Dynamic Equations Of Motion Research Articles

INTELLIGENT CONTROLLING THE GRIPPING FORCE OF AN OBJECT BY TWO COMPUTER-CONTROLLED COOPERATIVE ROBOTS

This paper presents a Multiple Adaptive Neuro-Fuzzy Inference System (MANFIS)-based method for regulating the handling force of a common object. The foundation of this method is the prediction of the inverse dynamics of a cooperative robotic system made up of two 3-DOF robotic manipulators. Considering the no slip in contact between the tool and the object, an object is moved. to create and feed the MANFIS database, the inverse kinematics and dynamic equations of motion for the closed chain of motion for both arms are established in Matlab. Results from a SimMechanic simulation are given to demonstrate how well the suggested ANFIS controller works. Several manipulated object movements covering the shared workspace of the two manipulator arms are used to test the proposed control strategy.

Novel Physics-Informed Artificial Neural Network Architectures for System and Input Identification of Structural Dynamics PDEs

Herein, two novel Physics Informed Neural Network (PINN) architectures are proposed for output-only system identification and input estimation of dynamic systems. Using merely sparse output-only measurements, the proposed PINNs architectures furnish a novel approach to input, state, and parameter estimation of linear and nonlinear systems with multiple degrees of freedom. These architectures are comprised of parallel and sequential PINNs that act upon a set of ordinary differential equations (ODEs) obtained from spatial discretization of the partial differential equation (PDE). The performance of this framework for dynamic system identification and input estimation was ascertained by extensive numerical experiments on linear and nonlinear systems. The advantage of the proposed approach, when compared with system identification, lies in its computational efficiency. When compared with traditional Artificial Neural Networks (ANNs), this approach requires substantially smaller training data and does not suffer from generalizability issues. In this regard, the states, inputs, and parameters of dynamic state-space equations of motion were estimated using simulated experiments with “noisy” data. The proposed framework for PINN showed excellent great generalizability for various types of applications. Furthermore, it was found that the proposed architectures significantly outperformed ANNs in generalizability and estimation accuracy.

Investigation of Size-Dependent Vibration Behavior of Piezoelectric Composite Nanobeams Embedded in an Elastic Foundation Considering Flexoelectricity Effects

This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. An analytical geometrical model is adopted to obtain the equivalent geometrical variables of the perforated core. To capture the Poisson’s ratio effect, the three-dimensional continuum mechanics adopted to express the kinematics are kinetics relations in the framework of the Euler–Bernoulli beam theory (EBBT). The nonlocal strain gradient theory is utilized to incorporate the size-dependent electromechanical effects. The Hamilton principle is applied to derive the nonclassical electromechanical dynamic equation of motion with flexoelectricity impact. A closed form solution for resonant frequencies is obtained. Numerical results explored the impacts of geometrical and material characteristics on the nonclassical electromechanical behavior of nanobeams. Obtained results revealed the significant effects of the mechanical, electrical, and elastic foundation parameters on the dynamic behavior of piezoelectric composite nanobeams. The developed procedure and the obtained results are helpful for many industrial purposes and engineering applications, such as micro/nano-electromechanical systems (MEMS) and NEMS.

Trajectory Tracking Nonlinear Controller for Underactuated Underwater Vehicles Based on Velocity Transformation

This paper proposes an algorithm that performs the task of tracking the desired trajectory for underactuated marine vehicles (primarily underwater) that move horizontally. The control scheme, which takes into account model inaccuracies and external disturbances, was designed using the quantities obtained after the transformation of the dynamic equations of motion resulting from the decomposition of the inertia matrix. This, in turn, led to the equation of dynamics with a diagonal inertia matrix. A specific feature of the offered controller is its dual role. It not only allows tracking the desired trajectory, but at the same time, makes it possible to estimate the impact of dynamic couplings when the vehicle is in motion. Such an approach to the tracking task is important at the initial design stage when the choice of the control algorithm has not yet been decided and experimental tests have not been performed. This is feasible because the new variables after the velocity transformation include not only vehicle parameters, but also actual velocities and forces. Therefore, it is also possible to track the original variables. The theoretical results were followed up with simulation tests conducted on a model with three degrees of freedom for two underwater vehicles.

Viscoelastic Effects on the Nonlinear Oscillations of Hard-Magnetic Soft Actuators

AbstractThe hard-magnetic soft materials (HMSMs) belong to the magnetoactive category of smart polymers that undergo large actuation strain under an externally applied magnetic field and can sustain a high residual magnetic flux density. Because of these remarkable characteristics, HMSMs are promising candidates for the remotely controlled actuators. The magnetic actuation behavior of the hard-magnetic soft actuators (HMSAs) is considerably affected by the viscoelastic material behavior of HMSMs. In this article, we aim at developing an analytical dynamic model of a typical planar model of HMSAs concerning the viscoelasticity of HMSMs. A Zener rheological model in conjunction with an incompressible neo-Hookean model of hyperelasticity and Rayleigh dissipation function is employed for defining the constitutive behavior of the viscoelastic HMSA. The governing equations of dynamic motion are deduced by implementing the nonconservative form of the Euler–Lagrange equation. The established dynamic model is utilized for providing preliminary insights pertaining to the effect of the viscoelasticity on the nonlinear oscillations of the actuator. The phase–plane portraits, Poincaré maps, and the time–history response are plotted to investigate the stability, resonant behavior, and periodicity of the actuator. The results and inferences reported here should provide the initial step toward the design and the development of modern actuators for diverse futuristic applications in the medical and engineering fields.

A discrete model for the geometrically nonlinear mechanics of hard-magnetic slender structures

Hard-magnetic soft (HMS) materials and structures, which can undergo rapid configurational transformation under non-contact magnetic stimuli, have attracted extensive attentions in a wide range of engineering applications, such as soft robotics, biomedical devices and stretchable electronics, etc. In order to realize the full potentials of HMS structures, it is crucial to be able to predict their mechanical (both static and dynamic) responses. In this work, we propose a discrete magneto-elastic rod model with the aim to analyse the mechanical behaviours of slender structures made of HMS materials under magnetic loading. The configuration of a slender object is described by multiply connected nodes and edges, from which the force vector and the associated Hessian matrix are derived by taking the variation of Kirchhoff-like magneto-elastic potentials. The nonlinear dynamical equations of motion are next evaluated through Newton-type optimization, and the static analysis can be obtained using dynamical relaxation method. For verification, we quantitatively compare our numerical results with either analytical solutions or experimental data for several representative cases. Good agreements in all these cases indicate the correctness and accuracy of our discrete model. We further extend the model to take the dipole–dipole interaction and viscous effect into consideration. Finally, as a demonstration, we perform simulations to reproduce the locomotion of a magnetic crawling robot. The developed discrete magneto-elastic model significantly improves the computational efficiency, enabling the practicability of simulating the mechanical, especially dynamic, behaviours of the hard-magnetic slender structures.

Submarine control system using sliding mode controller with optimization algorithm

<span>The purpose of this paper is to design and implement the pitch and depth control system of an autonomous underwater vehicles (AUV). This control system will determine the best pitch angle as well as the depth automatically when there are changes in speed, weight, etc. In this paper, the kinematic and dynamic equations of motion for the AUV are derived to obtain the pitch angle and depth transfer functions. The control strategies applied here, are firstly, the sliding mode controller (SMC) driven by particle swarm optimization (PSO) algorithm. Secondly, the proportional integral derivative controller (PID) tuned by PSO algorithm as a standard controller. The PSO algorithm is used as an efficient algorithm to search for the optimal controllers’ parameters and hence improving the performance of the system. The findings show that the designed sliding mode control (SMC) could improve the stability and performance and provides more realistic behavior for the AUV compared to other classical controllers and according to pitch and the depth changes.</span>

New modeling on vibrations and bifurcations of FGGP reinforced pretwisted composite rotating blade under axial aerodynamic force: Theoretical and numerical researches

A new modeling on the vibrations and bifurcations is proposed for the pretwisted composite rotating blade reinforced by the functionally graded graphene platelet (FGGP) subjected to the leakage flow at the tip clearance, aerodynamic force and high rotating speed for the first time. The blade is simplified to the dynamic model of a FGGP reinforced pretwisted composite rotating cantilever plate subjected to the in-plane and external excitations. The novel non-uniform axial excitation is applied to simulate the aerodynamic pressure of the airflow at the tip clearances subjecting to the FGGP reinforced pretwisted rotating composite blade. Three different distribution types of the graphene platelets (GPs) are studied. According to the first-order shear deformation theory and von-Karman nonlinear geometric relationship, the new differential governing equation of motion is established for the FGGP reinforced rotating pretwisted composite cantilever plate. The nonlinear dynamic equations of motion are derived by utilizing the energy functions and Lagrange equation. The validity is verified by comparing the obtained results with those of other references. The natural frequencies, bifurcations and stability are respectively studied by utilizing Rayleigh–Ritz and Newton Raphson methods. The instability regions are obtained for the FGGP reinforced pretwisted composite rotating cantilever plate. The influences of the rotating speeds, setting angles and weight fractions on the natural frequencies and vibrations are presented for the pretwisted rotating cantilever plate under three different distributions of the GPs. The obtained results illustrate that the static critical loads increase with the increase of the rotating speeds, setting angles and weight fractions under the X distribution plate for the FGGP reinforced pretwisted composite rotating cantilever plate subjected to the axial aerodynamic force and high rotating speed.

Penalty function method for FEM dynamic analysis of trusses with nonlinear multi-node constraints under harmonic load

This work introduces the establishment of the FEM model for investigating the dynamic behavior of trusses, subjected to multi-node constraints, under harmonic excitation based on utilizing the method of Penalty function. The technique for treating the nonlinear relationship of multi-node constraints is developed by using the Penalty function to extremum the Hamiltonian augmented potential energy function and to convert the multi-node constrained relation. The method of Newmark integration is utilized to convert dynamic differential equations of a truss system having multi-node boundary constraints subjected to a time-dependent harmonic force to incremental equations. The incremental-iterative algorithm had been developed based on the Newton-Raphson method, used for solving the dynamic incremental equation of motion for the truss system. Utilizing the constructed algorithm, the Matlab program is written to compute the investigated truss system’s internal force-time response and displacement-time response subjected to harmonic load. The advice for choosing the weight value of the Penalty function is proposed based on analyzing numerical results.

Modeling dynamic control model of a two-link crane-manipulator

The problem of controlling a two-link crane-manipulator depends on the level of complexity of the system. When using a two-link manipulator, two problems need to be solved. The first problem is that you need to define the control parameters in such a way that the given position of the manipulator changes according to the corresponding trajectory. The second problem is that in order to achieve the desired position of the manipulator, it is necessary to correctly parameterized the mathematical model of the control system. One of the problems that affects the accuracy of manipulator control is the correct construction of adequate dynamic control models.
 In this article was propose to consider a direct method of developing a dynamic model of the crane-manipulator. It was propose to apply a mathematical model, which is built on the principles of theoretical mechanics by applying the Lagrange equations of the second kind.
 To modeling a dynamic model of a two-link crane-manipulator, the kinetic and potential energies of the component systems of the manipulator were determined, and on the basis of the Lagrange equation of the second kind, dynamic equations of motion were obtained.
 The dependences between the capturer coordinates and the generalized coordinates were also determined. These dependencies helped to establish the control equations that allow controlling the movement characteristics of the two-link manipulator.

Influence of spatially varying ground motions on the seismic responses of bridge structures with KDampers

KDamper has been applied to control the seismic responses of bridge structures very recently. However, previous studies considered its performance under uniform ground motions only, the influence of the inevitable spatially varying ground motions (SVGMs) is not yet explored. To address this issue, this study systematically investigates the seismic responses of a large-span bridge structure equipped with KDampers subjected to SVGMs. In particular, the analytical model of a classical bridge equipped with KDampers is developed, and the corresponding dynamic equations of motion are formulated. Subsequently, KDampers are optimized by minimizing the mean peak response of the bridge deck in the frequency domain. Finally, parametric analyses are performed to comprehensively evaluate the influence of SVGMs (including wave passage and coherency loss effects) on the seismic responses of the bridge in both the frequency and time domains. The analytical results reveal that the optimized KDampers are effective in reducing the displacement and absolute acceleration responses of the bridge. Moreover, the effectiveness of KDampers is more evident when SVGMs are considered as compared to the uniform ground motions. This research can contribute to an in-depth understanding of the control effectiveness of KDampers, especially for the cases considering SVGMs.

Dynamics of a massive superfluid vortex in rk confining potentials

We study the motion of a superfluid vortex in condensates having different background density profiles, ranging from parabolic to uniform. The resulting effective point-vortex model for a generic power-law potential $\propto r^k$ can be experimentally realized with recent advances in optical-trapping techniques. Our analysis encompasses both empty-core and filled-core vortices. In the latter case, the vortex acquires a mass due to the presence of distinguishable atoms located in its core. The axisymmetry allows us to reduce the coupled dynamical equations of motion to a single radial equation with an effective potential $V_{\rm eff}$. In many cases, $V_{\rm eff}$ has a single minimum, where the vortex precesses uniformly. The dynamics of the vortex and the localized massive core arises from the dependence of the energy on the radial position of the vortex and from the $r^k$ trap potential. We find that a positive vortex with small mass orbits in the positive direction, but the sense of precession can reverse as the core mass increases. Early experiments and theoretical studies on two-component vortices found some qualitatively similar behavior.

Micro-satellite orientation control system with rotation wheels

The task of developing a microsatellite orientation control system using rotation wheels with limited control moments is under consideration. For the synthesis of control laws by the method of analytical construction of optimal regulators by minimization of the integral-quadratic functional, the dynamic equations of the rotational motion of the satellite are linearized. The governing bodies of the satellite are three rotation wheels and magnetic coils. Algorithms for controlling the satellite during stabilization, turning and stabilization of the angular position have been developed. Algorithms are tuned depending on the parameters of the satellite and ensure its stable movement in all modes. Considered examples of simulation the satellite movement using full nonlinear models, which showed the effectiveness and universality of the algorithms. The effectiveness of control algorithms for the use of the rotation wheels and magnetic coils is compared.

Dynamic snap-through of bi-stable laminates with simply supported at four corners under impact loads

In this paper, nonlinear dynamic responses of bi-stable laminate being simply supported on four corner points, which is subjected to various impact loads, are analyzed from theoretical viewpoints. Consider a four layers asymmetric cross-ply bi-stable laminate composited by the carbon fiber reinforced resin matrix. A novel configuration function that satisfies the boundary condition is proposed to predict the equilibrium configuration. Then, employing the first order shear deformation theory, the von Kàrmàn strains and Hamilton principle, nonlinear dynamic equations of motion expressed by two curvatures are derived. To obtain the two stable configurations of the laminate, the inertia terms are ignored. With the aids of static equilibrium equation, the side length and curvature of the system are solved by using NLPSolve functions in the Maple software. The stable configurations are verified by comparing present results with those reported in available literatures. Consider the incremental load loading, the decreasing loading, the sinusoidal loading, the step loading, the triangular loading and periodic loading, the nonlinear dynamic response of the bi-stable laminate are discussed. The dynamic snap-through behavior, the intra-well oscillations and inter-wall oscillations are studied by numerical simulation in detail.

Metaheuristic Identification for an Analytic Dynamic Model of a Delta Robot with Experimental Verification

The dynamic-parameter identification process for developing a suitable precise mathematical model for the implementation and operation of parallel-link robots has received attention. In this study, an efficient and reliable system-identification method for a delta robot is proposed. The parallel-link robot’s dynamic behavior was mathematically modeled according to the principle of virtual work. The dynamic equations of motion are extended to the system of equations that explicitly characterizes the inertial and centripetal/Coriolis forces, and the frictional effects on the robot’s dynamic behavior. Next, the dynamic-parameter identification technique is presented to directly estimate a set of uncertain parameters that are included in the extended dynamic model. In addition, the development of the dynamic model with a generalized inertia matrix for determining the impact of the inertia-coupling characteristic on the robot’s dynamic behaviors is examined. Experimental results indicate that the proposed parameter-estimation technique is an extremely useful tool that can achieve the high-quality identification of an analytic dynamic model for a parallel-link robot.

Double-layered granular soil modulus extraction for intelligent compaction using extended support vector machine learning considering soil-structure interaction

Intelligent Compaction (IC) has been acquiring a growing interest in real-time quality control of compacted soil layers because of its high efficiency and full-area coverage. The current intelligent compaction technology allows the determination of the uniformity level of compaction over large areas according to the dynamic response of the roller. However, accurate real-time determination of the soil modulus during compaction based on roller acceleration has been challenging due to the multi-layered composite nature of the soil and the nonlinearities of the governing dynamic equations of motion and soil response. This study adopts a double-layered soil profile, and a three-dimensional finite element model, accounting for soil-drum interaction, is utilised for the analysis. The isotropic hardening elastoplastic hysteretic model was implemented to simulate the soil behaviour subjected to cyclic loading ranging from small to large strain amplitudes and account for stiffness degradation. The comprehensive dataset composed of the roller acceleration response and ground characteristics is then used to correlate the predicted soil modulus via an advanced machine learning approach. The adopted machine learning method incorporating Gaussian Kernel and Generalised Gegenbauer Kernel functions can reasonably predict the double-layered soil modulus during roller compaction. Additional analyses were conducted to observe the proper training size and number of iterations to achieve real-time quality control to be used by site engineers. Furthermore, the influences of the relative modulus ratio, drum length and top layer modulus on the soil surface dynamic displacement are discussed.

A dynamic model of a skydiver with validation in wind tunnel and free fall

An innovative approach of gaining insight into motor skills involved in human body flight is proposed. The key idea is the creation of a model autonomous system capable of virtually performing skydiving maneuvers.A dynamic skydiver model and simulator is developed, comprising biomechanical, aerodynamic, and kinematic models, dynamic equations of motion, and a virtual reality environment. Segment relative orientations, and resulting inertial body angular position and velocity are measured in skydiving experiments in a vertical wind tunnel and in free fall. These experimental data are compared with corresponding simulation data to tune and verify the model for basic skydiving maneuvers. The model is further extended to reconstruct advanced aerial maneuvers, such as transitions between stable equilibria. The experimental data are used to estimate skydiver’s conscious inputs as a function of time, via an Unscented Kalman Filter modified for this purpose.

Entangled microwave photons generation using cryogenic low noise amplifier (transistor nonlinearity effects)

This article mainly focuses on important quantum phenomenon called entanglement arising the nonlinearity property. This study uses a unique approach in which transistor nonlinearity effect (third-order nonlinearity) entangled microwave photons are created in a cryogenic low-noise amplifier (LNA). For entanglement analysis, the Hamiltonian of the designed cryogenic LNA (containing two coupled oscillators) is derived, and then, using the dynamic equation of motion, the oscillator’s number of photons and the phase-sensitive cross-correlation factor are calculated in the Fourier domain to calculate the entanglement metric. The oscillators are coupled to each other through the gate–drain capacitor, and nonlinear transconductance is as an important factor strongly manipulating the entanglement. As a main conclusion, the study shows that the designed circuit using transistor third-order nonlinearity has the ability to generate the entangled microwave photons at very low intrinsic transconductance and more importantly when the noise figure (NF) is strongly minimized. As a complementary task, the printed circuit board of the cryogenic LNA is designed and simulated to verify the ability of the circuit to achieve an ultralow NF, by which the probability of the generation of entangled microwave photons is increased.

Nominal geometry and force measures for solids and fluids

AbstractUnderstanding solid‐ and fluid‐inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents. Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity, having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics. This paper proposes developing new continuum‐based nominal measures for the characterization of the oscillations and forces. By using a material‐point approach, these new nominal measures, which have their roots in the continuum‐mechanics partial‐differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. The paper proposes a data‐driven‐science approach to define a nominal continuum space‐curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP), which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero‐force axis (IZFA) along which the resultant of all forces vanishes. While using the material‐point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components, which can lead to accidents such as in the case of vehicle rollovers.

Seismic analysis of liquid storage tank using oblate spheroid base isolation system based on rolling friction

The seismic isolation of ground-supported cylindrical liquid storage tank using the newly developed oblate spheroid base isolation (OSBI) system is investigated. The OSBI is an ellipsoidal-shaped isolator in both of its horizontal axes and dissipates seismic input energy in rolling friction apart from period lengthening achieved through the oblateness. The detailed mathematical formulation and governing dynamical equations of motion for a tank mounted on the non-linear OSBI are derived and analyzed using the numerical integration technique to unravel the underlying mechanics behind its dynamic behavior. An idealized mechanical model of the tank consists of three-lumped masses: convective, impulsive, and rigid. The dynamic responses are investigated for the tank subjected to uni-directional sinusoidal harmonic motion as well as to five time-varying, bi-directional horizontal components of earthquakes. The seismic response of the liquid storage tanks with the OSBI system is compared with that of the same tank either isolated using pure-friction (P-F) system or kept non-isolated. In order to understand the dynamic behavior of the tank mounted on the OSBI system, the influence of different isolator parameters such as eccentricity, coefficient of rolling friction, and aspect ratio of the tank are studied. The energy responses are also evaluated to assess the performance of the OSBI system. From the present study, it is found that the OSBI system is effective in mitigating the seismic response in the liquid storage tanks.