Approximate analytical solution to oscillations of a conductor in a magnetic field

An approximate analytical solution to a system exhibiting oscillations of a conductor in a magnetic field which is controlled by a discrete waveform is sought by means of multiple scales. The system involves the use of a solenoid driven by a RLC circuit, coupled with a solid state relay (SSRL), to generate large electromagnetic forces acting on a conductor, which oscillates within the solenoid. The steady state response of the metal bar, in terms of oscillations is described. This solution is expressed in terms of system and circuit parameters, valid in the weakly nonlinear region, which is identified to be small oscillatory displacement near the center of the solenoid. By analyzing different cases of resonance, period-1 and period-2 like motions are identified and validated through experimental studies. The solution provides a guideline to design an effective control strategy so as to guide the system to a desirable attractor.     

Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems

In this paper, we present the design, modelling and experimental validation of a novel experimental cam-follower rig for the analysis of bifurcations and chaos in piecewise-smooth dynamical systems with impacts. Experimental results are presented for a cam-follower system characterized by a radial cam and a flat-faced follower. Under variation of the cam rotational speed, the follower is observed to detach from the cam and then show the emergence of periodic impacting behaviour characterized by many impacts and chattering. Further variations of the cam speed cause the sudden transition to seemingly aperiodic behaviour. These results are compared with the numerical simulation of a mathematical model of the system which shows the same qualitative behaviour. Excellent quantitative agreement is found between the numerical and experimental results.     

Rotating a pendulum with an electromechanical excitation

The objective of this paper is showing investigation of pendulum rotations via vertical, non-linear electromechanical excitation generated using a RLC-circuit-powered solenoid, which is originally built for an electro-vibro-impact mechanism. Various non-linear phenomena of pendulum dynamics, namely period-1 rotation, period-1 oscillation and period-2 oscillation, have been observed experimentally from the proposed apparatus. A mathematical model has been developed for the experimental rig and the system parameters have also been identified for the mathematical model. Finally, numerical results have been generated using the developed mathematical model and identified parameters, and their correlations with experimental observations have been discussed.     

Energy harvesting from pendulum oscillations

In this work we analyse the possibility of energy harvesting from the vibration of the environment. The investigations are performed using experimental rig, which consists of a parametrically forced pendulum and an energy harvester, and the mathematical model developed based on the experimental rig. Numerical studies focus on the oscillating motion of pendulum in 2:1 resonance and show good agreement with experimental results. We present that the energy harvesting is possible and is more efficient for shorter reduced length of the pendulum, as proved numerically and experimentally.     

Electro-mechanical coupling bifurcation and bulging propagation in a cylindrical dielectric elastomer tube

This paper explores the critical and post-bulging bifurcation of a cylindrical dielectric elastomer (DE) tube undergoing finite deformation under electro-mechanical coupling loading. Explicit expressions for the critical conditions of electro-mechanical bifurcation are derived by using a simplified mathematical method. The post-bifurcation path is comprehensively investigated by specifying the material model as ideal dielectric elastomer. In the post-bifurcation analysis, we analytically establish conditions for the phase coexistence of steady propagation and analyze the physical implications. We demonstrate a global instability under force or voltage control and a localized instability under volume or charge control. Cylindrical tube experiments have been carried out under electro-mechanical coupling loading to verify the theoretical predictions. Good agreements on the critical conditions as well as the post-bifurcation path are obtained. This work characterizes the bifurcation mechanism of rubber-like materials under complex coupling loading.     

Modeling and dynamic analysis of a magnetically actuated butterfly valve

In this work, a magnetically actuated butterfly valve is considered and a novel and accurate mathematical model is derived. The equilibrium of the system is investigated and the effects of the inlet velocity and direct current voltage (DC) on the stable rotation angle of the valve are presented. Considering a time periodic perturbation arising from electric circuit, the effects of the operating angle, inlet velocity, and driving parameters on the periodic and chaotic dynamics of the system are investigated. It is observed that, for an opening angle less than the cut-off angle, there exists a unique DC voltage for a stable equilibrium. The stability of this equilibrium depends nonlinearly on the inlet velocity and the seating torque. An expression is derived for the threshold value for the stability of the valve. Under periodic voltage, the inlet velocity and stable angle induce a backward shift on the resonant frequency, and jump phenomena and subharmonics are observed for some values of the driving amplitude. The highest amplitudes of vibration are detected for a fully open valve, for an almost closed valve, and for a valve with large inlet velocity. Using bifurcation diagrams and Lyapunov exponents, it is shown that the system exhibits a route to chaos with windows of period doubling and unbounded motion. Some guidance for design of magnetically actuated butterfly valves is proposed as well as recommendations for future work.     

Numerical and experimental investigation on multibody systems with revolute clearance joints

A comprehensive combined numerical and experimental study on the dynamic response of a slider-crank mechanism with revolute clearance joints is presented and discussed in this paper to provide an experimental verification and validation of the predictive capabilities of the multibody clearance joint models. This study is supported in an experimental work in a test rig, which consists of a slider-crank mechanism with an adjustable radial clearance at the revolute joint between the slider and the connecting rod. The motion of the slider is measured with a linear transducer and an accelerometer. Dynamic tests at different operating crank speeds and with several clearance sizes are performed. The maximum slider acceleration, associated with the impact acceleration, is used as a measure of the impact severity. The obtained results demonstrate the dynamical behavior of a multibody mechanical system with a clearance joint. Finally, the correlation between the numerical and experimental results is presented and discussed leading to validated models of clearance revolute joints.     

A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator

This paper investigates the electro-mechanical behaviour of a thick, laminated actuator with piezoelectric and isotropic lamina under externally applied electric loading using a new two-dimensional computational model. The elastic core is relatively thick and thus it is modelled by Timoshenko thick-beam theory. Although the piezoelectric lamina is a beam-like layer, it is formulated via a two-dimensional model because of not only the strong electro-mechanical coupling, but also of the presence of a two-dimensional electric field. It is shown in this paper that a one-dimensional model for the piezoelectric beam-like layer is inadequate. The piezoelectric model is constructed within the scope of linear piezoelectricity. The actuation response is induced through the application of external electric voltage. Under the strong coupling of elasticity and electricity, the strain energy and work of electric potential are presented. The electro-mechanical response of the laminated Timoshenko beam is formulated and determined via a variational energy principle. Numerical examples presented illustrate convincing comparison with finite element solutions and existing published data. New numerical solutions are also presented to investigate the geometric effect on the electro-mechanical bending behaviour.     

Use of Time Resolved PIV for Validating LES/DNS of the Turbulent Flow within a PCB Enclosure Model

In this paper an approach to the validation of transient numerical simulations of turbulent flows through the use of time resolved PIV data is presented and applied to the case of turbulent flow within a simplified model of printed circuit board (PCB) enclosure. The comparison between numerical and experimental data is not limited here to the time averaged fields, but transient flow structures are also addressed. With this purpose a set of conditionally sampled averages, or cluster averages, are obtained through a Fuzzy Clustering technique. Further, the time history of the flow is analyzed on the base of this set of cluster averages, yielding time sequence relations among them that simplify their interpretation in terms of flow dynamics. In this way, events of alternate vortex shedding have been identified in a selected portion of the flow, and showed to exist in both numerical and experimental sets of data.Supported by FPI/DPI2003-06725-C02-01 from DGI, Ministerio de Educación y Cultura y Fondos FEDER, and grant S/B/CE/33/07 from PDT Uruguay.     

Modeling motion-induced fluid release from partially saturated fibrous media onto surfaces with different hydrophilicity

Modeling the rate of fluid release from moving partially saturated nonwoven sheets in contact with a solid surface is a challenge, as the release rate depends on many parameters, some of which are difficult to quantify. In this paper, we report on a diffusion-controlled boundary treatment which we have developed to simulate fluid release from partially saturated porous materials onto surfaces with different hydrophilicy. The new boundary treatment considers the solid impermeable surface as a fictitious porous layer with a known fluid diffusive coefficient. Motion of the porous sheet on the surface is incorporated in the simulations by periodically resetting the saturation of the fictitious layer equal to zero, with a period obtained from the sheet’s speed of motion. Fluid transport inside the fibrous sheets is calculated by solving Richards’ equation of two-phase flows in porous media. Our numerical simulations are accompanied with experimental data obtained using a custom-made test rig for the release of liquid from partially saturated media at different speeds. It is demonstrated that the novel mathematical formulations presented here can correctly predict the rate of fluid release from moving fibrous sheets onto solid surfaces with different hydrophilicity as a function of time.     

Sizing the slenderness of free-standing rocking columns to withstand earthquake shaking

This paper investigates the problem of sizing the width of tall free-standing columns with a given height which are intended to rock, yet shall remain stable during the maximum expected earthquake shaking. The motivation for this study is the emerging seismic design concept of allowing tall rigid structures to uplift and rock in order to limit base moments and shears. The paper first discusses the mathematical characterization of pulse-like ground motions and the dimensionless products that govern the dynamics of the rocking response of a free-standing block and subsequently, using basic principles of dynamics, derives a closed-form expression that offers the minimum design slenderness that is sufficient for a free-standing column with a given size to survive a pulse-like motion with known acceleration amplitude and duration.     

Proof-of-concept prototype development of the self-propelled capsule system for pipeline inspection

This paper studies the prototype development for the self-propelled capsule system which is driven by autogenous vibrations and impacts under external resistance forces. This project aims for proof-of-concept of its locomotion in pipeline environment in order to mitigate the technical complexities and difficulties brought by current pressure-driven pipeline inspection technologies. Non-smooth multibody dynamics is applied to describe the motion of the capsule system, and two non-smooth nonlinearities, friction and impact, are considered in modelling. The prototype of the self-propelled capsule system driven by a push-type solenoid with a periodically excited rod has been designed to verify the modelling approach. The prototype contains a microcontroller, a power supply, and a wireless control module, which has been tested in a clear uPVC pipe via remote control. Various control parameters, e.g. impact stiffness, frequency and amplitude of excitation, are studied experimentally, and finally, the fastest progression of the system is obtained.     

Finite element formulation of slender structures with shear deformation based on the Cosserat theory

This paper addresses the derivation of finite element modelling for nonlinear dynamics of Cosserat rods with general deformation of flexure, extension, torsion, and shear. A deformed configuration of the Cosserat rod is described by the displacement vector of the deformed centroid curve and an orthogonal moving frame, rigidly attached to the cross-section of the rod. The position of the moving frame relative to the inertial frame is specified by the rotation matrix, parameterised by a rotational vector. The shape functions with up to third order nonlinear terms of generic nodal displacements are obtained by solving the nonlinear partial differential equations of motion in a quasi-static sense. Based on the Lagrangian constructed by the Cosserat kinetic energy and strain energy expressions, the principle of virtual work is employed to derive the ordinary differential equations of motion with third order nonlinear generic nodal displacements. A cantilever is presented as a simple example to illustrate the use of the formulation developed here to obtain the lower order nonlinear ordinary differential equations of motion of a given structure. The corresponding nonlinear dynamical responses of the structures are presented through numerical simulations using the MATLAB software. In addition, a MicroElectroMechanical System (MEMS) device is presented. The developed equations of motion have furthermore been implemented in a VHDL-AMS beam model. Together with available models of the other components, a netlist of the device is formed and simulated within an electrical circuit simulator. Simulation results are verified against Finite Element Analysis (FEA) results for this device.     

Numerical flow models to simulate tuned liquid dampers (TLD) with slat screens

The tuned liquid damper (TLD) is increasingly being used as an economical and effective dynamic vibration absorber to mitigate the dynamic response of structures. In this paper the results of two numerical flow models of TLD behaviour are compared with experimental data. These include the free surface motion, the resulting base shear forces, and the energy dissipated by a TLD with slat screens. The importance of this experimental study is that it examines TLD behaviour over a large range of normalized excitation amplitude values, covering the practical range of serviceability accelerations for buildings subjected to wind loads and larger excitation amplitudes more representative of earthquake motion. In addition, the experimental results are used to assess the models for larger fluid depth to tank length values, and for the use of modelling TLDs equipped with multiple screens. For screens consisting of a number of thin plate slats, a method for determining the loss coefficient is presented, which is a required parameter for the models used in this paper. Findings indicate that the linear model is capable of providing an initial estimate of the energy dissipating characteristics of a TLD. The nonlinear model can accurately describe the response characteristics within the range of excitation amplitudes experimentally tested.     

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.     

Vibrations of a rigid body with a controlled frictional electromagnetic seismic damper: nonlinear model

A nonlinear mathematical model of a gravitational vibratory system with a controlled electromagnetic seismic damper is developed. The dependence of the force of attraction of ferromagnetic bodies by the solenoid of the frictional device on the solenoid current is established for a specific solenoid design. The analytic expression for this force is derived by the least-squares method using a system of continuous piecewise-linear functions. It is used to describe the pressure of the solenoid on the friction surface. For multifrequency inertial excitation, the acceleration amplification factor is evaluated depending on the time constant and gain for two cases of control. The possibility of damping vibrations by controlling the absolute velocity and acceleration is established     

直撞式霍普金森压杆二次加载技术

利用传统分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验技术来实现试件在较低应变率下的大变形时,需要使用超长的压杆系统,杆件的加工和实验空间限制了该技术的推广应用。鉴于此,提出一种直撞式霍普金森压杆二次加载实验技术,利用透射杆中的应力波在其末端的准刚性壁反射实现对试件的二次加载,并分析了准刚性质量块尺寸对二次加载的影响规律;采用二点波分离方法对叠加的应力波进行了有效分离和计算,在总长4 m的压杆系统中实现了1.2 ms的长历时加载,并可以准确获得试件的加载应变率曲线和应力应变关系。建立了直撞式霍普金森压杆二次加载有限元模型,数值仿真结果表明,该实验技术能有效地实现试件的二次加载,与超长SHPB系统获得的仿真结果相比较,两者的试件应力应变关系完全一致。利用该技术对1100铝合金材料进行动态压缩实验,实现了其在102 s?1量级应变率下的大变形动态力学性能测试。     

电感式磨粒监测传感器的磁场均匀性研究

在介绍电感式磨粒监测传感器结构原理的基础上 ,提出可采用检测线圈内部磁场均匀性的方法来弥补颗粒运动轨迹和流型变化带来的检测误差 ,以提高检测灵敏度 .通过分析不同几何尺寸的线圈中轴线上磁场的变化情况 ,并借助直螺线管的径向和轴向公式 ,对轴外磁场均匀性进行了探讨 .数学模型和优化结果表明 :在检测传感器线圈中部范围内为非匀强磁场 ,且呈非线性变化 ,细长管磁场相对均匀 ;当选取 R/ L <0 .2 ,磁场在线圈轴向长度范围内 ,径向在90 %范围内可近似看作均匀磁场 .所得结果可以确定传感器检测区域的磁场均匀性范围 ,为设计电感式磨粒监测传感器提供依据 .     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.