Academic literature on the topic 'Linearized Driving Forces'

There is no literature mentioned the modeling of the microstructures subjected to traveling electrostatic forces. This paper is the first time to present an analytical approach to investigate the dynamics of a micro-ring structure driven by the traveling bias voltage. The traveling electrostatic forces may come from the sequentially-actuated actuating electrodes arranged around the flexible ring. A linearized distributed model considering the electromechanical coupling effect is derived based on the small deflection assumption. According to the analytical results, the stiffness of the micro-ring will be softened periodically with the traveling speed of the driving voltage and the variation increases with the increasing of the voltage.

This paper presents a systematic design of the combined control of vehicle longitudinal and lateral motions for the Intelligent Vehicle Highway Systems (IVHS). A fully coordinated control of the steering and the accelerating/braking actions is presented to maximize the ability of distributing the traction forces in a desired way. This control method covers a broad range of driving condition by removing several conventional simplification on vehicle dynamics, such as the linearized lateral traction force assumption, the bicycle model assumption, and the non-slip assumption. The nominal traction force concept is also introduced to handle the unknown traction forces. Robust Adaptive Control (RAC) by backstepping for MIMO nonlinear systems is utilized to control the unmatched nonlinear vehicle dynamics, in the presence of parametric uncertainties and uncertain nonlinearities.

Abstract. The dynamics of growing collisional orogens are mainly controlled by buoyancy and shear forces. However, the relative importance of these forces, their temporal evolution and their impact on the tectonic style of orogenic wedges remain elusive. Here, we quantify buoyancy and shear forces during collisional orogeny and investigate their impact on orogenic wedge formation and exhumation of crustal rocks. We leverage two-dimensional petrological–thermomechanical numerical simulations of a long-term (ca. 170 Myr) lithosphere deformation cycle involving subsequent hyperextension, cooling, convergence, subduction and collision. Hyperextension generates a basin with exhumed continental mantle bounded by asymmetric passive margins. Before convergence, we replace the top few kilometres of the exhumed mantle with serpentinite to investigate its role during subduction and collision. We study the impact of three parameters: (1) shear resistance, or strength, of serpentinites, controlling the strength of the evolving subduction interface; (2) strength of the continental upper crust; and (3) density structure of the subducted material. Densities are determined by linearized equations of state or by petrological-phase equilibria calculations. The three parameters control the evolution of the ratio of upward-directed buoyancy force to horizontal driving force, FB/FD=ArF, which controls the mode of orogenic wedge formation: ArF≈0.5 causes thrust-sheet-dominated wedges, ArF≈0.75 causes minor wedge formation due to relamination of subducted crust below the upper plate, and ArF≈1 causes buoyancy-flow- or diapir-dominated wedges involving exhumation of crustal material from great depth (>80 km). Furthermore, employing phase equilibria density models reduces the average topography of wedges by several kilometres. We suggest that during the formation of the Pyrenees ArF⪅0.5 due to the absence of high-grade metamorphic rocks, whereas for the Alps ArF≈1 during exhumation of high-grade rocks and ArF⪅0.5 during the post-collisional stage. In the models, FD increases during wedge growth and subduction and eventually reaches magnitudes (≈18 TN m−1) which are required to initiate subduction. Such an increase in the horizontal force, required to continue driving subduction, might have “choked” the subduction of the European plate below the Adriatic one between 35 and 25 Ma and could have caused the reorganization of plate motion and subduction initiation of the Adriatic plate.

AbstractLarge-amplitude [±100 Sv (1 Sv ≡ 106 m3 s−1)], high-frequency oscillations in the Pacific Ocean’s meridional overturning circulation within 10° of the equator have been found in integrations of the NEMO ocean general circulation model. Part I of this paper showed that these oscillations are dominated by two bands of frequencies with periods close to 4 and 10 days and that they are driven by the winds within about 10° of the equator. This part shows that the oscillations can be well simulated by small-amplitude, wind-driven motions on a horizontally uniform, stably stratified state of rest. Its main novelty is that, by focusing on the zonally integrated linearized equations, it presents solutions for the motions in a basin with sloping side boundaries. The solutions are found using vertical normal modes and equatorial meridional modes representing Yanai and inertia–gravity waves. Simulations of 16-day-long segments of the time series for the Pacific of each of the first three meridional and vertical modes (nine modes in all) capture between 85% and 95% of the variance of matching time series segments diagnosed from the NEMO integrations. The best agreement is obtained by driving the solutions with the full wind forcing and the full pressure forces on the bathymetry. Similar results are obtained for the corresponding modes in the Atlantic and Indian Oceans. Slower variations in the same meridional and vertical modes of the MOC are also shown to be well simulated by a quasi-stationary solution driven by zonal wind and pressure forces.

The goal of the research was to clarify the regularities of the dynamics of gas release from the surface of the outcrop of the developed coal seam. The main research methods were theoretical methods of mathematical physics and non-equilibrium thermodynamics. Gas-bearing coal seams are usually mined underground. When driving development workings, outcropping surfaces of gas-bearing coal seams appear and gases in the seams under excessive pressure are released into the atmosphere of the mine workings. Gas-bearing coal seams are usually mined underground. When driving preparatory workings, surfaces of outcropping of gas-bearing coal seams arise and gases that are in the seams under excessive pressure are released into the atmosphere of the mine workings. The most important gas-dynamic characteristic of this process is the rate of gas release, which represents the volume of gases released from a unit area of exposure of a coal seam per unit of time. A generalized law of resistance for gas filtration in a rock mass is recommended, and a fairly rigorous thermodynamic substantiation is given. It is shown that the densities of gas mass flows in accordance with the postulate of their linear relationship with the driving forces are determined by the Onsager relation. The results obtained and their discussion is presented. Mathematical models are proposed for engineering calculations of the dynamics of methane release from the outcropping surface of medium-thick coal seams. The error of the adopted approximations does not exceed 3%. The intensity of methane release is directly related to the planogram of work in the working face. Analysis of this dependence indicates that during the extraction cycle, methane release increases due to an increase in the area of the gas-release surface. The main conclusions are as follows: mathematical modeling of the processes of gas movement in a porous sorbing medium using approximate mathematical models representing linearized equations of mathematical physics; the regularities of the dynamics of the rate of gas release from the surface of the outcrop of a gas-bearing coal seam is the theoretical basis for the mathematical description of the process of gas release; the use of a linearized hyperbolic filtration equation most accurately describes the processes of methane release from the outcropping surface of mined coal seams.

To account for the dominant formation of diamond over graphite in the gas-activated chemical vapor deposition (CVD) process we have theoretically examined the free energy function of a small carbon-atom cluster as a function of the cluster size. The scalar potential around a charged spherical cluster was derived using the linearized Poisson–Boltzmann equation. It was shown that the repulsive electrostatic energy associated with the growth of the charged diamond cluster was proportional to the fifth power of the cluster size. This suggests the existence of a deep potential-energy-well for the cluster size larger than the critical size corresponding to the free energy barrier for the nucleation. Thus, the growing diamond cluster will be trapped in this potential well before it transforms to the thermodynamically stable graphite. Considering all the relevant thermodynamic driving forces, we have constructed the free energy function in terms of the cluster size. The numerical computation also supports the existence of the potential-energy-well. Therefore, the present theoretical model clearly explains why the charged diamond cluster does not transform to the neutral graphite cluster when the thermodynamic stability is reversed above a certain critical size during the growth.

The purpose of this study is to determine the effect of retarded forces in elasticity and damping on the dynamics of mixed forced, parametric, and self-oscillations in a system with limited excitation. A mechanical frictional self-oscillating system driven by a limited-power engine was used as a model. Methods. In this work, to solve the nonlinear differential equations of motion of the system under consideration, the method of direct linearization is used, which differs from the known methods of nonlinear mechanics in ease of use and very low labor and time costs. This is especially important from the point of view of calculations when designing real devices. Results. The characteristic of the friction force that causes self-oscillations, represented by a general polynomial function, is linearized using the method of direct linearization of nonlinearities. Using the same method, solutions of the differential equations of motion of the system are constructed, equations are obtained for determining the nonstationary values of the amplitude, phase of oscillations and the speed of the energy source. Stationary motions are considered, as well as their stability by means of the Routh–Hurwitz criteria. Performed calculations obtained information about the effect of delays on the dynamics of the system. Conclusion. Calculations have shown that delays shift the amplitude curves to the right and left, up and down on the amplitude–frequency plane, change their shape, and affect the stability of motion.

Dynamics of a pinned dislocation kink controlled by the acting DC and AC forces is studied analytically. The motion of the kink, described by sine-Gordon (sG) equation, is explored within the framework of McLaughlin–Scott perturbation theory. Assuming weakness of the acting AC force, the equation of motion of the dislocation kink in the pinning potential is linearized. Based on the equations derived, we study stochastic behavior of the kink, and determine the probability of its depinning. The dependencies of the depinning probability on DC and AC forces are analyzed in detail.

The present paper addresses the derivation of a 3 DOF mathematical model of a spherical pendulum attached to a crane boom tip for uniform slewing motion of the crane. The governing nonlinear DAE-based system for crane boom uniform slewing has been proposed, numerically solved, and experimentally verified. The proposed nonlinear and linearized models have been derived with an introduction of Cartesian coordinates. The linearized model with small angle assumption has an analytical solution. The relative and absolute payload trajectories have been derived. The amplitudes of load oscillations, which depend on computed initial conditions, have been estimated. The dependence of natural frequencies on the transport inertia forces and gravity forces has been computed. The conservative system, which contains first time derivatives of coordinates without oscillation damping, has been derived. The dynamic analogy between crane boom-driven payload swaying motion and Foucault’s pendulum motion has been grounded and outlined. For a small swaying angle, good agreement between theoretical and averaged experimental results was obtained.