Equations Of Motion Research Articles

A new coupled dynamic model to study the vibration and lubrication characteristics of slipper/swash-plate interface in an axial piston pump

A new integrated dynamic model is developed by examining the motion equations and kinematics of the slipper and piston, coupled with the lubrication properties of the oil film. This model simultaneously addresses the dynamic vibrations of the slipper and piston along with the characteristics of the oil film lubrication. To validate this model, a test apparatus is constructed. It is found that the power loss simulated from the slipper pair comprises approximately 20–65% of the measured power loss, while the simulated leakage flow rate generated by the slipper pair constitutes around 30–50% of the measured leakage flow rate. The vibration responses of the slipper and piston, as well as the oil film lubrication characteristics, are analyzed under various load pressures and speeds. The first several harmonics of the differences in the vibration responses of the piston and slipper and the central oil film thickness between the slipper and swash plate are in the magnitude of micrometer. The relative motions between the piston and slipper influence the oil film thickness, and the nonlinear attributes of the oil film impact the vibration behaviors of the piston and slipper. The dynamic central oil film thickness at harmonic frequencies decreases with increasing load pressure, while most harmonic-related oil film thickness increases with rising speed.

Noether symmetries of test charges in the magnetic monopole field

We consider the motion of charged test particles in the presence of a Dirac magnetic monopole. We use an extension of Noether’s theorem for systems with magnetic forces and integrate explicitly the corresponding equations of motion.

Extracting equations of motion from superconducting circuits

Alternative computing paradigms open the door to exploiting recent innovations in computational hardware to probe the fundamental thermodynamic limits of information processing. One such paradigm employs superconducting quantum interference devices (SQUIDs) to execute classical computations. This, though, requires constructing sufficiently complex superconducting circuits that support a suite of useful information processing tasks and storage operations, as well as understanding these circuits' energetics. First-principles circuit design leads to prohibitive algebraic complications when deriving the effective equations of motion—complications that to date have precluded achieving these goals, let alone doing so efficiently. We circumvent these complications by (i) specializing our class of circuits and physical operating regimes, (ii) synthesizing existing derivation techniques to suit these specializations, and (iii) implementing solution-finding optimizations which facilitate physically interpreting circuit degrees of freedom that respect physically grounded constraints. This leads to efficient and practical circuit prototyping, as well as accessing scalable circuit architectures. The analytical efficiency is demonstrated by reproducing the potential energy landscape generated by a SQUID. We then show how inductively coupling two SQUIDs produces a device that is capable of executing two-bit computations via its composite potential energy landscape. More generally, the synthesized methods detailed here provide a basis for constructing universal logic gates and investigating their thermodynamic performance. Published by the American Physical Society 2025

Classical Integrability in the Presence of a Cosmological Constant: Analytic and Machine Learning Results

AbstractThe integrability of two‐dimensional theories that are obtained by a dimensional reduction of certain four‐dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the presence of a potential for the neutral scalar fields is studied. For a certain solution subspace, partial integrability is demonstrated by showing that a subset of the equations of motion in two dimensions are the compatibility conditions for a linear system. Subsequently, the integrability of these two‐dimensional models is studied from a complementary one‐dimensional point of view, framed in terms of Liouville integrability. In this endeavor, various machine learning techniques are employed to systematize our search for numerical Lax pair matrices for these models, as well as conserved currents expressed as functions of phase space variables.

Covariant interacting fractons

We show that there exists a natural analog of the Yang-Mills equations using the Frölicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-2 tensor, and when one constrains it to be symmetric, then the system exhibits fractonic behaviors. In the linearized limit, the constrained equations of motion reduce to those of the covariant fracton model [., ., and Notes from the bulk, Ph.D. thesis, Università di Genova, 2024.]. Published by the American Physical Society 2025

Free and forced vibrations of circular plates made of functionally graded graphene origami-enabled auxetic metamaterials

Presented herein is a numerical investigation into the free and forced vibrational characteristics of circular plates made of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs). The material properties of FG-GOEAM are estimated using genetic programing-assisted micromechanical models considering two graphene content distribution patterns. The effects of graphene content, size and folding degree on the material properties are taken into account by the models. The formulation of the paper is in the context of first-order shear deformation plate theory, and the governing equations of motion are achieved utilizing Hamilton’s principle. In the solution approach, the variational differential quadrature (VDQ) method is employed by which the variational statement of problem is directly derived and discretized using matrix differential and integral operators. Selected numerical results are presented to study the effects of graphene origami (GOri) content, folding degree, and distribution pattern on the free and forced vibration responses of FG-GOEAM circular plates with clamped and hinged boundary conditions.

Numerical and experimental approach on vibration characterization of non-uniform hybrid sandwich plates

In this paper, the free vibrational response of various non-uniform composite sandwich plates with different hybrid honeycomb core types and varied weight percentages of multi-walled carbon nanotube (MWCNT) is analyzed experimentally and numerically. The governing differential equations of motion of the various honeycomb non-uniform composite sandwich plates are derived using higher order shear deformation theory and numerically solved. The various non-uniform fiber-reinforced composite face plate configurations were fabricated using the vacuum-assisted hand lay-up technique with the ply-dropping off at different domains to achieve different taper configurations. The honeycomb core was fabricated using a corrugated die, and hand lay-up method to yield various configurations. In the corrugated honeycomb core, apart from the standard hexagonal shape, composite laminated strips were longitudinally reinforced between the corrugated shape continuously and intermediately to increase the strength and damping property of the structure. The various weight percentages of R-COOH functionalized MWCNT were distributed homogeneously into epoxy using the titanium probe-assisted ultra-sonication method. Material properties such as Young’s modulus and Poison’s ratio, were evaluated for the face plate using ASTM E1876. An alternative dynamic approach was carried out to obtain the shear moduli along the corrugated direction (Gxz ) and joining direction (Gyz ) of the various core models with and without MWCNT reinforcement. An experimental and numerical investigation was performed on the various prototypes of non-uniform sandwich plates with various hybrid honeycomb core material to obtain natural frequencies and loss factors under various boundary conditions. The effect of MWCNT reinforcement in face sheet and various honeycomb core material, aspect ratio at various boundary conditions on the free vibration and transverse vibrational responses of the structure was also studied. It was found that the MWCNT reinforcement in the various honeycomb core materials increases the shear modulus considerably, thus enhancing the overall dynamic behavior of the various non-uniform honeycomb composite sandwich plates.

A Neural-Metaheuristic Kalman Filter for Moving Microburst Wind Shear Identification

A Neural-Metaheuristic Kalman Filter for Moving Microburst Wind Shear Identification

Numerical and experimental investigation of vibration of a car chassis and its effect with road gradient on noise and response optimization with factorial design method

This paper delves in to a numerical and experimental investigation of vibration of a car chassis and its effect with road gradient on noise and response optimization. Peak acceleration, peak amplitude as vibration response parameters in vertical motion, internal and pass by noise as a noise response parameters. Vibration parameters obtained numerically by developing a mathematical model of car and equation of motion. Newmark Beta method programmed in MATLAB software used to solve the equation of motion. Experimental investigation of the vibration were carried on a car consist of monocoque chassis, three cylinder engine, Macpherson front suspension and twist beam rear suspension. FFT analyzer and digital sound level meter were used for the data collection. Pass by noise data of vehicle were collected at two locations with gradient 1.15° and 11.31° on state highway (MH SH-44) near Konchi Maharashtra state, India. Comparison between numerical and experimental investigated values of vibration parameters shows minimum error of 0.6035% and average error of 2.81% which validates the car model. Factorial design method was used to optimize the index of response parameters which shows reduction in peak acceleration, peak amplitude, internal noise and pass by noise level by 65.61%, 17.70%, 7.13% and 19.41% respectively. The methodology proposed in this study provides reference to improve the performance of car suspension and passenger comfort.

Quantum Field Theory of black hole perturbations with backreaction. Part III. Spherically symmetric 2nd order Maxwell sector

In this paper we extend reduced phase space approach to black hole perturbation theory to Maxwell matter. We expand the resulting reduced Hamiltonian to second order in the graviton and photon perturbations and find that the corresponding equations of motion match the ones derived in the literature. Accordingly our approach reproduces previous results at second order. Its real virtue lies in the fact that it extends to any order in perturbation theory in a manifestly gauge invariant fashion, includes backreaction effects and covers the black hole interior due to working in the regular Painlevé Gullstrand gauge.

Numerical and experimental study on effects of net-bullet ejection angles and initial distances on space-debris capture

Numerical and experimental study on effects of net-bullet ejection angles and initial distances on space-debris capture

Quantum Field Theory of black hole perturbations with backreaction. Part II. Spherically symmetric 2nd order Einstein sector

In this second paper of our series we focus on the classical pure gravity sector of spherically symmetric black hole perturbations and expand the reduced Hamiltonian to second order. To compare our manifestly gauge invariant formalism with established results in the literature we have to translate our results derived in Gullstrand-Painlevé gauge to the gauges used in those works. After several canonical transformations we expectedly find exact agreement with the Hamiltonian given by Moncrief which generates the Regge-Wheeler and Zerilli equations of motion for the linear axial (often denoted odd) and polar (often denoted even) perturbations respectively. This confirms the validity of our method which includes backreaction and easily generalises to higher orders.

Noether symmetry of multi-delay Birkhoffian system and its conserved quantity

The Birkhoffian system, an important mechanical system in analytical mechanics, is studied in the background of multiple time delays. Both the multi-delay Birkhoffian system and the Hamiltonian system are investigated. First, the more general framework is discussed. The Pfaff–Birkhoff action is presented with multiple time delays. The multi-delay differential equations of motion are derived for both Birkhoffian and Hamiltonian models. Second, the invariance and two different kinds of Noether symmetries of the multi-delay Pfaff action are studied. Third, due to the effects of different time delays, the corresponding Noether-type theorems of multi-delay Birkhoffian systems are obtained. Two examples are presented to demonstrate the applications of the results.

Removing spurious degrees of freedom from EFT of gravity

In the effective field theory approach to gravity, the Lagrangian density forgeneral relativity is supplemented by generally covariant terms of higher orderin the Riemann tensor and its derivatives. At face value, these terms will resultin higher derivative equations of motion and additional degrees of freedombeyond those of general relativity. This is seemingly at odds with the goal ofeffective field theory which is to encode ultraviolet correctionsin terms of existing low energy degrees of freedom. Here we apply anaction-based procedure for the removal of spurious degrees of freedom for thecase of general relativity supplemented by a term cubic in the Riemanntensor.To the order we work in, the resulting reduced theory takes the form ofminimally modified gravity, which is a class of modifiedgravity theories that propagate just the massless spin-2 graviton, but exhibit a preferredframe at short distances due to a deformation of time diffeomorphisms.Our work suggests that this class of theories can be understood as aneffectivetheory of gravity, capturing effects of unknown ultraviolet physics.

Gravitational-wave signatures of gravito-electromagnetic couplings

Gravitational waves (GWs) can undoubtedly serve as a messenger from the early Universe acting as well as a novel probe of the underlying gravity theory. In this work, motivated by one-loop vacuum-polarization effects on curved spacetime, we investigate a gravitational theory with non-minimal curvature-electromagnetic coupling terms of the form ξR/M Pl2 F μν F μν , where M Pl is the reduced Planck mass, R is the scalar curvature and F μν the Faraday tensor, being responsible for the generation of primordial electromagnetic fields. We study then the GW signatures of such coupling terms deriving in particular for the first time to the best of our knowledge the modified tensor modes equation of motion. Remarkably, we find a universal infrared (IR) frequency scaling f 5 of the electromagnetically induced GW (EMIGW) signal, which, depending on the energy scale of inflation, the duration of inflation and reheating as well as the dynamical behaviour of the coupling function ξ, can be well within the detection sensitivity bands of GW experiments such as SKA, LISA, ET and BBO, being thus potentially detectable in the future by GW observatories.

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Free vibration and buckling analysis of axially functionally graded tapered Timoshenko beams using B-spline-based isogeometric analysis.

This study considers Timoshenko beam theory and the isogeometric analysis method to investigate the free vibration and buckling of axially functionally graded (AFG) tapered beams. The governing equations are obtained from the kinematic assumptions of Timoshenko beam theory and Hamilton's principle. The isogeometric analysis approach is implemented to solve the motion equations. One-dimensional B-spline basis functions are used to estimate the displacement field, describe the geometry, and illustrate the deformed shapes of the beam. Due to suffering the isogeometric approach from the shear locking phenomenon, the selectively reduced integration is applied. It is shown that this method can mitigate the effect of shear locking. In this attempt, the effect of material non-homogeneity parameters, mass density, Young's modulus, and taper ratio on the critical buckling loads and natural frequencies are considered for various boundary conditions. Several numerical examples show the accuracy and reliability of this method. The obtained results are in accord with the ones in the related articles and can be adopted as future reference solutions.

Ocean Wave Energy Converter

This research paper presents a comparative analysis of power extraction from an Oscillating Water Column (OWC) and a Point Absorber using mathematical modeling. Both systems are modeled under the same wave input conditions, with the OWC utilizing airflow dynamics to drive a turbine, and the Point Absorber modeled through heave motion equations. Linear wave theory and hydrodynamic interactions are applied to calculate power output. Results indicate that the OWC performs optimally in nearshore environments with consistent waves, while the Point Absorber is more efficient in offshore conditions. The comparison highlights how different wave characteristics influence energy capture efficiency.

Free linear vibrations of a viscoelastic spherical shell with filler

Purpose. Thin multilayered shells are widely used in aviation, shipbuilding, and mechanical engineering. Recently, interest in the dynamic analysis of shell structures under various load effects has increased. This study examines the effect of moving normal internal pressure on a viscoelastic cylindrical shell. Methods. The viscoelastic medium filling the spherical shell has a significantly lower instantaneous modulus of elasticity than the shell itself. The solution is presented for the free vibrations of the viscoelastic system "shell–filler."An analytical frequency equation in the form of a transcendental equation is derived and solved numerically using the M¨uller method. Results. It has been found that, at certain values of viscoelastic and density parameters, low-frequency natural vibrations occur. These vibrations represent an aperiodic motion since the imaginary part of the natural frequency is large. For viscoelastic mechanical systems, the dependence of damping coefficients on physical and mechanical parameters has been identified. Conclusion. A theory and methods for calculating the complex natural frequencies of vibrations of an elastic spherical inhomogeneity in an elastic medium have been developed. A classification of such vibrations into radial, torsional, and spheroidal modes has been carried out. The problem is reduced to finding those frequencies at which the system of motion equations has nonzero solutions in the class of infinitely differentiable functions.

Brock's approaching zero method improved as approaching fixed point frequency to solve optimum damping ratio of dynamic vibration absorber in machine tools and experimental confirmation.

The design parameters of the dynamic vibration absorber significantly affect the motion performance of the main vibration system. The Brock's approaching zero method was improved as approaching the fixed point frequency method. A general method of obtaining the explicit exact solution to the optimum damping ratio was presented to improve the accuracy of calculating the dynamic vibration absorber's optimum parameter. Some exact closed-form solutions, for example displacement amplitude gain, fixed point coordinate, and optimum damping ratio, were deduced with the real number form of differential equation of load motion and employing L'Hospital first rule. Many computational parameters of the main vibration system were attained. The fixed point theory essentially computes the extreme large value, not the maximum value. The numerical simulation results of the present paper's absorber are closer to the vibrational experimental results than those of the Ormondroyd absorber and Lanchester absorber. Moreover, the present paper's absorber has larger band width than the Ormondroyd absorber and Lanchester absorber. The current answers may be applicable to realize and control the accurate dynamic performances of the main vibration system and dynamic vibration absorber in operation.