Analytical Dynamic Model Research Articles

Combined analytical and molecular dynamics model of electrocaloric effect in poly(VDF‐co‐TrFE) copolymer

AbstractA combined analytical and molecular dynamics model for the electrocaloric effect in ferroelectric poly(vinylidene difluoride‐co‐trifluoroethylene) copolymer (poly(VDF‐co‐TrFE)) is developed. The model calculates the polymer polarization, , and temperature change under adiabatic electric field variation, , as functions of temperature. An analytical component of the model is based on the Landau phenomenological theory adapted for modeling of the first order phase transitions in a polymer crystal from a ferroelectric β phase to a paraelectric conformationally disordered (condis) phase. Parameters of the free energy functional are calibrated through molecular dynamics simulations of poly(VDF‐co‐TrFE) perfect crystal. Random orientation and the scatter of the phase transition temperature for various crystallites in a real amorphous‐crystalline polymer are incorporated into the model. Comparison of the model prediction with experimental data shows good agreement for while the model overestimates the value of by approximately 2.5 times. We attribute this discrepancy to the presence of structural defects in real polymer crystallites, which reduces the entropy change under the phase transition compared to the perfect crystal simulated in our molecular dynamics approach. The theoretical limit of calculated by the model indicates that can be increased up to 3 times compared to the currently observed experimental value of .

Vibro-acoustic control of a programmable meta-shell with digital piezoelectric shunting

In this paper, a programmable piezoelectric meta-shell is designed to actively control the structural and sound radiation responses. The meta-shell consists of a cylindrical shell, Macro-fiber Composite (MFC) patches and digital shunting circuits. Due to the electro-mechanical coupling effect of the MFC patches, the mechanical properties of the meta-shell structure can be tuned by changing the electric field. The high-order digitally resonant circuits are designed to realize programmable control of the bandgap behaviors of the meta-shell. An analytical structural dynamic model for analyzing the vibration and radiated sound responses of the programmable piezoelectric meta-shell in light fluid is established. The vibro-acoustic characteristics of the meta-shell with the piezoelectric shunting and the effects of electric parameters (including dimensionless gain and electric damping ratio) on the structural and acoustic control performances of the shell are discussed. Experiments on the vibration and acoustic control of a programmable piezoelectric meta-shell are carried out to verify the high-order bandgap characteristic and its programmability. The experimental results demonstrate that the vibration and sound radiation responses of the shell can be effectively suppressed in multiple frequency bands.

An Analytical Dynamic Model for Vibration Suppression of a Multi-Span Continuous Bridge by Tuned Mass Dampers

In this paper, an analytical dynamic model is proposed for vibration suppression of a multi-span continuous bridge by tuned mass dampers (TMDs). Firstly, the partial differential equations (PDEs) that govern the motion of the multi-span continuous bridge and the TMDs are obtained, respectively. According to the matching conditions and the boundary conditions, the mode shapes of the multi-span continuous bridge are derived, and the orthogonality relations of the mode shapes are proven. By using the mode shapes and their orthogonality relations, the PDEs that govern the motion of the bridge and the TMDs are truncated into the ordinary differential equations (ODEs) that describe the motion of the entire system. To verify the proposed model, the natural frequencies solved by the frequency equation are compared with those obtained by the finite element software ANSYS. According to the ODEs in this model, the dynamical responses of the system are worked out to study the influence of the location and the number of TMDs on the vibration suppression of the bridge.

Low-thrust station-keeping towards exploiting the inclined geosynchronous dynamics

Small satellite constellations in Inclined Geosynchronous Orbits (IGSO) provide an alternative to the increasingly crowded Geostationary Orbit belt. Satellite platforms equipped with full-electric propulsion systems are of great capacity for the advantages of significant propellant saving. This work focuses on the IGSO constellation design and its low-thrust station-keeping strategies. An analytical dynamical model based on a triple-averaged Hamiltonian formulation with respect to the ecliptic plane is first applied for a preliminary selection of the frozen orbits, which can serve as the baseline orbit for the whole constellation. Afterwards, the impact of the inclination on the manifolds in the eccentricity vector space is analyzed and the station-keeping slot for IGSO satellites is defined. Then, the low-thrust arc is designed to make the drifting arc closed, which maximize the long-term behaviors due to the resonances. Moreover, by feeding a three-impulse solution to the initial costate guess, an efficient solver to guarantee the convergence of the indirect optimization is proposed. Finally, the efficiency of the constellation design approach and the low-thrust SK strategy are validated via numerical simulations.

Decentralized yaw optimization for maximizing wind farm production based on deep reinforcement learning

This study describes a deep reinforcement learning (DRL) based decentralized yaw optimization method to maximize the power production of wind farms. Specifically, we apply the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) algorithm to design agents separately for each turbine in the wind farm to make yaw decisions independently. This design allows setting different yaw rewards for the agents to promote faster and better convergence of MADDPG. To test the control effect of the proposed method, a novel analytical dynamic wake model is derived first, which can dynamically reflect the wake propagation of the wind turbine after the inflow wind speed, axial induction factor, and yaw angle change. Then, the static and dynamic characteristics of the proposed wake model are verified. The wind farm simulation is realized through the dynamic wake model, which provides an interactive environment for the simulation experiments to test the effect of the proposed DRL-based decentralized yaw optimization method. The results show that the proposed method can significantly increase the power generation of the wind farm, and the set yaw reward helps to guide MADDPG to converge to the optimal strategy.

Radio Frequency Cavity’s Analytical Model and Control Design

Reduction or suppression of microphonic interference in radio frequency (RF) cavities, such as those used in Electron Linear Accelerators, is necessary to precisely control accelerating fields. In this paper, we investigate modeling the cavity as a cylindrical shell and present its free vibration analysis along with an appropriate control scheme to suppress vibrations. To this end, we first obtain an analytical mechanical dynamic model of a nine-cell cavity using a modified Fourier-Ritz method that provides a unified solution for cylindrical shell systems with general boundary conditions. The model is then verified using the ANSYS software in terms of a comparison of eigenfrequencies which prove to be identical to the proposed model. We also present an active observer-based vibration control scheme to suppress the dominant mechanical modes of the cavity. The control system performance is investigated using simulations.

Совершенствование аналитического метода расчета наличной пропускной способности с применением имитационного моделирования

Purpose: To develop method for calculating actual capacity on railway line on the basis of the improvement of analytical formulas and the use of simulation tools. Correction of mathematical apparatus and calculation of simulation modeling coefficient. Methods: Analytical method, simulation and dynamic modeling, mathematical modeling, AnyLogic Software Package tools were applied. Research results: New calculation approach that allows to raise railway line throughput precision. In its turn, the new approach will allow to optimize operating costs for the maintenance and current repair of railway infrastructure and rolling stock. Practical significance: The results obtained can be used in the analytics, prediction and modeling of transportation processes in the dispatch centers of JSC "Russian Railways" transportation management.

Математическая модель и способ расчета пропускной способности

Purpose: To propose methodology for calculating actual throughput on railway line with full consideration of racing and drag effect of trains along their way on resulting actual throughput. Methods: Methods of analytical review, simulation and dynamic modeling, mathematical modeling were applied. Results: Analytical transformations of well-known formula for calculating throughput were performed. Analytical formula has been obtained that allows calculating actual throughput with higher accuracy. Practical significance: The results of the study can be used in the dispatch centers of JSC "Russian Railways" transportation management for more complete analysis of the operation of the polygon of a road, railway lines or individual sections in order of more detailed analysis of work, performed on transportation.

Design of a redundant actuated 4-PPR planar 3-DOF compliant nanopositioning stage

The compliant planar positioning stage actuated by voice coil motors can obtain nanoscale motion accuracy within a millimeter motion range and has received increasing attention in precision engineering. However, there is always a contradiction between the actuation force and the output stiffness in the design of the stage. This study presents the design of a novel redundant actuated planar 3-DOF-compliant nanopositioning stage. A redundant actuated configuration can increase the output stiffness of the stage and decrease the peak actuating force. The analytical stiffness model, kinetostatic model, and dynamic model of the stage are established, which illustrate the high force transmission efficiency and dynamic decoupling feature of the stage. The geometric parameters were optimized based on the established models, and model validation and performance evaluation of the stage were conducted via finite element analysis. Finally, a prototype positioning stage is fabricated. Experimental results show that the proposed stage can achieve a motion range of up to ±2.5 mm × ±2.5 mm × ±2.5° with a resolution of 80 nm and 0.28″, and the tracking error ratio for a composite Lissajous trajectory is within 0.102%.

Viscoelastic Effects on the Nonlinear Oscillations of Hard-Magnetic Soft Actuators

AbstractThe hard-magnetic soft materials (HMSMs) belong to the magnetoactive category of smart polymers that undergo large actuation strain under an externally applied magnetic field and can sustain a high residual magnetic flux density. Because of these remarkable characteristics, HMSMs are promising candidates for the remotely controlled actuators. The magnetic actuation behavior of the hard-magnetic soft actuators (HMSAs) is considerably affected by the viscoelastic material behavior of HMSMs. In this article, we aim at developing an analytical dynamic model of a typical planar model of HMSAs concerning the viscoelasticity of HMSMs. A Zener rheological model in conjunction with an incompressible neo-Hookean model of hyperelasticity and Rayleigh dissipation function is employed for defining the constitutive behavior of the viscoelastic HMSA. The governing equations of dynamic motion are deduced by implementing the nonconservative form of the Euler–Lagrange equation. The established dynamic model is utilized for providing preliminary insights pertaining to the effect of the viscoelasticity on the nonlinear oscillations of the actuator. The phase–plane portraits, Poincaré maps, and the time–history response are plotted to investigate the stability, resonant behavior, and periodicity of the actuator. The results and inferences reported here should provide the initial step toward the design and the development of modern actuators for diverse futuristic applications in the medical and engineering fields.

Unveiling the capabilities of bipolar conical channels in neuromorphic iontronics.

Conical channels filled with an aqueous electrolyte have been proposed as promising candidates for iontronic neuromorphic circuits. This is facilitated by a novel analytical model for the internal channel dynamics [T. M. Kamsma, W. Q. Boon, T. ter Rele, C. Spitoni and R. van Roij, Phys. Rev. Lett., 2023, 130(26), 268401], the relative ease of fabrication of conical channels, and the wide range of achievable memory retention times by varying the channel lengths. In this work, we demonstrate that the analytical model for conical channels can be generalized to channels with an inhomogeneous surface charge distribution, which we predict to exhibit significantly stronger current rectification and more pronounced memristive properties in the case of bipolar channels, i.e. channels where the tip and base carry a surface charge of opposite sign. Additionally, we show that the use of bipolar conical channels in a previously proposed iontronic circuit features hallmarks of neuronal communication, such as all-or-none action potentials and spike train generation. Bipolar channels allow, however, for circuit parameters in the range of their biological analogues, and exhibit membrane potentials that match well with biological mammalian action potentials, further supporting their potential biocompatibility.

Moving Horizon Estimation for Digital Twins using Deep Autoencoders

Digital twins have emerged in recent years as black-box, software-based simulation tools that can mirror the behavior of complex dynamical systems. Digital twin simulations generate the same outputs as the target system using internal states; however, these states are not readily available online from the real system. In this paper, we develop a data-driven moving horizon estimation framework capable of using online noisy measurements of the real system in order to estimate digital twin states. Our framework combines the high expressiveness of deep autoencoders with a moving horizon state estimator that accurately predicts the internal state of the black-box digital twin without access to an analytical model of the system dynamics. We demonstrate that our approach outperforms extended and Koopman Kalman filter solutions on a benchmark reverse van der Pol oscillator example.

An improved analytical model of protein dynamics at the sub-nanosecond timescale.

Thermal fluctuations of proteins at the ps-ns timescales are important for their functions and have extensively been studied using quasi-elastic neutron scattering (QENS). In general, the QENS spectra of proteins are analyzed in terms of two populations of atoms, i.e., the immobile fraction of atoms, the motions of which are too slow to be resolved within the instrumental energy resolution employed, and the mobile fraction of atoms, from which the average amplitude and frequency of protein atomic motions are characterized. On the other hand, it has been shown using molecular dynamics simulations that atomic motions are gradually enhanced as going from the protein core to the protein surface. Therefore, it is essential to further deconvolute the mobile fraction of atoms to study in detail the dynamical behavior of proteins. Here, an improved analytical model using QENS to deconvolute the mobile fraction of atoms into two populations of atoms, i.e., atoms with high mobility (HM atoms) and those with low mobility (LM atoms), is proposed. It was found that both the HM atoms and the LM atoms showed gradually enhanced dynamics with an increase in temperature even though any temperature-dependent terms are not included in the model. The presented model yields physically reasonable values for dynamical parameters and hence its future application will be useful to understand the molecular mechanism of various protein functions where atoms with higher mobility on or close to the protein surface play a crucial role.

Москвіченко І. М., Стаднік В. Г., Коросан А. П. ПІДВИЩЕННЯ ЯКОСТІ ПОСЛУГ ОРГАНІЗАЦІЇ ДОСТАВКИ КОНТЕЙНЕРНИХ ВАНТАЖІВ КОМПАНІЯМИ ЛОГІСТИЧНОГО АУТСОРСИНГУ З УКРАЇНИ В УМОВАХ МОРСЬКОЇ БЛОКАДИ ПОРТІВ

Annotation. The purpose of the article is to develop theoretical and applied approaches to selecting effective supply chains for container cargo by logistics outsourcing companies from Ukraine in the context of the sea blockade of ports. Research methodology. The goal set in the article is achieved using the following research methods: logical generalization and scientific abstraction, structural analysis, and the analytical method. Findings. The cost of various container export delivery schemes through European seaports with cargo delivery to the port of departure by various modes of transport was calculated. As a result, the most efficient delivery scheme was chosen - the export of containers with Ukrainian grain through the Port of Gdynia to the port of Xingang by rail, which is offered by Western Container Terminal LLC, using the sea freight tariff of the Hapag-Lloyd container line. At the current stage, the existence of Ukrainian logistics companies depends on the development of the most variable transport delivery schemes, so the prospects for further research are in the use of dynamic simulation modeling of supply chains, for example, using the AnyLogistix platform, which combines analytical optimization and dynamic modeling in one platform. Dynamic modeling makes it easy to experiment with your supply chain and choose the best solutions to implement. A dynamic simulation model can serve as a digital double of the supply chain, which allows you to experiment with improvements and track all important indicators: costs, revenue, inventory dynamics, service quality, bullwhip effect, capacity, inbound/outbound orders. Logistics outsourcing companies will be able to test multiple supply chain transformation scenarios, vary parameters, and make business decisions based on testing and evaluating results in a risk-free virtual environment. Practical value. The practical use of the proposed theoretical and applied approaches will improve the effectiveness and quality of services of Ukrainian logistics outsourcing companies. Logistics companies can test multiple supply chain transformation scenarios, vary parameters, and make business decisions based on testing and evaluating results in a risk-free virtual environment.

Investigating day-to-day route choices based on multi-scenario laboratory experiments, Part I: Route-dependent attraction and its modeling

In the area of urban transportation networks, a growing number of day-to-day (DTD) traffic dynamic theories have been proposed to describe the network flow evolution, and an increasing amount of laboratory experiments have been conducted to observe travelers' behavior regularities. However, the "communication" between theorists and experimentalists has not been made well. This paper devotes to 1) detecting unanticipated behavior regularities by conducting a series of laboratory experiments, and 2) improving existing DTD dynamics theories by embedding the observed behavior regularities into a route choice model. First, 312 subjects participated in one of the eight decision-making scenarios and make route choices repeatedly in congestible parallel-route networks. Second, three route-switching behavior patterns that cannot be fully explained by the classic route-choice models are observed. Third, to enrich the explanation power of a discrete route-choice model, behavioral assumptions of route-dependent attractions, i.e., route-dependent inertia and preference, are introduced. An analytical DTD dynamic model is accordingly proposed and proven to steadily converge to a unique equilibrium state. Finally, the proposed DTD model could satisfactorily reproduce the observations in various datasets. The research results can help transportation science theorists to make the best use of laboratory experimentation and to build network equilibrium or DTD dynamic models with both real behavioral basis and neat mathematical properties.

Dynamic Modeling and Controller Design for a Parabolic Trough Solar Collector

The current study unveils an analytical dynamic model of a parabolic trough solar collector (PTSC) and subsequently presents the process to derive the transfer function of the PTSC system. The presented generalized transfer function derivation can be utilized to relate different operating parameters with the output temperature for any PTSC module. Presented model and derivation are applied on a PTSC module tested by Sandia National Laboratory, USA and a transfer function relating the outlet temperature of heat transfer fluid (HTF) with flowrate is derived. PID controller is designed to maintain the HTF outlet temperature by manipulating the flowrate. Controller tuning is performed <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">via</i> nature-inspired algorithms (NIAs) which is rare in the context of the control systems for PTSCs. Two NIAs namely Self-adaptive Differential Evolution (SaDE) and African Vultures Optimization Algorithm (AVOA) were used for tuning with minimization of integral of time-weighted absolute error (ITAE) as an objective. It is concluded that SaDE-PID tuned controller outperforms AVOA-PID tuned controller with lower ITAE and in terms of other controller characteristics. Also, the designed controller is examined on various grounds as transient response characteristics and performance indexes. This completes the investigation of the integrity of the presented model, process, and controller.

Improved Mesh Stiffness Method and Vibration Analysis of a Planetary Gear System with a Spatial Tooth Crack

Dynamic modeling and analysis are generally regarded as effective tools to investigate the vibration characteristics and fault mechanisms of planetary gear systems with a tooth crack fault. In actual gearboxes, the tooth crack is always a three-dimensional spatial surface, but it was usually simplified as a two-dimensional domain in most previous studies. In this paper, the tooth crack is modeled as a spatial shape that propagates along the crack depth, length and height directions simultaneously. Based on the potential energy principle, an improved analytical method is proposed to calculate the time-varying mesh stiffness (TVMS) of a planetary gear system with a spatial tooth crack. Furthermore, a coupled translational–torsional dynamic model is established for a planetary gear system including time-varying parameters and nonlinear factors. Numerical simulations are conducted to reveal the influences of the spatial crack propagation on the TVMS and vibration responses. In addition, an experimental study is carried out on a gear transmission test rig to verify the proposed analytical method and dynamic model. The mesh stiffness calculation method of the spatial cracked tooth and corresponding analysis results in this study might provide references to detect tooth crack faults in planetary gear systems.

가변속 전동 스크롤 압축기의 스윙 부시 설계에 관한 연구

For a variable speed electric scroll compressor used for vehicle heat pump system, an eccentric bush combined with counterweight, so called swing bush, is widely used as a radial compliance device to control orbiting radius. Rotation radius of swing bush is a key design parameter in determining both sealing force magnitude exerted on the scroll wrap flank and restoring ability of the orbiting scroll back to its normal position after recess due to abnormal chamber pressure rise caused by the presence of refrigerant droplets, for instance. In this study, an analytical model for swing bush dynamics is presented and a way of optimum design is illustrated by a parametric study.

Metaheuristic Identification for an Analytic Dynamic Model of a Delta Robot with Experimental Verification

The dynamic-parameter identification process for developing a suitable precise mathematical model for the implementation and operation of parallel-link robots has received attention. In this study, an efficient and reliable system-identification method for a delta robot is proposed. The parallel-link robot’s dynamic behavior was mathematically modeled according to the principle of virtual work. The dynamic equations of motion are extended to the system of equations that explicitly characterizes the inertial and centripetal/Coriolis forces, and the frictional effects on the robot’s dynamic behavior. Next, the dynamic-parameter identification technique is presented to directly estimate a set of uncertain parameters that are included in the extended dynamic model. In addition, the development of the dynamic model with a generalized inertia matrix for determining the impact of the inertia-coupling characteristic on the robot’s dynamic behaviors is examined. Experimental results indicate that the proposed parameter-estimation technique is an extremely useful tool that can achieve the high-quality identification of an analytic dynamic model for a parallel-link robot.

Development of Non-sticking Steady-State solution for structures with hybrid damping mechanism

Energy dissipation occurs through Coulomb friction and is considered a conventional type of mechanical damping mechanism in structures subjected to external loads. Structures that are subjected to severe dynamic excitations such as ground motion or wind are required to employ a supplementary dampening system in addition to the Coulomb damping to mitigate the adverse impact of vibration in structures.Therefore, this study aims to develop a new Hybrid Damping Mechanism (HDM) for a single-degree-of-freedom (SDOF) system which is subjected to harmonic loads through a Viscous Damper System (VDS) to enhance the energy dissipation efficiency besides the Coulomb friction. Therefore, an analytical dynamic model for the non-sticking steady-state response was formulated where the effects of the viscous damper were implemented in the governor equation of the motion to estimate the structural response under harmonic loads. Subsequently, the Maximum Displacement (MD) and the Maximum Velocity (MV) were estimated by assuming deviation from the equilibrium point. Finally, a genuine borderline equation and a boundary limit were derived for the force amplitude ratio, where the maximum external load was divided by kinetic friction. It is an appropriate guideline for structural designers to avoid the sticking phase in the dynamical analysis of the structural systems equipped with frictional dampers.Based on the application of the final solution to a numerical example, the proposed HDM in the SDOF system considerably diminished the MD with velocity deviation ranging between 5% and 98% and 3% to 94%, respectively. Meanwhile, the analysis also revealed that the VDS damping ratio and the force amplitude ratio were the most effective parameters in reducing the MD and velocity deviation with a frequency ratio (β) between 0.85 and 1.15.The developed hybridized SDOF system can also be applied as a Tuned Mass Damper (TMD) in the structures to ameliorate their dynamic response.