Equations Of Motion Research Articles

Respiratory system mechanics during noninvasive proportional assist ventilation: A model study

AbstractPurposeTo assess the accuracies of airway resistance (Raw) and compliance (Crs) calculations using the expiratory time constant (RCexp) method as well as the accuracy of Pmus estimation in obstructive lung models.MethodsA Respironics V60 ventilator was connected to an active lung simulator. The driving pressure was maintained at 5–10 cmH2O and positive end-expiration pressure (PEEP) was 5 cmH2O. Maximal Pmus, estimated based on equations of motion and respiratory mechanical properties, was calculated by the RCexp method to derive respiratory system compliance (Crs) and inspiratory (Rinsp) and expiratory (Rexp) resistance.ResultsDuring PAV, the assist proportion was adjusted to 55% and 40% with Pmus of 5 and 10 cmH2O, respectively. Pmus measurement errors were <20% of the preset values in most lung conditions. In the active lung model with PAV, an overestimation of Raw was found in the normal resistance condition, and Rinsp was underestimated in the severe obstructive model (P < 0.01). Crs was overestimated significantly except in the severe obstructive model at a Pmus of 10 cmH2O (all P < 0.01). Using the RCexp method, the target of ≤20% between the calculated and preset values in airway resistance was achieved in most obstructive models at a Pmus of 5 cmH2O.ConclusionsThe RCexp method might provide real-time assessments of respiratory mechanics (elastance and resistance) in the PAV mode. With low inspiratory effort, the estimation error was acceptable (<20%) in most obstructive lung models.

Use of a Semi-Explicit Probabilistic Numerical Model for Concrete Cracking: From Static to Dynamic Loadings

In this paper, concrete cracking is investigated in dynamics through finite element modeling. A probabilistic semi-explicit model, previously developed and validated for static loading, is extended for dynamic loading. The model in statics is based on two material mechanical parameters: the tensile strength and the critical strain-energy release rate in mode I, GIC, of the Linear Elastic Fracture Mechanics (LEFM) theory. Concerning the dynamic aspects of the model, the tensile strength rate effect is modeled by an empirical dynamic-to-static strength ratio (Dynamic Increase Factor—DIF) and a similar formulation is proposed for GIC. The structural rate effect is naturally captured when mass and damping are included in the equation of motion. For static and dynamic loading, only macroscopic crack propagation is considered. Some numerical simulations in statics and dynamics are presented in the present paper. The main results related to this work can be summarized as follows: the dispersion of the numerical results related to the load–displacement curves decreases with the loading rate. The crack pattern considerably changes with loading rate (numerically and experimentally); the agreement between the experimental and numerical results (load–displacement curves and crack pattern) indicates the model is promising for engineering applications.

Sensorless Position Control in High-Speed Domain of PMSM Based on Improved Adaptive Sliding Mode Observer

To improve the speed buffering and position tracking accuracy of medium–high-speed permanent magnet synchronous motor (PMSM), a sensorless control method based on an improved sliding mode observer is proposed. By the mathematical model of the built-in PMSM, an improved adaptive super-twisting sliding mode observer is constructed. Based on the LSTA-SMO with a linear term of observation error, a sliding mode coefficient can be adjusted in real time according to the change in rotational speed. In view of the high harmonic content of the output back electromotive force, the adaptive adjustment strategy for the back electromotive force is adopted. In addition, in order to improve the estimation accuracy and resistance ability of the observer, the rotor position error was taken as the disturbance term, and the third-order extended state observer (ESO) was constructed to estimate the rotational speed and rotor position through the motor mechanical motion equation. The proposed method is validated in Matlab and compared with the conventional linear super twisted observer. The simulation results show that the proposed method enables the observer to operate stably in a wide velocity domain and reduces the velocity estimation error to 6.7 rpm and the position estimation accuracy error to 0.0005 rad at high speeds, which improves the anti-interference capability.

Asymmetric limit cycles within Lorenz chaos induce anomalous mobility for a memory-driven active particle

On applying a small bias force, nonequilibrium systems may respond in paradoxical ways such as with giant negative mobility (GNM)—a large net drift opposite to the applied bias, or giant positive mobility (GPM)—an anomalously large drift in the same direction as the applied bias. Such behaviors have been extensively studied in idealized models of externally driven passive inertial particles. Here, we consider a minimal model of a memory-driven active particle inspired from experiments with walking and superwalking droplets, whose equation of motion maps to the celebrated Lorenz system. By adding a small bias force to this Lorenz model for the active particle, we uncover a dynamical mechanism for simultaneous emergence of GNM and GPM in the parameter space. Within the chaotic sea of the parameter space, a symmetric pair of coexisting asymmetric limit cycles separate and migrate under applied bias force, resulting in anomalous transport behaviors that are sensitive to the active particle's memory. Our work highlights a general dynamical mechanism for the emergence of anomalous transport behaviors for active particles described by low-dimensional nonlinear models. Published by the American Physical Society 2024

On the laminar solutions and stability of accelerating and decelerating channel flows

We study the effect of acceleration and deceleration on the stability of channel flows. To do so, we derive an exact solution for laminar profiles of channel flows with an arbitrary, time-varying wall motion and pressure gradient. This solution then allows us to investigate the stability of any unsteady channel flow. In particular, we restrict our investigation to the non-normal growth of perturbations about time-varying base flows with exponentially decaying acceleration and deceleration, with comparisons to growth about a constant base flow (i.e. the time-invariant simple shear or parabolic profile). We apply this acceleration and deceleration through the velocity of the walls and through the flow rate. For accelerating base flows, perturbations never grow larger than perturbations about a constant base flow, while decelerating flows show massive amplification of perturbations – at a Reynolds number of $500$ , properly timed perturbations about the decelerating base flow grow $ {O}(10^5)$ times larger than perturbations grow about a constant base flow. This amplification increases as we raise the rate of deceleration and the Reynolds number. We find that this amplification arises due to a transition from spanwise perturbations leading to the largest amplification to streamwise perturbations leading to the largest amplification that only occurs in the decelerating base flow. By evolving the optimal perturbations through the linearized equations of motion, we reveal that the decelerating base flow achieves this massive amplification through the Orr mechanism, or the down-gradient Reynolds stress mechanism, which accelerating and constant base flows cannot maintain.

Determination of the characteristics of the perturbed transition orbit to transfer from LEO to GEO

This paper aims to study, the process of satellite transition between different orbits and evaluate the characteristics of the turbulent transitional orbit of transferring a satellite from Low Earth Orbit (LEO) to geostationary orbit (GEO) (hp=35790km). The measurements in this research involve considering different LEO characteristics of perigee heights (h_p=200, 400, 600,800) and eccentricities (e=0.01, 0.05 and 0.1), whereas the inclination is fixed to be (i= 23.445 degree).Also, the transfer of the satellite was studied in two stages. The first stage was from the perigee of the first orbit at height 200 km, to the apogee of the second orbit at height 945 km with eccentricity (0.01). the second stage, was the transition the satellite from the perigee of the second orbit at height 800 km to the final orbit (GEO) with the same eccentricity. Two types of turbulence were considered which are atmospheric drag and perturbation (Geopotential acceleration The perturbing acceleration effects on satellite due to the Earth’s gravity potential represent as function of J2 parameter). A program in MATLAB was designed to calculate the speed that for the transition, time and the ratio mass change, which represents the percentage of fuel as well as the extent of the effect of turbulence on the orbital elements of the transitional orbit.The perturbed equation of motion was solved using Runge–Kutta method. The results showed that the increase altitude, the lower ΔV(velocity required to transition), where the ΔV at altitude of 800 km was the best results, reaching (2.244 km/sec). As for the transition in two stage, it may need a higher energy for the transition, as the difference between it and the direct phase in (ΔV= 0.011 km/sec). As the height of the initial orbit increases, the effect of the disturbance on the orbital elements of the transitional orbit decreases, and since the transition time is less than half a day (0.44 day), the effect of the disturbance is clear, so it cannot be neglected.

Exploring dynamics, stability, and bifurcation in a coupled damped oscillator with piezoelectric energy harvester

In this work, we analyze and investigate the mathematical modeling of a dynamical system connected to a piezoelectric device. Piezoelectric transducers are established as highly effective energy harvesting (EH) devices, often employed in real-world mechanical systems. The structure of the dynamical model contains a damped Duffing oscillator acting as the major component, which is connected to an unstretched pendulum and simultaneously to the piezoelectric harvester. To derive the governing equations of motion (EOM), Lagrange’s equations are applied based on the system’s generalized coordinates, in which they are analytically solved using the multiple scales (MS) perturbation method up to the second approximation. Moreover, the solutions achieved are compared with numerical ones to increase transparency and demonstrate the accuracy of the approximate solutions. In addition, comprehensive graphical representations have been produced to investigate the nonlinear stability of the modulation equations. Phase portraits, bifurcation diagrams, and Lyapunov spectra are displayed to depict various system behaviors, alongside Poincaré maps for deeper understanding. The various stability ranges are also explored and discussed. In conclusion, mechanical vibrations are transformed into electricity by the piezoelectric transducer connected to the dynamic model, which has widespread applications and includes crystal oscillators, medical ultrasound, gas igniters, and displacement transducers.

Derivation of a generalized Langevin equation from a generic time-dependent Hamiltonian

Abstract The traditional Mori-Zwanzig formalism yields equations of motion, so-called generalized Langevin equations (GLEs), for phase-space observables of interest from the microscopic dynamics of a many-body system governed by a time-independent Hamiltonian using projection techniques. By using time-ordered propagators and time-independent projection operators, we derive the GLE for a scalar observable from a generic time-dependent Hamiltonian. The only restriction in our derivation is that the time-dependent part of the Hamiltonian and the observable of interest depend on spatial phase-space variables only. If the observable obeys Gaussian statistics and the time-dependent part of the Hamiltonian can be expressed as an odd power of the observable, the friction memory kernel in the GLE becomes proportional to the second moment of the complementary force, as is the case for a time-independent Hamiltonian in the Mori-Zwanzig formalism.

Precession motions of a gyrostat, having a fixed point, in three homogeneous force fields

The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of a gyrostat motion are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations was conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2:1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It was proved that the obtained solutions can be described by elementary functions of time.

Dynamic modelling and predictive position/force control of a plant-inspired growing robot

This paper presents the development and control of a dynamic model for a plant-inspired growing robot, termed the 'vine-robot', using the Euler-Lagrangian method. The unique growth mechanism of the vine-robot enables it to navigate complex environments by extending its body. We derive the dynamic equations of motion and employ model predictive control to regulate the task space position, orientation, and interaction forces. Simulation experiments are conducted to evaluate the performance of the proposed model and control strategy. The results demonstrate that the model effectively achieves sub-millimeter precision in the position control in both static and time varying refrence trajectroies, and sub micronewton in force control.

Mathematical Modeling of Cylindrical Reinforcement Loaded with Distributed Load in Various Directions

Discusses the mathematical modeling of the stress-strain state of cylindrical fittings loaded with a distributed load in various directions. The main attention is paid to the determination of internal stress and the law of its distribution for fittings created on the basis of basalt rocks. A mathematical model is constructed that includes equations of motion, strength conditions, and the relationship between stress and deformation.

A fully enclosed wave energy converter and effects of cable-based PTO on power absorption

Abstract Existing wave energy converters (WECs) are limited by high unit energy costs, narrow bandwidths and vulnerability to seawater corrosion, making it difficult for wave energy to compete with solar and wind energy. This paper presents a fully enclosed WEC based on cable-driven parallel mechanisms, which absorbs energy from multiple directions to enhance the total energy absorption efficiency and bandwidth. The configuration of the inner cable-parallel mechanism (CDPM) is the key to this improved absorption efficiency. A configuration synthesis method of cable-driven parallel mechanisms is proposed to generate more configurations for the fully enclosed WEC. The motion equation of the fully enclosed WEC is derived to evaluate the power absorption performance. Moreover, a configuration synthesis method for realizing n-DOF configurations in the fully constrained CDPMs is proposed, and the configurations of these n-DOF fully-constrained CDPMs with (n + 1) cables are acquired. Then, the power absorption performance under different PTO parameters and wave frequencies is calculated, and the effects of the CDPM configuration are investigated. The results indicate that the proposed WECs exhibit excellent performance in mean absorbed power and bandwidth. Several principles for configuration selection are provided to further improve the performance of the CDPM-based fully enclosed WEC.

Eccentric mergers in AGN Discs: Influence of the supermassive black-hole on three-body interactions

Abstract There are indications that stellar-origin black holes (BHs) are efficiently paired up in binary black holes (BBHs) in Active Galactic Nuclei (AGN) disc environments, which can undergo interactions with single BHs in the disc. Such binary-single interactions can potentially lead to an exceptionally high fraction of gravitational-wave mergers with measurable eccentricity in LIGO/Virgo/KAGRA. We here take the next important step in this line of studies by performing post-Newtonian N-body simulations between migrating BBHs and single BHs set in an AGN disc-like configuration, with a consistent inclusion of the central supermassive black hole (SMBH) in the equations of motion. With this setup, we study how the fraction of eccentric mergers varies in terms of the initial size of the BBH semi-major axis relative to the Hill sphere, as well as how it depends on the angle between the BBH and the incoming single BH. We find that the fraction of eccentric mergers is still relatively large, even when the interactions are notably influenced by the gravitational field of the nearby SMBH. However, the fraction as a function of the BBH semi-major axis does not follow a smooth functional shape, but instead shows strongly varying features that originate from the underlying phase-space structure. The phase-space further reveals that many of the eccentric mergers are formed through prompt scatterings. Finally, we present the first analytical solution to how the presence of an SMBH in terms of its Hill sphere affects the probability for forming eccentric BBH mergers through chaotic three-body interactions.

Scalable O(log2n) Dynamics Control for Soft Exoskeletons

Robotic exoskeletons are being actively applied to support the activities of daily living (ADL) for patients with hand motion impairments. In terms of actuation, soft materials and sensors have opened new alternatives to conventional rigid body structures. In this arena, biomimetic soft systems play an important role in modeling and controlling human hand kinematics without the restrictions of rigid mechanical joints while having an entirely deformable body with limitless points of actuation. In this paper, we address the computational limitations of modeling large-scale articulated systems for soft robotic exoskeletons by integrating a parallel algorithm to compute the exoskeleton’s dynamics equations of motion (EoM), achieving a computation with O(log2n) complexity for the highly articulated n degrees of freedom (DoF) running on p processing cores. The proposed parallel algorithm achieves an exponential speedup for n=p=64 DoF while achieving a 0.96 degree of parallelism for n=p=256, which demonstrates the required scalability for controlling highly articulated soft exoskeletons in real time. However, scalability will be bounded by the n=p fraction.

Numerical Study of the Influence of Boundary Conditions on Calculations of the Dynamics of Polydisperse Gas Suspension

The work numerically simulates the flow of a polydisperse gas suspension in a channel. The carrier medium was described as a viscous, compressible, heat-conducting gas. The mathematical model implemented a continuum technique for the dynamics of multiphase media, taking into account the interaction of the carrier medium and the dispersed phase. For each component of the mixture, a complete hydrodynamic system of equations of motion for the carrier phase and dispersed phase fractions was solved. The dispersed phase consisted of particles with different sizes of dispersed inclusions. For the carrier medium, homogeneous Dirichlet boundary conditions were specified on the side surfaces of the channel. For fractions of the dispersed phase, boundary conditions for slippage. The influence of the boundary conditions of the flow of the carrier medium on the dynamics of gas suspension fractions has been revealed.

Closed-Form Solution for Scale-Dependent Frequencies of Shear Deformable Cellular Microplates Coated by Piezoelectric Polymeric Skins Consisting of FG Distributed CNTs

In this work, a rectangular cellular microplate is taken into consideration which is embedded between two functionally graded carbon nanotube-reinforced composite layers that have the piezoelectric ability. Different patterns for the carbon nanotube dispersion are considered. Moreover, an external electrical voltage is applied to them. The displacements are described based on a higher-order shear deformation theory which is called hyperbolic theory and the size influence is captured via the modified couple stress formulations. The governing motion equations are then derived using the variational technique and Hamilton’s principle. Then, for simply supported edge conditions, a closed-form solution is provided. Next, it turns to validate the results in simpler states, and after that, the effect of the most prominent parameters on the results is investigated. It is observed that by increasing the external applied voltage to the face sheets, the frequencies are reduced. Also, the natural frequencies have a tendency to decrease as the dimensionless material length scale parameter increases. This study’s outcomes may help design and manufacture micro-/nano-electro systems, sensors and actuators, small-scale devices, and other engineering structures.

Pattern phase transition of spin particle lattice system

To better understand the pattern phase transition of both physical and biological systems, we investigate a two-dimensional spin particle lattice system using statistical mechanics methods together with XY model governed by Hamiltonian equations of motion. By tweaking the coupling strength and the intensity of the generalization field, we observe phase transitions among four patterns of spin particles, i.e., vortex, ferromagnet, worm and anti-ferromagnet. In addition, we analyze the effect of space boundaries on the formations of vortex and worm. Considering the inherent dynamics of individual particles, we revealed the forming mechanism of such phase transitions, which provides a new perspective for understanding the emergence of phase transition of spin particles systems.

Uphill dynamics: A spring-mass model analysis of sloped walking

This study explores the biomechanics of uphill running by adjusting and analyzing the spring- mass model. Modifications specific to slope conditions were made to the equations of motion. Despite facing challenges in code execution, an in-depth investigation of the models physical characteristics was conducted through both static and dynamic state analyses. The findings aid in the theoretical understanding of motion on sloped surfaces and provide valuable experience for subsequent research.

New effectual configuration of bistable nonlinear energy sink

The study presents a new configuration of nonlinear energy sinks (NESs) which is adaptable to function as either stable or bistable NES. The proposed NES is based on the spring-loaded inverted pendulum (SLIP) in which a torsional stiffness element couples the SLIP to the linear oscillator (LO). The bistable configuration provides a critically stable position when the SLIP is vertically aligned with respect to the LO motion. At this critical stability position, the SLIP NES incorporates pre-stored potential energy which generates the bistability characteristics resembling that of a stiffness-based bistable NES. The equations of motion of the coupled LO with the SLIP NES are derived based on the Euler–Lagrange method in non-dimensional form. The parameters of the considered SLIP NESs are optimized to achieve an optimum energy absorption from the LO. The proposed B-SLIP NES is also applied to suppress seismic ground motion and forced torsional vibrations. The obtained numerical simulation and analytical response results verify the robustness of the B-SLIP NES in vibration suppression performance compared with the tuned mass damper and the cubic stiffness NES.

Transient analysis of functionally graded axisymmetric plates via finite element method in the Laplace domain

The principal goal of this research article is to examine the forced vibration of Functionally Graded Material (FGM) axisymmetric plates with the aid of the finite element method in the Laplace space. The material properties are assumed to be isotropic, linear viscoelastic, or elastic and vary continuously in the direction of the thickness of the plate. The governing equations of motion are transferred to the Laplace domain and solved for a set of Laplace parameters. Then, a modified Durbin’s inverse Laplace method is employed to retransfer the obtained results back to the time domain. A convergence analysis is conducted to optimize the number of Laplace parameters and time steps. An 8-node quadratic quadrilateral element featuring two degrees of freedom per node is employed to generate the model of the axisymmetric plates. Different loads such as step load, square wave, and sawtooth wave loads are used to observe the impact of load type on the transient response of FGM plates. In viscoelastic analysis, the Kelvin damping model is preferred, and the effect of the damping ratio is investigated. The obtained results are validated with the aid of the available literature and the accuracy of the suggested model is confirmed. It is carried out that the material variation significantly affects the dynamic behavior of the plates, for instance as the material coefficient increases, displacement amplitudes decrease, and periods increase. The novelty of this paper is the employment of the finite element method together with Laplace transformation for addressing the present class of problems for the first time.