Equations Of Motion Research Articles

Vibrational dynamics of a subjected system to external torque and excitation force

This work focuses on the dynamical response of a novel auto-parametric two-degrees-of-freedom (DOF) dynamical system when it is subjected to external torque and force. It consists of a forced oscillator with nonlinear stiffness that is connected to a linear spring. In accordance with the system’s DOF, an organizing system of equations of motion (EOM) is produced using Euler–Lagrange’s equations. To obtain the analytical approximate solutions (ASs) of the equations of this system, the multiple scales technique (MST) is employed. The provided solutions are being juxtaposed with the numerical solutions (NSs) for comparison to show how closely they agree, as well as the precision of the MST. In view of removing secular terms, the system’s solvability criteria are obtained. All arising resonance cases are classified, and two of them are then examined at once. The relevant system of modulation equations is solved numerically to illustrate the advantageous influence of diverse factors on the behavior of the modified phases and amplitudes. Based on the values of these parameters, the frequency response curves (FRCs) are drawn to explore different zones of stability and instability. A wide variety of values for the system’s parameters shows that its behavior is steady. The achieved outcomes are deemed novel, as the MST has been applied on a new dynamical model. The results have broad relevance and can be implemented in various engineering contexts, including the analysis of ship movements, in which nonlinear coupling between rolling and pitching motions can be found.

Black hole — wormhole transitions in two dimensional string theory

We study charged black hole and wormhole solutions of Type 0A/IIA string theory in two dimensions, by analysing their low energy equations of motion at leading order in α′. There is a competition between Euclidean wormholes and near extremal black holes in the thermodynamic ensemble. In a certain regime of phase space, the former can disassociate into the latter. Since such solutions are of string scale near the wormhole throat that takes an AdS2 form, there is a need for an exact worldsheet description. We discuss relevant WZW coset models which we argue will shed light on this problem. Finally, we present appropriate versions of the Type 0A/IIA matrix quantum mechanics models that are expected to describe these geometries.

Coupled modal characteristics of a bladed rotor bearing system under aerodynamic and rotor excitations: Modelling and numerical study

Bladed Rotor Bearing System is considered in the coupled vibration analysis among blades and the rotor system. The governing equations of motion are derived based on Lagrange’s equation, which accounts for the coupled vibrational modes. The model is discretised based on the Galerkin finite element method. A comparative analysis on the influence of uniform and pre-twisted blade configurations on the BRBS and on individual blades is carried out. Free vibration analysis for various blade geometry configurations is studied and results show that natural frequencies of the blades are reduced in the presence of pre-twist whereas the same is increased with double-taper. The Campbell diagram revealed the presence of frequency veering among the blades and rotor loci of natural frequencies for a specific blade configuration. The influence of aerodynamic and external excitations on the blades and the rotor, respectively, are considered in the forced response analysis, where the resulting effects of both the excitations on the individual blades and the BRBS for different blade configurations are studied.

The Finite Element Method in Time for Multibody Dynamics

Abstract The generalized-α scheme has become the approach of choice for the time integration of the equations of motion of multibody systems. Despite its simplicity, this scheme presents drawbacks: the time-step size cannot be changed easily, making it difficult to implement time adaptivity, and the solution of periodic problems cannot be found easily. This paper explores an alternative approach based on the finite element method in time. The basic principles underpinning the approach are presented and both time-continuous and time-discontinuous approaches are investigated. Two types of Galerkin schemes will be presented here: the time-continuous and the time-discontinuous schemes. In the former, the displacement field is continuous across interelement boundaries, whereas discontinuities or “jumps” are allowed across interelement boundaries for the latter. Simple problems are treated to identify the best schemes. Families of schemes of various accuracies are presented. The first family, based on time-continuous elements, features schemes that do not present numerical dissipation. Asymptotic annihilation is achieved by the time-discontinuous elements that form the second family. The problem of kinematic constraints is treated within the framework of the finite element method in time. Special emphasis is devoted to the satisfaction of the kinematic constraints and their time derivative within a time element.

Reducing the Constrained Multibody Dynamics Problem to the Solution of a System of Ordinary Differential Equations Via Velocity Partitioning and Lie Group Integration

Abstract In multibody dynamics, formulating the equations of motion in absolute Cartesian coordinates results in a set of index-3 differential algebraic equations (DAEs). In this work, we present an approach that bypasses the DAE problem by partitioning the velocities in the system into dependent and independent coordinates, thereby reducing the task of producing the time evolution of the mechanical system to one of solving a set of ordinary differential equations (ODEs). In this approach, the independent coordinates are integrated directly, while the dependent coordinates are recovered through the kinematic constraint equations at the position and velocity levels. Notably, Lie group integration is employed to directly obtain the orientation matrix A at each time-step of the simulation. This eliminates the need to choose generalized coordinates to capture the orientation of a body, as the matrix A is a by-product of the solution algorithm. Herein, we outline the new approach and demonstrate it in conjunction with four mechanisms: a single pendulum, a double pendulum, a four-link mechanism, and a slider crank. We report on the convergence order behavior of the proposed method and compare its performance with an established method that combines coordinate partitioning with an Euler parameter formulation. The Python code developed to generate the reported results is open-source and available in a public repository for reproducibility studies.

A non-invasive method to monitor respiratory muscle effort during mechanical ventilation.

This study introduces a method to non-invasively and automatically quantify respiratory muscle effort (Pmus) during mechanical ventilation (MV). The methodology hinges on numerically solving the respiratory system's equation of motion, utilizing measurements of airway pressure (Paw) and airflow (Faw). To evaluate the technique's effectiveness, Pmus was correlated with expected physiological responses. In volume-control (VC) mode, where tidal volume (VT) is pre-determined, Pmus is expected to be linked to Paw fluctuations. In contrast, during pressure-control (PC) mode, where Paw is held constant, Pmus should correlate with VT variations. The study utilized data from 250 patients on invasive MV. The data included detailed recordings of Paw and Faw, sampled at 31.25Hz and saved in 131.1-second epochs, each covering 34 to 41 breaths. The algorithm identified 51,268 epochs containing breaths on either VC or PC mode exclusively. In these epochs, Pmus and its pressure-time product (PmusPTP) were computed and correlated with Paw's pressure-time product (PawPTP) and VT, respectively. There was a strong correlation of PmusPTP with PawPTP in VC mode (R² = 0.91 [0.76, 0.96]; n = 17,648 epochs) and with VT in PC mode (R² = 0.88 [0.74, 0.94]; n = 33,620 epochs), confirming the hypothesis. As expected, negligible correlations were observed between PmusPTP and VT in VC mode (R² = 0.03) and between PmusPTP and PawPTP in PC mode (R² = 0.06). The study supports the feasibility of assessing respiratory effort during MV non-invasively through airway signal analysis. Further research is warranted to validate this method and investigate its clinical applications.

Setting the connection free in the Galilei and Carroll expansions of gravity

We obtain a Palatini-type formulation for the Galilei and Carroll expansions of general relativity, where the connection is promoted to a variable. Known versions of these large and small speed of light expansions are derived from the Einstein-Hilbert action and involve dynamical Newton-Cartan or Carroll geometry, along with additional gauge fields at subleading orders. The corresponding Palatini actions that we obtain in this paper are derived from an appropriate expansion of the Einstein-Palatini action, and the connection variable reduces to the Galilei- or Carroll-adapted connection on shell. In particular, we present the Palatini form for the next-to-leading-order Galilean action and recover the known equations of motion. We also compute the leading-order Palatini-type action for the Carrollian case and show that, while it depends on the connection variable, it reduces on shell to the known action of electric Carroll gravity, which only depends on extrinsic curvature. Published by the American Physical Society 2024

Impact dynamic response of stiffened porous functionally graded materials sandwich doubly-curved shells with Arc-type auxetic core

The Arc-type auxetic core is based on the traditional concave hexagonal core and incorporates a bending configuration, facilitating a smooth transition of the cell elements. This modification proves highly effective in alleviating stress concentration. To extend its use in sandwich structures, the dynamic behavior of stiffened porous functionally graded materials (PFGMs) doubly-curved sandwich shell with Arc-type auxetic core under low-velocity impact is a concern that this research addresses. The material properties of external PFGM panels are controlled by two grading patterns (P-FGM and E-FGM) and has four different porosity distributions. The core layer is made of Arc-type auxetic core. A theoretical model that utilizes Hertzian elasticity theory and first-order shear deformation theory (FSDT) is proposed, and the equations of motions are derived using the Hamilton's principle. In addition, to simulate the contact force interaction in dynamic process, the spring-mass model is employed. The analytical solution is presented by using Duhamel's principle and Navier's method to anticipate the transverse displacement. The effectiveness of the obtained data is verified by comparing the findings with those of the existing literature and the numerical results established by the Abaqus commercial software. On this basis, efficient methods for optimizing the PFGM doubly-curved sandwich shell are presented by analyzing the effect of porosity, porosity distribution, gradient index, grading pattern, auxetic core inclined angle and circular arc radius on the energy absorption capability, wherein the sandwich shell of P-FGM reduces the transverse displacement by 24.5 % over E-FGM, and the corresponding gain effects for different porosity distributions are Type B > Type D > Type C > Type A.

Asymptotic Analysis of an Elastic Layer under Light Fluid Loading

Asymptotic analysis for an elastic layer under light fluid loading was developed. The ratio of fluid and solid densities was chosen as the main small parameter determining a novel scaling. The leading- and next-order approximations were derived from the full dispersion relation corresponding to long-wave, low-frequency, antisymmetric motions. The asymptotic plate models, including the equations of motion and the impenetrability condition, motivated by the aforementioned shortened dispersion equations, were derived for a plane-strain setup. The key findings included, in particular, the necessity of taking into account transverse plate inertia at the leading order, which is not the case for heavy fluid loading. In addition, the transverse shear deformation, rotation inertia, and a number of other corrections appeared at the next order, contrary to the previous asymptotic developments for fluid-loaded plates not assuming a light fluid loading scenario.

New non-supersymmetric flux vacua from generalised calibrations

We construct a new class of non-supersymmetric ten-dimensional type II flux vacua, by studying first order differential equations which are deformations of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions. We do so within the context of Generalised Complex Geometry, where there is a natural interpretation of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{N}$$\\end{document} = 1 supersymmetry conditions in terms of calibration conditions for probe D-branes, called D-string, domain-wall or space-filling branes, depending on them wrapping two, three or four non-compact dimensions. We focus on the class of non-supersymmetric vacua violating the D-string calibration condition, and write down their general equations of motion in the language of pure spinors. We solve them for a subclass of vacua, where the deformation of the calibration condition is dictated by the foliated geometry of the internal space. We also construct backgrounds violating both the domain-wall and D-string calibration conditions, generalising the one-parameter DWSB class of backgrounds introduced in Lüst et al. We present several explicit solutions with SU(2) and SU(3) structures, and we investigate briefly their associated low energy effective theories.

Data-driven discovery of interpretable Lagrangian of stochastically excited dynamical systems

Exploring the intersection of deterministic and stochastic dynamics, this paper delves into Lagrangian discovery for conservative and non-conservative systems under stochastic excitation. Traditional Lagrangian frameworks, adept at capturing deterministic behavior, are extended to incorporate stochastic excitation. The study critically evaluates recent computational methodologies for learning Lagrangians from observed data, highlighting the limitations in interpretability and the exclusion of stochastic excitation. To address these gaps, an automated data-driven framework is proposed for the simultaneous discovery of Lagrange densities and diffusion coefficients of stochastically excited dynamical systems by leveraging sparse regression. This novel framework offers several advantages over existing approaches. Firstly, it provides an interpretable description of the underlying Lagrange density, allowing for a deeper understanding of system dynamics under stochastic excitations. Secondly, it identifies the interpretable form of the diffusion coefficient of generalized stochastic force, addressing the limitations of existing deterministic approaches. Additionally, the framework demonstrates robustness and versatility through numerical case studies encompassing both stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs), with results showing almost exact approximations to true system behavior and minimal relative error in derived equations of motion.

N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}=4 Supergravity with Local Scaling Symmetry in Four Dimensions

We construct the most general four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supergravity coupled to an arbitrary number n of vector multiplets in which the global scaling symmetry is gauged, in addition to a subgroup of SL(2, ℝ) × SO(6, n). The various gaugings are parametrized by an embedding tensor built out of 2n+63+4n+6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 2\\left(\\begin{array}{c}n+6\\\\ {}3\\end{array}\\right)+4\\left(n+6\\right) $$\\end{document} parameters that satisfy a specific set of quadratic consistency constraints, to which we provide explicit solutions. We also derive the local supersymmetry transformation rules and the equations of motion for the four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 matter-coupled supergravity with local scaling symmetry. Such supergravity theories do not possess an action, since the scaling symmetry is only an on-shell symmetry of the corresponding ungauged theories.

Model Simplification for Asymmetric Marine Vehicles in Horizontal Motion—Verification of Selected Tracking Control Algorithms

This paper addresses a trajectory tracking control algorithm for underactuated marine vehicles moving horizontally in which the current in the North–East–Down frame is constant. This algorithm is a modification of a control scheme based on the input-output feedback linearization method, for which the application condition was that the vehicle was symmetric with respect to the left and right sides. The proposed control scheme can be applied to a fully asymmetric model, and, therefore, the geometric center can be different from the center of mass in both the longitudinal and lateral directions. A velocity transformation to generalized vehicle equations of motion was used to develop a suitable controller. Theoretical considerations were supported by simulation tests performed for a model with 3 degrees of freedom, in which the performance of the proposed algorithm was compared with that of the original algorithm and the selected control scheme based on a combination of backstepping and integral sliding mode control approaches.

Non-Abelian T-dualities in two dimensional (0, 2) gauged linear sigma models

We consider two dimensional (2D) gauged linear sigma models (GLSMs) with (0, 2) supersymmetry and U(1) gauge group which posses global symmetries. We distinguish between two cases: one obtained as a reduction from the (2, 2) supersymmetric GLSM and another not coming from a reduction. In the first case we find the Abelian T-dual, comparing with previous studies. Then, the Abelian T-dual model of the second case is found. Instanton corrections are also discussed in both situations. We explore the vacua for the scalar potential and we analyse the target space geometry of the dual model. An example with gauge symmetry U(1) × U(1) is discussed, which posses non-Abelian global symmetry. Non-Abelian T-dualization of U(1) (0, 2) 2D GLSMs is implemented for models that arise as a reduction from the (2, 2) case; we study a model with U(1) gauge symmetry and SU(2) global symmetry. It is shown that for a positive definite scalar potential, the dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} constitutes a disk. Instanton corrections to the superpotential are obtained and are shown to be encoded in a shift of the holomorphic function E. We conclude by analyzing an example with SU(2) × SU(2) global symmetry, obtaining that the space of dual vacua to \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} × \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb{P}}^{1}$$\\end{document} consists of two copies of the disk, also for the case of positive definite potential. Here we are able to fully integrate the equations of motion of non-Abelian T-duality, improving the analysis with respect to the studies in (2, 2) models.

Non-Local Cosmology: From Theory to Observations

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function F(R,□−1R), where R denotes the Ricci curvature scalar and the operator □−1 introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of f(R,□−1R) gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.

Nonadiabatic dynamics of molecules interacting with metal surfaces: A quantum-classical approach based on Langevin dynamics and the hierarchical equations of motion.

A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum-classical methods based on Langevin equations to models containing strong electron-electron or quantum electronic-vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule-metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions.

Research on moving object tracking with a large number of outliers based on TRESAC++ algorithm

In contrast to the method based on motion equations, image registration proves effective for tracking moving objects in missions where establishing a motion model is unfeasible. However, in cases where the object is captured at varying imaging angles or against a similar background, a large number of outliers may arise during the process of image feature extraction. Consequently, when confronted with a large number of outliers, image registration methods exhibit a drawback in accurate outlier filtering, especially when spatial constraints on feature matching pairs are constrained. Ultimately, these factors can render object tracking inaccurate or even unattainable. In light of the aforementioned circumstances, this paper proposes TRESAC++, which based on a triplet relation feature matching method to effectively filter outliers. To enhance the operational efficiency of the algorithm, Principal Component Analysis is employed for dimensionality reduction, aiming to decrease the incidence of triple matches and subsequently mitigate execution time. To fortify the algorithm's robustness, a triplet relation linked with an initial data subset selection strategy is additionally proposed. Experimental results on five challenging experiments show that TRESAC++ rivals current state-of-the-art techniques in terms of computational cost, while the implementation exhibits better outlier filtering. Additionally, Experiment 4 and Experiment 5 use moving object datasets to confirm TRESAC++'s superior capability in precise object tracking.

Vibrating roller with compacted soil interaction modelling

Introduction. Vibrating rollers are the most common means of compacting soils in construction. The nature of stress development on the contact surface of the roller with the ground depends on the technical characteristics of the vibrating roller (the mass of the roller, the mass of the roller frame, the frequency and driving force of vibrations, the number and characteristics of the roller shock absorbers) and the properties of the soil.Materials and methods. Simulation of the interaction of a vibrating roller with compacted soil was carried out using a three-mass rheological model of the frame-roller-soil system. Differential equations of mass motion in contact and separation modes were solved numerically. To determine the numerical values of the loading time (increase in contact stresses from zero to the maximum value) and the unloading time (decrease in contact stresses from the maximum value to zero), as well as the maximum reaction force of the soil, a computational experiment was conducted on a rheological model. The mass of the vibrating roller module (the mass of the front axle) and the relative driving force were used as independent parameters of the vibrating roller. The coefficients of elastic and viscous resistance of the soil were chosen as independent parameters of the soil. The total number of combinations of factors was 192. The values of the time of loading and unloading of the soil, as well as the maximum strength of the soil reaction, were determined by oscillograms of changes in the strength of the soil reaction over time.Results. Using the STATISTICA program, regression equations, to calculate the numerical values of the loading and unloading time of the soil, as well as the maximum reaction force of the soil and the corresponding values of the reliability coefficients of the multiple approximation, were obtained.Discussion and conclusion. The rheological model reproduces the asymmetric nature of changes in contact stresses during soil compaction by a vibrating roller, observed in experimental stress oscillograms obtained during field experimental studies. The results obtained are important for calculating the depth of stress propagation in the ground and the distribution of stresses in the ground after the passage of a vibrating roller using a wave approach to describing stress propagation in the ground. In the future, it is advisable to conduct a computational experiment with an expanded list of independent parameters of the roller, including the oscillation frequency.

Mathematical model of a lightweight three-axle off-road vehicle construction for Arctic zone of Russia

Introduction. The model and results of calculating the smoothness of a light three-axle off-road vehicle for the Arctic zone of Russia are considered. The model on standard approaches and uses a system of assumptions that limits the number of degrees of freedom for the vehicle body to three, as well as one degree of freedom for the unsprung masses is based. The mathematical model is a system of ordinary differential equations and is supplemented with the necessary algebraic equations, as well as initial conditions. The system is integrated using the 4th order RungeKutta method, for which a program was written in C++. The calculations presented in the article demonstrate the possibility of conducting research on the smoothness of a vehicle under conditions of arbitrary terrain, typical for off-road conditions in the winter conditions of the Arctic zone. The dimensions and other parameters of the vehicle were taken from a full-scale model that was used in real expeditions in 2003-2019. Based on the model, suspension characteristics will be developed for a new all-terrain vehicle.Theory. When operating a wheeled vehicle in a wide range of conditions, even in northern regions, transverseangular vibrations are very often insignificant, so only vertical linear and longitudinal-angular vibrations of the frame can be considered. This problem enables to construct a system of equations of vehicle motion using selected degrees of freedom. From a mathematical point of view, these equations are classified as second-order ordinary differential equations with a variable structure of the right-hand sides, which reflects the non-linear nature of the behavior of the suspension in terms of its geometric constraints.Methods. The work uses numerical methods to solve the equations of the constructed model, which enables to gradually weaken the accepted assumptions and build more general calculation algorithms. The main integration method for ensuring the stability of solutions is the multi-step Adams method, which, with the correct choice of step, ensures the necessary stability of the solution over sufficiently long model times. However, in this work, the 4th order Runge-Kutta method was adopted, which turned out to be quite sufficient.Results and conclusions. The paper presents the results of a numerical study of the oscillatory processes of an off-road vehicle during uniform translational motion of the vehicle on a horizontal surface with a given profile of irregularities. The graphs show a transition process of oscillations, which ends with reaching a steady state. The shape of oscillations in a steady state can be irregular and significantly depends on the given speed of the all-terrain vehicle. Analysis of the dependencies presented in the figures shows that the shape of the oscillations of the allterrain vehicle’s frame, as well as the amplitude and frequency, significantly depend on the speed of the vehicle (at a constant road profile). Changing the road profile leads to corresponding changes in the forms and characteristics of forced vibrations of a vehicle on a suspension, which makes it possible to build the necessary amplitude-frequency characteristics, optimize the elastic and dissipative parameters of suspensions, optimize their number and location, and also monitor the movements of arbitrary points at which various units are located.

Size-dependent effect on the interaction of surface waves in micropolar thermoelastic medium with dual pore connectivity

Abstract This research tackles a critical knowledge gap in Rayleigh surface wave propagation. It offers a comprehensive analysis that surpasses previous limitations. A size-dependent micropolar medium with unique void distributions and thermal effects is considered in this work. The constitutive relations and equations of motion for a nonlocal micropolar thermoelastic medium with double voids (MTMWDV) have been established by using Eringen's nonlocal elasticity theory. Employing the three-phase-lag thermoelasticity theory (TPLTE), the study utilizes a wave-mode method to derive analytical solutions for Rayleigh waves in a nonlocal MTMWDV. To gain a comprehensive understanding of wave behavior, we solve the characteristic equation and analyze its roots, applying a filter based on the surface wave decay condition. A medium with stress-free and isothermal boundaries is explored through computational simulations to determine the attenuation coefficient and phase velocity. Furthermore, particle motion analysis is conducted to complement the analytical and computational approaches. Moreover, the influence of the nonlocal parameter and various thermoelastic models on these wave phenomena is investigated. The validity of the current mathematical model is confirmed through the derivation of particular scenarios.