Analytical Dynamic Model Research Articles

Modelling connected and autonomous bus on dynamics of mixed traffic in partially connected and automated traffic environment

Since connected and autonomous buses (CABs) have great potential of being operated in partially connected environment and raise great impact on mixed traffic flow, this study develops an analytical model for modeling system dynamics of mixing connected and autonomous vehicles (CAV), human-driven vehicles (HV), and CABs in both cases of dedicated bus lane and non-dedicated bus lane, in which the impact of CABs is specifically quantified under varied levels of connected vehicle penetration. A Vissim-Matlab simulation evaluation is also developed for validating the model’s effectiveness. The results demonstrate that the proposed model performs well with an accuracy of over 85%, and it can be up to 95% in case of non-dedicated bus lane when the inflow rate is higher than 2000veh/h. Besides, the impacts of CABs’ volume, bus dwelling time, and bus stop location on the performance of mixed traffic flow are verified in two CAB operating environments. The obtained results can be used as the basis for planning and operating CABs in partially connected environment.

Real-time deep learning-based model predictive control of a 3-DOF biped robot leg

Our research utilized deep learning to enhance the control of a 3 Degrees of Freedom biped robot leg. We created a dynamic model based on a detailed joint angles and actuator torques dataset. This model was then integrated into a Model Predictive Control (MPC) framework, allowing for precise trajectory tracking without the need for traditional analytical dynamic models. By incorporating specific constraints within the MPC, we met operational and safety standards. The experimental results demonstrate the effectiveness of deep learning models in improving robotic control, leading to precise trajectory tracking and suggesting potential for further integration of deep learning into robotic system control. This approach not only outperforms traditional control methods in accuracy and efficiency but also opens the way for new research in robotics, highlighting the potential of utilizing deep learning models in predictive control techniques.

Analytical model for spin dynamics in radical pairs under the spin-locking condition.

Spin dynamics in triplet radical pairs are theoretically studied under the spin-locking condition, where singlet-triplet mixing is blocked by the resonant microwave field. A key assumption in the theory is simultaneous excitations of T+-T0 and T--T0 transitions in triplet radical pairs. This assumption allows for the application of a three-state model [Yago, J. Chem. Phys. 151, 214501 (2019)] to describe the spin dynamics of triplet radical pairs. The analysis based on the three-state model shows that the triplet states are quantized along the direction of a microwave-induced magnetic field (B1) in the rotating frame under the spin-locking condition. This gives rise to a new spin-locking phenomenon where T+-T0 and T--T0 mixing are most enhanced at magnetic fields that deviate from the resonance by ±B1. It is also shown that the quantum beats observed under the spin-locking condition originate from the spin dynamics in triplet radical pairs.

Analytical Dynamic Energy-Carbon Flow Model and Application in Cost Allocation for Integrated Energy Systems

Analytical Dynamic Energy-Carbon Flow Model and Application in Cost Allocation for Integrated Energy Systems

Nonlinear dynamic modelling and analysis of a rotating composite thin-walled beam considering ice coating

For rotating structures operating in severe weather conditions, ice coating phenomenon is an established issue that impairs the reliability and effectiveness of the structures by changing the dynamic behaviors. To explore the influence mechanisms of ice coating on the dynamic behaviors of rotating structures, this work presents an analytical dynamic model for nonlinear forced vibration of a composite thin-walled beam under both rotating and ice coating conditions. The ice coating is considered as C-shaped configuration which can affect the system parameters of the beam, especially aerodynamic performance. With effect of out-of-plane warping taken into account, the nonlinear dynamic equation of the beam is established using Hamilton's principle. The Galerkin discrete method together with the incremental harmonic balance method (IHB) as well as pseudo arclength continuation technique are adopted to obtain the periodic response of the nonlinear system. Then, a detailed parametric study on natural frequency, frequency-response and bifurcation behaviors is numerically conducted. Special attention is paid to the effects of ice coating, rotating angular velocity, inflow velocity and design parameters on the linear and nonlinear dynamic behaviors of the beam. Results reveal a prominent change in natural frequency, vibration amplitude and cusp bifurcation of multivalued region under the combined effects of ice coating and rotating motion. Such ice-induced changes exhibit the requirement of vibration control and optimization design consideration for rotating structures operating in icing coating conditions.

Analytical model for bare soil evaporation dynamics following wetting with concurrent internal drainage

Under natural conditions, infiltrated rainwater redistributed into the soil profile, becomes partially sheltered from surface evaporative losses relative to undrained wet surfaces. Surface evaporation rates and internal drainage dynamics are both sensitive to soil hydraulic properties and initial soil hydration state. We report a novel analytical framework for quantifying surface evaporation rates with concurrent internal drainage, considering soil properties and dynamic surface evaporation resistance. Interplay among soil hydraulic properties, boundary conditions, and atmospheric demand result in nonlinear relationships between cumulative evaporative losses and initial water content. The new analytical solution shows good agreement with laboratory column experiments and literature data. Results highlight the role of soil texture on evaporative losses and the nonlinear effects of initial wetness on evaporation. The largest evaporative losses per rainfall amount are predicted for small rainfall events over initially dry loamy soils due to the detention of infiltrated rainwater near the surface for soils with large porosity and low hydraulic conductivity. The analytical framework uses readily available parameters hence can be implemented in land surface models to explicitly consider how soil properties and rainfall event size affect surface evaporation dynamics.

Scaling up tree growth to assess forest resilience under increasing aridity: the case of Iberian dry-edge pine forests

ContextMediterranean managed dry-edge pine forests maintain biodiversity and supply key ecosystem services but are threatened by climate change and are highly vulnerable to desertification. Forest management through its effect on stand structure can play a key role on forest stability in response to increasing aridity, but the role of forest structure on drought resilience remains little explored.ObjectivesTo investigate the role of tree growth and forest structure on forest resilience under increasing aridity and two contrasting policy-management regimes. We compared three management scenarios; (i) “business as usual”-based on the current harvesting regime and increasing aridity—and two scenarios that differ in the target forest function; (ii) a “conservation scenario”, oriented to preserve forest stock under increasing aridity; and (iii), a “productivity scenario” oriented to maintain forest yield under increasingly arid conditions.MethodsThe study site is part of a large-homogeneous pine-covered landscape covering sandy flatlands in Central Spain. The site is a dry-edge forest characterized by a lower productivity and tree density relative to most Iberian Pinus pinaster forests. We parameterized and tested an analytical size-structured forest dynamics model with last century tree growth and forest structure historical management records.ResultsUnder current management (Scenario-i), increasing aridity resulted in a reduction of stock, productivity, and maximum mean tree size. Resilience boundaries differed among Scenario-ii and -Scenario-iii, revealing a strong control of the management regime on resilience via forest structure. We identified a trade-off between tree harvest size and harvesting rate, along which there were various possible resilient forest structures and management regimes. Resilience boundaries for a yield-oriented management (Scenario-iii) were much more restrictive than for a stock-oriented management (Scenario-ii), requiring a drastic decrease in both tree harvest size and thinning rates. In contrast, stock preservation was feasible under moderate thinning rates and a moderate reduction in tree harvest size.ConclusionsForest structure is a key component of forest resilience to drought. Adequate forest management can play a key role in reducing forest vulnerability while ensuring a long-term sustainable resource supply. Analytical tractable models of forest dynamics can help to identify key mechanisms underlying drought resilience and to design management options that preclude these social-ecological systems from crossing a tipping point over a degraded alternate state.

Analysis of the joint trading of local green power certificates, carbon emissions rights, and electricity considering demand flexibility

Establishing synergy among distinct yet associated markets through market orientation is crucial because it can facilitate a clean and low-carbon energy transition. However, researchers have not yet developed a quantitative analytical dynamic model for studying market participants in the context of the joint electricity-carbon-green power certificates market. Moreover, the solution algorithm merits further exploration. This article proposes an analytical method for evaluating the joint trading of local green power certificates, carbon emission rights, and electricity, while taking into account the demand flexibility. First, a framework for the joint trading of local green power certificates, carbon emission rights, and electricity is designed. Second, market participants, such as traditional thermal power plants, renewable energy power plants, and load aggregators, are modelled via system dynamics theory. On this basis, a deep distributed reinforcement learning algorithm is applied to solve the problem. Finally, the effectiveness of the proposed theoretical approach is verified through real-life simulations, and the sensitivity of the key factors influencing joint trading is also analysed.

Rigid-flexible coupling modeling of the dual-rotor system for aero-engine

The dual-rotor system is the core component of advanced aero-engine. Establishing a reasonable, accurate, and efficient dynamics model is the key to studying the dynamics and vibration of the rotor system for aero-engine. This manuscript takes a representative aircraft engine dual-rotor system as a prototype, considers the rig-id-flexible coupling characteristics of different stiffness elastic supports and rotor structures, and establishes an analytical dynamic model of the dual-rotor system. Based on the established dynamic model, the natural char-acteristics of the dual-rotor system are analyzed. The model was validated using two different research methods: the rigid-flexible coupling multi-body system dynamics simulation platform ADAMS, and finite element analy-sis. The dynamic model of the dual-rotor system established in this paper can meet the requirements of hierar-chical rigid-flexible coupling of system and structure, overall mass distribution, and stiffness distribution. In particular, it can also effectively realize the simulation of multi-facet and multi-phase unbalanced vibration of the rotor system. The research methods of this paper can further enrich the basic theory of dynamics and vibration of the aero-engine rotor system.

An analytical dynamic force model for sawing force prediction considering the material removal mode

Diamond circular saw blades are indispensable tools in the industry of granite processing. Accurate prediction of sawing force is essential for optimizing the processing in advance. In this study, the calculation method for uncut chip thickness and instantaneous chip thickness was improved based on granite sawing characteristics. Furthermore, an analytical prediction force model was proposed in view of deep and intermittent grinding, which comprehensively considers the characteristics of diamond grits (including grit size, location distribution, and protrusion height) and material removal mode. The error between the predicted results and the experimental results is <12 %, indicating that the model can accurately predict the cutting force. The proposed analytical model provides a method to optimize the sawing parameters without the need for extensive experiments. This model can also extend to calculate parameters such as energy consumption and carbon emissions in the stone processing industry.

Improving the Efficiency of the Organization Based on the Automation Criterion

The modern development of information technologies involves their introduction into the technological processes of enterprises and organizations. At the same time, the head of an enterprise or organization is faced with a stream of problems arising in the work of the system he manages, must make timely decisions to identify the flow of problems arising in the system, identify them and neutralize them as soon as possible, for this he needs to have an analytical dynamic solution model. The published literature currently considers models based on the analysis. Consideration of the model on the basis of a natural-scientific approach will allow you to build a model adequate to the situation under consideration, which will bring results. In this study, an analytical dynamic decision model for a decision maker (LPR) has been developed. Formed on the basis of the synthesis process, the transformation of a management decision into a solution model. The solution model will depend on the basic components of the system under consideration for the occurrence of a flow of problems, identification of a flow of problems and neutralization of a flow of problems. The resulting synthesis indicator of the implementation of the management solution allows you to identify the flow of problems in the managed system and neutralize it, as well as to obtain characteristics about the operation of the managed system. By setting the required indicator of the effectiveness of the implementation of a management decision and solving the inverse problem, the manager can obtain the necessary characteristics of the system to guarantee the achievement of the goal of the activity. As a result, the manager receives the automation criterion and, with the help of the resources available to him, adjusts the work of the organization to the required level of the indicator. The automation criterion obtained in the work will be the rule by which the automation of the enterprise takes place, which will allow solving important tasks for the LPR and timely counteract emerging problems in the management system.

Dynamic properties investigation of an acoustic black hole beam with dynamic vibration absorber based on analytical method

Acoustic Black Holes (ABHs) have attracted much attention in recent years due to their characteristics of focusing vibration energy. Combining the focusing property of an ABH in a wide frequency band with the advantage of a dynamic vibration absorber (DVA), which could effectively suppress the vibration response at any tuning frequency, is expected to achieve excellent effective wide-band vibration reduction. However, the underlying mechanism and design method have not been provided by any existing open literature. In this work, the analytical dynamic model of a beam with an integrated one-dimensional ABH and a DVA (ABH+DVA) is established based on the transfer matrix method. The vibration attenuation of this ABH+DVA beam is investigated through this analytical model. Results demonstrate that, in comparison to a uniform-thickness beam with DVA and ABH beam with a damp layer in certain situations, the ABH+DVA beam provides superior vibration attenuation. Furthermore, the concept of region-specific vibration focusing ratio is proposed and defined to quantify the influence of ABH characteristic length on the focusing effect and focusing area of the ABH beam. Then based on the knowledge of focusing effect of the ABH beam, the influence of DVA placement on vibration reduction effect is studied and the mechanisms of the ABH beam attached with DVA are explained. Generally, the excellent vibration reduction effect of the ABH+DVA beam is closely related to the outstanding vibration focusing characteristic of an ABH beam.

Divergent dynamics: disasters and conflicts as 'drivers' of internal displacement?

Disasters and conflicts are both widely recognised as 'drivers' of internal displacement. Yet, despite a growing body of research and policy, there has been little consideration to date of how the different features of each 'context' shape the micro-level dynamics of internal displacement. Where and why are these dynamics similar across the two contexts and how do they differ? This paper draws on general concepts from the disaster field to develop a comparative analytical model of internal displacement dynamics in the disaster and conflict contexts. Based on inferences from the patchy extant data across the two contexts, it identifies and explains points of convergence and divergence between internal displacement dynamics in both the disaster and conflict contexts. This 'contextual' model of the micro-level dynamics of internal displacement has implications for academic debates, as well as for policy and practice, in the disaster, conflict, peace, climate change, and forced migration/displacement fields.

The Price Distribution of Consumer Goods in Retail Markets

Derived is an analytic dynamic model of the price distribution of consumer goods in retail markets. The stationary price distribution is established from the conservation equation of offered units and two simplifying assumptions. Under the condition that independent traders make small random price variations around a nearly constant supply price, the stationary price distribution of a good must have the form of a fat-tailed Laplace distribution. The standard deviation of the distribution is determined by the price volatility of the goods. Also, the price distribution of an ensemble of goods is established and applied to empirical data with good quantitative agreement.

Analytical dynamic modeling of damping of a multi-hierarchical mechanical system and mobile power engine shaft with the help of multi-mass rheological models

The article analytically modeled a multi-hierarchical mechanical system based on the method of multi-mass rheological models. Using this model, the ways of using as an example of obtaining and modeling the motor shaft of the damper-case of a mobile power vehicle are shown. The developed model makes it possible to find the amplitude-frequency characteristics of relative displacements, vibration velocity and vibration acceleration of moving mechanisms of mobile equipment.

Analytical and simulation model of fighter flight dynamics with a limiter for the permissible flight envelope when performing the split-S maneuver

The article substantiates the relevance to develop an analytical-simulation model of fighter flight dynamics with a limiter for the permissible flight envelope during the split-S maneuver. The structure of the analytical and simulation model of a fighter, consisting of a combination of a flight test bench, a model of fighter flight dynamics, a model of an astatic limiter for the permissible flight envelope and a model of pilot control actions based on the theory of fuzzy sets, is presented. The structure of the model of fighter flight dynamics with a limiter for the permissible flight envelope, consisting of a system of differential and algebraic equations, a model of an integrated control system, a geometry, mass and balance unit, a unit for calculating aerodynamic forces, a power plant unit, a bank of aerodynamic performance, a unit for calculating feedback on efforts from flight controls, is presented. The model differs from the known ones by the availability of the split-S simulation unit, which is designed for the split-S simulation and the multi-iteration split-S simulation with different initial conditions to determine the basic split-S parameters, the kinematic flight operation performance and to construct the split-S implementation area. The split-S simulation unit comprises the specified value functions, a pilot control actions model, a unit for processing simulation results, a unit for determining the basic split-S parameters, and a database of operating modes. The specified value functions determine the specified values of the kinematic aircraft movement parameters, which are used to implement control in various phase coordinates of the maneuver. The model makes it possible to obtain reliable values of the kinematic fighter movement parameters under the semi-natural simulation with the participation of the pilot and the simulation split-S maneuver modeling using the pilot control actions model.

A fully analytical nonlinear dynamic model of spindle-holder-tool system considering contact characteristics of joint interfaces

The productivity, surface finish, and dimensional accuracy during machining are directly related to the vibration characteristics of tool tip. Moreover, the dynamics of tool tip is not only determined by the flexibility of tool, collet, holder and spindle, but also depends on the contact characteristics of joint interfaces. This paper proposes a fully analytical model of the spindle-holder-tool system considering the nonlinear contact characteristics of joint interfaces. The dynamics of spindle, holder, collet and tool are modeled applying Timoshenko beam theory considering the combined shear and rotational effects, in which the tapered sections of spindle, holder and collet are modeled using multi-stepped beam to account for the taper effect. Under highly dynamic cutting load, the variation in the spacing of joint interfaces will induce the changes in the contact characteristics due to the corresponding vibrations. Therefore, the contact behaviors of spindle/holder, collet/holder, collet/nut, and tool/collet interfaces are analytically modeled using the distributed nonlinear spring-damping layers. The fractal theory and the slicing method are applied to derive the vibration displacement-dependent stiffness matrix of nonlinear springs in joint interfaces considering the surface morphology, geometry, material properties, and locking force of joint interfaces. Furthermore, the five degree of freedom (DOF) nonlinear stiffness model of the spindle-bearing joint dependent on vibration displacement is also considered. The effectiveness of the established analytical dynamic model is verified through vibration testing and modal hammering experiments. The changes in the vibration characteristics by considering the connection ways of joint interfaces, the fractal parameters of joint interfaces and the rotation speed are also investigated. The developed model can provide some theoretical principles for the optimization at design stage without prototypes.

Self-consistent dynamical models with a finite extent – III. Truncated power-law spheres

ABSTRACT Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking a model with an infinite extent and applying a truncation in binding energy. This method, however, cannot be used to generate models with a preset analytical mass density profile. We investigate the self-consistency and dynamical properties of a family of power-law spheres with a general tangential Cuddeford (TC) orbital structure. By varying the density power-law slope γ and the central anisotropy β0, these models cover a wide parameter space in density and anisotropy profiles. We explicitly calculate the phase–space distribution function for various parameter combinations, and interpret our results in terms of the energy distribution of bound orbits. We find that truncated power-law spheres can be supported by a TC orbital structure if, and only if, γ ≥ 2β0, which means that the central density slope–anisotropy inequality is both a sufficient and a necessary condition for this family. We provide closed expressions for structural and dynamical properties such as the radial and tangential velocity dispersion profiles, which can be compared against more complex numerical modelling results. This work significantly adds to the available suite of self-consistent dynamical models with a finite extent and an analytical description.

3D-spatial vibration global modes of a flexible arm-supported ring antenna and its dynamic analysis

Due to the complexity and high degrees of freedom of the structure, dynamical modelling of ring truss antenna (RTA) is a challenging job. The three-dimensional (3D) vibration of each component of RTA is spatial and coupled to each other, and thus assumed modes cannot depict its vibration accurately and dynamical models obtained by FEM generally have high dimensions, by which it is very hard to either conduct dynamical analysis or design its vibration controller. To overcome these obstacles, a dynamical modeling method named the 3D-Global Mode Method is proposed to obtain the low-dimensional analytical dynamical model of a flexible arm-supported ring antenna (ASRA) that vibrates spatially. The natural characteristics of a RTA is investigated by simplifying it as a flexible arm-supported closed multi-beam structure. Natural frequencies and the corresponding analytical 3D global modes are obtained by solving the eigen-equation formed by the spatial matching conditions and the boundary conditions. Orthogonality relations of the 3D analytical global modes are established and then used to transform the partial differential equations of spatial motion into a set of reduced-order ordinary differential equations. Taking the simulation results obtained from the FEM as a reference, the validity of the proposed method is verified by comparing the natural frequencies and 3D global mode shapes with those obtained from FEM. The mode localization phenomenon of ASRA is found and the influence of the parameters of RTA on mode characteristics is investigated. Through the proposed model, dynamical responses of the ASRA excited by orbital maneuvering acceleration are simulated numerically. This study paves an effective way to obtain the analytical global modes of spatially vibrating ASRAs and other similar spatial flexible combined structures, and to establish the low-degree-of-freedom dynamical model.

Dynamic Modeling and Analysis of Spacecraft with Multiple Large Flexible Structures

An analytical dynamic model is presented for a spacecraft with multiple large flexible structures. Based on the partial differential equations (PDEs) of the motion of the solar panel and deployable arm, the governing equations of the main-body and deployable antenna and the boundary conditions at each end point are used to obtain the frequency and mode shapes of the system. Then, the ordinary differential equations (ODEs) of the system can be obtained from the orthogonality relations and mode shape. The influence of the deployable antenna on the frequencies and mode shapes of the spacecraft is investigated. The frequency veering and mode interchanged phenomenon are observed with the variation of the diameter of the deployable antenna. Using the ODEs, the dynamic responses of the spacecraft are calculated to study the influence of the control torque on the attitude and position of the antenna in the attitude maneuver.