微谐振梁的多场耦合效应,在考虑范德华力、电场力的情况下建立了谐振子的多场耦合非线性动力学方程。采用林滋泰德-庞加莱法求解获得其非线性振动的动态位移,分析了多物理场参数对于谐振子振动位移平均值以及电容变化量的影响规律。运用微纳加工手段制作出十字型微谐振梁,采用静电激励-电容检测方法进行了谐振频率和振动位移导致的电容变化量测试。结果表明:十字型谐振梁增大了极板面积,电容变化量增加,其信号强度更强。当面积增大75%时,电容变化量为原来的4.2倍,信号强度增强5.0倍,因此更加便于电容检测。

十字型微谐振梁多场耦合非线性振动分析

为了提高电容检测传感器的检测精度,提出了一种十字型微谐振梁。将其简化为多场耦合振动模型,在考虑分子力与电场力的情况下建立动力学方程。求得其非线性振动固有频率及其变化规律,分析了不同参数对位移响应的影响。利用微加工技术制作十字型微谐振梁,采用静电激励—电容检测方法对其测试。创新性地将激振端与拾振端采用隔离带分开,使输出的电压信号不掺杂激励信号,结果更加真实准确。使用Owen交流电桥进行检测。结果表明:谐振梁尺寸较小时,分子力对谐振梁非线性振动影响较大。在忽略与考虑分子力时,相对误差分别为4.706%与1.971%,考虑分子力时理论值更加贴近于实测值。十字型微谐振梁的品质因数为105.8,较传统一字梁,检测信号更为明显。