Dynamic Equations Of Motion Research Articles

Effects analysis of bias and excitation conditions on power output of an environmental vibration energy harvesting device using Fe-Ga slice

With the advent of low power VLSI designs and the mass manufacture of CMOS, the power consumption of wireless sensor nodes has been significantly reduced from mW to μW. This opens up a new and interesting research field, that is, the possibility of converting environmental vibration energy to electrical energy for supplying power to the sensors. In this paper, using magnetostrictive materials slice, that is Fe-Ga alloy, a device for harvesting environmental vibration energy is designed and tested. Compared with piezoelectric materials and Terfenal-D alloy, Fe-Ga alloy offers excellent properties for surviving in tough ambient vibration conditions, including higher energy conversion efficiency, longer life cycles, excellent toughness, reduced depolarization and higher flexibility, etc. The designing of vibration energy harvesting process is based on the coupling characteristics of magnetostrictive inverse effect and Faraday electromagnetic induction. The device consists of a Fe-Ga alloy cantilever beam with a magnetostrictive direction throughout the length. It has magnetostrictive inverse effect during vibration and the internal magnetization state will change. A cantilever beam is surrounded by a pickup coil and voltage is induced due to the magnetic field according to Faraday's law. The energy conversion principle among mechanical, magnetic and electric energy is described through a dynamic equation of motion and in conjunction with an electromagnetic conversion equation. The influence law of bias and excitation conditions on output voltage, power and other characteristics of device are investigated in comprehensive experiments. By knowing these influence laws, it is possible to choose an appropriate number of pick up coil for a definite load resistance, to set an appropriate working frequency range, pre-tightening force and pre-magnetized magnetic field such that a maximum power can be harvested. The results derived here can be used as a design guideline for future studies in optimal design and the modeling of vibration energy harvester and force sensor.

Giant drag reduction on Leidenfrost spheres evaluated from extended free-fall trajectories

Vapor layer sustained on the surface of a heated sphere, by the means of the Leidenfrost effect, can dramatically reduce the hydrodynamic drag on a sphere due to an early drag crisis transition. Here we investigate the vapor layer effect on the free fall of heated metallic spheres in a fluorocarbon liquid, FC-72 (perfluorohexane), employing two tall liquid tanks: a 3 m tall 14 cm wide tank and a 2 m tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies. We use high-speed video camera recordings to track extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layers-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no vapor layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Results of this study are expected to stimulate the development on energy saving drag-reduction technologies based on lubricating gas layers.

Dynamic Soaring Kinetic Energy Reference Frames

Dynamic soaring in the boundary layer of a vertical variation of horizontal wind offers unmanned aerial vehicle gliders the ability to greatly extend mission endurance. By flying periodic trajectories within these gradients of horizontal winds, a dynamic soaring bird or glider uses the locally accelerating wind to its advantage, extracting sufficient energy from the environment during each trajectory cycle to overcome losses due to induced and parasitic drag. The dynamic soaring literature currently offers two competing definitions of aircraft kinetic energy, pointing to opposing views regarding the source of dynamic soaring energy exchange between the wind and the aircraft. A series of heuristics is developed to logically establish the wind-fixed/wind-aligned reference frame (that is, airspeed) as the appropriate choice for scalar kinetic energy computation while not imposing any such limitation on the usage of arbitrary reference frames for dynamic soaring equations of motion. Furthermore, while acknowledging that other kinetic energy reference frames are valid from the standpoint of physics, only wind-fixed frame kinetic energy tracks useful energy transfer from the vertical gradient of horizontal winds, with no attribution of kinetic energy from downwind turns.

Static form-finding of normal and defective catenaries based on the analytical exact solution of the tensile Euler–Bernoulli beam

The aim of this research is to propose and develop an analytical exact solution for finding the static equilibrium configuration of a catenary before and after incurring defects such as tension loss or a broken dropper. The procedure includes considering the steady-state solution of the dynamic motion equation of the contact wire and the messenger cable. The wire and the cable are considered as tensile Euler–Bernoulli beams. The stiffness matrix of the beam is configured and is used to calculate the dropper's dead load. Progressively, a novel method is proposed to find the equilibrium configuration of the same catenary after the defect. The results prove that the tension loss in the messenger cable is more precarious than the tension loss in the contact wire. The broken dropper causes a significant sag in the sub-span and increases the static forces of the adjacent droppers. A comparison with field measurements justifies the accuracy of the results of the proposed model.

Fully Dynamic Spontaneous Rupture Due to Quasi‐Static Pore Pressure and Poroelastic Effects: An Implicit Nonlinear Computational Model of Fluid‐Induced Seismic Events

AbstractFluid perturbations play a pivotal role in triggering earthquakes. However, the role of fluid in the coseismic rupture process remains largely unknown. To this end, we develop a 2‐D fully dynamic spontaneous rupture model for fluid‐induced earthquakes. The effect of fluid in the preseismic quasi‐static regime is modeled as either pore pressure diffusion or fully coupled poroelasticity, using our Jin and Zoback (2017, https://doi.org/10.1002/2017JB014892) computational model. The two approaches lead to radically different predictions on the time of earthquake nucleation. Correspondingly, the evolved fluid pressure or poroelastic stress on the fault, together with the spatially altered density of the fluid‐saturated hosting rock, is passed to the dynamic regime. Under the assumption of an undrained coseismic fluid‐solid system, we discretize the fully dynamic Cauchy equation of motion subjected to an exact fault contact constraint using a split‐node finite element method in space and an implicit Newmark family finite difference method in time. Within each time step, a fully implicit Newton‐Raphson scheme is implemented iteratively for linearizing the fully discrete equations. Within each Newton iteration, a physics‐based and nonstationary preconditioner is designed to accelerate the convergence of the selected generalized minimal residual method iterative linear solver. The effect of fluid is highlighted throughout the discretization and computational procedures. Finally, by conducting a numerical experiment, we illustrate that a fully coupled poroelastic model can lead to significantly different predictions on coseismic rupture behaviors and wavefields compared to a decoupled model. Our computational model can also serve as one of the earliest full‐physics modeling tool for fluid‐induced earthquakes.

Stability of the Rectilinear Motion of an Omni Vehicle with Consideration of Wheel Roller Inertia

The dynamics of a mobile vehicle with three omni wheels is considered for the case when the vehicle moves on a fixed perfectly rough plane by inertia. In order to study the effect of wheel roller inertia on the stability of the rectilinear motion of the vehicle, the fore wheel is modeled by the following rigid bodies: a wheel disk and a supporting roller such that the roller does not slip with respect to the plane. The rear wheels are modeled by disks slipping without friction in the direction perpendicular to their planes (an inertialess model of an omni wheel). We propose some dynamic equations of motion of the vehicle in the form of Tatarinov’s laconic equations for systems with differential constraints. These equations are related to the dynamic equations obtained for a vehicle with three inertialess omni wheels. The stability of rectilinear motions is analyzed.

Research of the manipulator dynamics installed on an elastic basis

In many scientific articles on construction topics, the problem of building density has recently been considered [1, 2]. When working construction equipment in the construction of such objects there is a problem of safety of work. For example, in work [3, 4] the possibility of an excavator with an offset digging axis is presented. But, such research for construc-tion cranes and construction robots is not enough. The elasticity of metal structures of real mechanical systems manipulators greatly affects their work [5]. When lifting cargo manipulator in its metal construction generated vibrations due to the complex dynamics of the machine. Fluctuations cargo the cause errors in its position and reduce life of the machine. For eliminate fluctuation make use of the dampers and devices regulate speed of the working body of the manipulator [5, 6]. It is necessary to develop the dynamic and mathematical models of the boom of the manipulator, which is mounted on an elastic base. The mathematical model must take into ac-count the parameters of the rigidity of the support arm of the manipulator, the mass of the jet and the load, as well as its geometrical parame-ters. The basic method of compiling the dynamic equations of motion, the Lagrange equations are used. The boundary conditions for the so-lution of the obtained differential equations for the angle of rotation the deformed prop were the boundary values of the displacements and the angle of rotation of the cantilever beam within the boundary of the strength of its cross-section.

A virtual power algorithm for dynamics analysis of a 3-RRcP spherical parallel robot using the screw theory

ABSTRACT Due to their closed-loop structure and kinematic constraints, dynamic modelling of parallel manipulators presents an inherent complexity. In the present research, an approach to obtain the nonlinear dynamics equations of motion of a 3-RRcP spherical parallel manipulator is presented. The proposed approach is based on the principle of virtual power and the screw theory. To obtain the dynamics equations of motion, we propose an influence matrix which relates the passive joint rates to the actuated joint rates for each branch. The presented method allows a straightforward computation of torques of the actuated joints in terms of the resultant external forces and the desired trajectory. In order to represent correctness and accuracy of the obtained equations of motion, two case studies are considered that their solutions are compared by a commercial dynamics software package (CDSP).

Influence of rotation on vibration characteristics of thick composite disks

Thick composite disks are utilized in fast-rotating machines, including turbine disks and flywheels. Dynamic equations of motion for a rotating composite disk have been formulated in a polar coordinate system using Hamilton’s principle, and numerical analysis has been performed by finite element interpolation. The natural frequencies of isotropic and laminated composite disks have been obtained when the rotational speed changes. The effects of transverse shear and rotary inertia on the vibration characteristics of rotating disks have also been investigated.

Aerodynamic and flight dynamic interaction in spin

PurposeThe purpose of this paper is to describe an integrated approach to spin analysis based on 6-DOF (degrees of freedom) fully nonlinear equations of motion and a three-dimensional multigrid Euler method used to specify a flow model. Another purpose of this study is to investigate military trainer performance during a developed phase of a deliberately executed spin, and to predict an aircraft tendency while entering a spin and its response to control surface deflections needed for recovery.Design/methodology/approachTo assess spin properties, the calculations of aerodynamic characteristics were performed through an angle-of-attack range of −30 degrees to +50 degrees and a sideslip-angle range of −30 degrees to +30 degrees. Then, dynamic equations of motion of a rigid aircraft together with aerodynamic loads being premised on stability derivatives concept were numerically integrated. Finally, the examination of light turboprop dynamic behaviour in post-stalling conditions was carried out.FindingsThe computational method used to evaluate spin was positively verified by comparing it with the experimental outcome. Moreover, the Euler code-based approach to lay down aerodynamics could be considered as reliable to provide high angles-of-attack characteristics. Conclusions incorporate the results of a comparative analysis focusing especially on comprehensive assessment of output data quality in relation to flight tests.Originality/valueThe conducted calculations take into account aerodynamic and flight dynamic interaction of an aerobatic-category turboprop in spin conditions. A number of manoeuvres considering different aircraft configurations were simulated. The computational outcomes were subsequently compared to the results of in-flight tests and the collected data were thoroughly analysed to draw final conclusions.

Adaptive Control of a Cable-Actuated Parallel Manipulator Mounted on a Platform with Differential Wheels under Payload Uncertainty

Cable-actuated parallel Manipulators (CPMs) are widely employed for object handling applications. In order to displace the carried object along the ground to an unlimited distance, the CPMs can be mounted on wheeled mobile robots (WMRs). The derivation of the dynamic equations of motion for this integrated system is presented using Lagrange method. Since in load carrying task, the inertia of the moving load is the main source of uncertainty, an adaptive control approach is considered for the CPM, whereas the WMR uses a feedback linearized sliding mode approach. In order to maintain the end-effector of the CPM in within its relative workspace in the WMR frame, the convergence rate in the two controllers should be similar. Decentralization of the control law can be accomplished if the inertia of the CPM motors are negligible compared with the other inertias of the system. This assumption is shown to be applicable if an introduced index is small enough to have noticeable effect on the tracking error.

Taming the Beast: Diffusion Method in Nonlocal Gravity

We present a method to solve the nonlinear dynamical equations of motion in gravitational theories with fundamental nonlocalities of a certain type. For these specific form factors, which appear in some renormalizable theories, the number of field degrees of freedom and of initial conditions is finite.

The dynamical equation of relative motion for non-material volumes

This paper is devoted to the description of the relative motion of a non-material volume. The dynamical equation of relative motion for non-material volumes is derived under a reference to some carried-fixed coordinate system moving generally with respect to a fixed-space coordinate. Three kinds of a special form of the dynamical equation of relative motion are proposed. An example is given to illustrate the application of the method, and four kinds of the dynamical equation of relative motion are obtained.

Experimental Estimation of Friction and Friction Coefficient of a Lightweight Hydraulic Cylinder Intended for Robotics Applications

Recently, hydraulic actuator has been used in several engineering applications such as: aeronautics, construction and robotics. This is due to the need of high torque and power density in such engineering applications. Despite these advantages, hydraulic actuators are fabricated from metallic materials, which provoke their heavy weight, which necessitate the development of a lightweight hydraulic actuator, fabricated of composite materials. Using composite materials in hydraulic cylinders, it is important to study the friction force characteristics and to estimate the friction coefficient between composites and O-rings, which is presented in this paper. This paper deals with the estimation of Coulomb friction and friction coefficient in the lightweight hydraulic cylinder fabricated mainly of composite materials. The actuator is presented by its dynamic equation of motion, where each term is discussed including the stiffness coefficient, the viscous damping coefficient, the kinematics and the pressure parameters. Meanwhile, these coefficients and parameters are obtained according to data recorded from conducted experiments. As a result, the new methodology which uses the experimental measurements combined the dynamic model has succeeded to evaluate the friction inside the hydraulic cylinder which has been estimated and found to be around 166[Formula: see text]N, while the corresponding coefficient of friction is computed (about 0.61 as average value). These results will be important for further optimization of the material choice and actuator design, which will help in the amelioration of the hydraulic cylinder.

Dynamics and vibration analysis of an electrostatically actuated FGM microresonator involving flexural and torsional modes

In this paper a nonlinear pedal like microresonator made of Functionally Graded material is introduced and modeled. Using Lagrangian formulation nonlinear equations of motion of the system are derived and the natural frequencies and mode shapes are extracted by linear analysis. The effects of various parameters such as geometry, FG material index and DC voltages on the natural frequencies and mode shapes are investigated. Static pull-in voltages of the system are obtained and it is found that depending on the type of actuation, both softening and hardening behaviors can be observed in the system. The results are compared with previous studies and finite element method where a good agreement is achieved. A two-mode reduced order model along with first-order averaging technique is implemented to derive the asymptotic dynamic equations of motion. The effects of different parameters including AC actuation level, damping and material power index on the dynamic response of the system are studied around resonance conditions. It is observed that when the system parameters are adjusted properly, the directly excited in-plane mode, in turn excites the out-of-plane torsional mode of the structure through internal resonance of 1:2 ratio within a specific frequency bandwidth. A wide range of frequency will be available by changing only the power index of the material and the system can be manipulated to be used in various MEMS applications such as mass sensors and RF filter-mixer devices.

Sliding Mode Observer Controller Design for a Two Dimensional Aeroelastic System with Gust Load

AbstractThe aim of this paper is to develop state estimation and sliding mode control schemes for the vibration suppression of an underactuated wing aeroelastic system in the presence of a gust load disturbance. Ignoring structural elastic deformation and using the concentrated elastic system (spring) to simulate the overall elastic deformation, this aeroelastic model consists of a straight wing and spring system, describing flap and pitch freedoms. The corresponding dynamic motion equation is established using the Lagrange method, and the gust is modeled as a typical “1‐cosine” gust. The aerodynamic lift and moment on the wing are computed by strip theory. The open loop system exhibits the limit cycle oscillations (LCOs) at a certain freestream velocity. The objective is to design a control system for suppressing the LCOs. For the purpose of control, a single trailing‐edge control surface is used. It is assumed that only the pitch angle is measured and the remaining state variables needed for full state feedback are estimated by the designed observer. Then an integral sliding surface is put forward on the estimation space; a new continuous reaching law is proposed to reduce the chattering phenomena. The finite‐time reachability of the predesigned sliding surface is proved and guaranteed by the designed sliding mode control law. The sufficient condition for the asymptotic stability of the closed‐loop system composed of the sliding mode dynamics and the error dynamical system is derived in terms of linear matrix inequality (LMI). The effectiveness of the proposed strategy is finally demonstrated by simulation results.

A rigorous proof for the equivalence of the projective Newton–Euler equations and the Lagrange equations of second kind for spatial rigid multibody systems

It is well known that the projective Newton–Euler equation and the Lagrange equation of second kind lead to the same result when deriving the dynamical equations of motion for holonomic rigid multibody systems. It can be shown that both approaches follow from the principles of d’Alembert or Jourdain. However, as to the author’s knowledge, no direct rigorous proof for the equivalence of these approaches is given in literature so far when it comes to spatial systems of rigid bodies. In this paper, we present a novel proof that directly addresses the projective Newton–Euler equation and the Lagrange equation of second kind without the detour via variational principles. The proof is mainly based on vector and matrix manipulations and elementary concepts of differential geometry. Although the mathematical framework is thereby kept simple, the argumentation is considerably more complex compared to the case of planar systems of rigid bodies or spatial systems of particles. An illustrative example is presented.

Singularity-Free Trajectory Planning of a 3-RPRR Planar Kinematically Redundant Parallel Mechanism for Minimum Actuating Effort

Kinematic redundancy is a way to enlarge the workspace and to eliminate the singularities of parallel mechanisms. The objective of the present research is to introduce a new motion planning strategy for singularity avoidance and reducing the actuator forces, especially in the vicinity of singular configurations. The method is implemented to a planar kinematically redundant mechanism categorized as 3-RPRR type. Dynamic equations of motion are derived using the principle of virtual work, and the optimum inverse dynamics is obtained. Some numerical examples are solved, and the results are compared with those obtained in the counterpart non-redundant mechanisms. It is illustrated that the redundant mechanism can avoid singular configurations and track the given trajectory with feasible generalized forces.

On the geometrically exact low-order modelling of a flexible beam: formulation and numerical tests.

This paper proposes a low-order geometrically exact flexible beam formulation based on the utilization of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam shapes approach is in contrast to the majority of geometrically nonlinear treatments in the literature in which element-based—and hence high-order—discretizations are adopted. The kinematic quantities approximated specifically pertain to shear and extensional gradients as well as local orientation parameters based on an arbitrary set of globally referenced attitude parameters. In developing the dynamic equations of motion, an Euler angle parametrization is selected as it is found to yield fast computational performance. The resulting dynamic formulation is closed using an example shape function set satisfying the single generic kinematic constraint. The formulation is demonstrated via its application to the modelling of a series of static and dynamic test cases of both simple and non-prismatic structures; the simulated results are verified using MSC Nastran and an element-based intrinsic beam formulation. Through these examples, it is shown that the nonlinear beam shapes approach is able to accurately capture the beam behaviour with a very minimal number of system states.

Nonperturbative effects in self-energy functions of quantum dots coupled to an acoustic phonon reservoir

The problem of description of the strong interaction of a quantum dot (QD) with an acoustic phonon reservoir is discussed. It is shown that the generalized dynamical equation of motion derived in [Gainutdinov R. Kh. 1989 J. Phys. A: Math. Gen. 22 269] as the most general equation of motion consistent with the current concepts of quantum physics and provides an effective way to solve the problem of the QD in the excitonic regime with the phonon reservoir beyond the perturbation theory. A nonperturbative solution for the exciton self-energy function was found. At temperatures, more than 10 K these self-energy functions differ profoundly from that obtained in the second-Born approximation.