Dynamic Formulation Research Articles

Review and comparison of empirical friction coefficient formulation for multibody dynamics of lubricated slotted joints

Review and comparison of empirical friction coefficient formulation for multibody dynamics of lubricated slotted joints

A Sensorized 3D-Printed Knee Test Rig for Preliminary Experimental Validation of Patellar Tracking and Contact Simulation

Experimental validation of computational simulations is important because it provides empirical evidence to verify the accuracy and reliability of the simulated results. This validation ensures that the simulation accurately represents real-world phenomena, increasing confidence in the model’s predictive capabilities and its applicability to practical scenarios. The use of musculoskeletal models in orthopedic surgery allows for objective prediction of postoperative function and optimization of results for each patient. To ensure that simulations are trustworthy and can be used for predictive purposes, comparing simulation results with experimental data is crucial. Although progress has been made in obtaining 3D bone geometry and estimating contact forces, validation of these predictions has been limited due to the lack of direct in vivo measurements and the economic and ethical constraints associated with available alternatives. In this study, an existing commercial surgical training station was transformed into a sensorized test bench to replicate a knee subject to a total knee replacement. The original knee inserts of the training station were replaced with personalized 3D-printed bones incorporating their corresponding implants, and multiple sensors with their respective supports were added. The recorded movement of the patella was used in combination with the forces recorded by the pressure sensor and the load cells, to validate the results obtained from the simulation, which was performed by means of a multibody dynamics formulation implemented in a custom-developed library. The utilization of 3D-printed models and sensors facilitated cost-effective and replicable experimental validation of computational simulations, thereby advancing orthopedic surgery while circumventing ethical concerns.

Cooperative lane-changing for connected autonomous vehicles merging into dedicated lanes in mixed traffic flow

Connected and automated vehicles (CAVs) have enormous potential to enhance traffic safety, efficiency, and emissions reduction. However, in the initial phases of CAV development, mixed traffic comprising CAVs and human-driven vehicles (HDVs) will inevitably coexist in the traffic system. To fully exploit the benefits of CAVs, dedicated lanes with independent rights of way will be established. This paper proposes an optimal control strategy for coordinating the mandatory lane-changing of CAVs from ordinary lanes to dedicated lanes. The strategy develops a centralized two-stage cooperative optimal control model to optimize the lane-changing sequence and trajectories of CAVs. In the first stage, a dynamic programming formulation is designed to determine the lane-changing sequence decisions. The model predictive control (MPC) controller is adopted to dynamically solve the optimal control problem with a fixed terminal state. In the second stage, we dynamically and cooperatively designed the longitudinal trajectories of related CAVs. The lateral trajectories of lane-changing CAVs are planned with a cubic polynomial. The objective function considers driving comfort and state tracking to ensure traffic smoothness. Simulation results show that: (1) the proposed strategy can improve the negative impact of lane-changing behavior under different traffic demand levels. (2) Compared to the benchmark approach, the proposed strategy can significantly enhance traffic efficiency and driving comfort, particularly in medium-traffic demand. The strategy can improve the average speed of CAVs by approximately 12 % and decrease the average acceleration by over 45 %. (3) The average fuel consumption is positively correlated with traffic demands and the difference in arrival speeds between lane-changing and dedicated lane CAVs. (4) The effectiveness of the strategy increases with the length of the lane-changing segment. However, the marginal benefit becomes negligible when the segment exceeds 300 m. Therefore, the findings of this paper can provide theoretical support for the cooperative control of CAVs in dedicated lanes of highways in the future.

Modeling dynamic crack growth in quasicrystals: Unraveling the role of phonon-phason coupling

In this work, we employed the phase-field fracture (PFF) model for dynamic brittle fracture in quasicrystals (QCs). The dynamic PFF formulation is derived using both elastodynamics and elasto-hydrodynamic theory. The temporal discretization is achieved using an implicit generalized-α method, which is unconditionally stable for a particular choice of constants. The model incorporates two distinct crack driving forces: (a) the contribution of elastic strain energy from both phonon and phason fields and (b) the contribution solely from the elastic energy associated with the phonon field. To validate the implementation of QCs, we have conducted benchmarking against recent results in the literature, particularly in the context of quasi-static loading. We addressed various paradigmatic case studies to demonstrate the dynamic crack nucleation and propagation in planar 2D decagonal QCs, with a primary emphasis on understanding the interplay between phonon and phason fields. Phason walls, representing low-energy crack paths resulting from atomic rearrangements, play a significant role in crack propagation by introducing an additional energy component. Notably, increasing the phonon-phason coupling constant expedites both crack initiation and propagation. Furthermore, variations in the phonon-phason coupling parameter result in different crack trajectories, observed in both uniaxial and biaxial loading scenarios. The developed code can be downloaded from https://github.com/Hirshikesh/Quasicrystal.git.

Thermodynamics and performance optimization of an open quantum engine

We start from the well-established methods to describe interactions between two standard quantum systems coupled to heat baths. We establish and work through the description of a regularly constructed dynamic formalism. The insight appears to come from considering the heat flow in the system, which allows us to evaluate a thermodynamic efficiency. It is found that this efficiency can take widely different values as the coupling strength is varied. In particular, our study gives insight into the engine vanishing power output problem and shows quantitative agreement between predictive theory and experiment.

Operator Formulation of Feynman Path Centroid Dynamics for Rotations.

An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.

An approach to nonlinear optimisation via set stabilisation of dynamical systems with an application to synchronous machines

An approach to constraint nonlinear optimisation is proposed, where the variables of the objective function and of the constraint function belong to the state of a nonlinear dynamical system. A nonlinear closed-loop feedback system is designed, whose solutions converge to a target set consisting of the optimal points of the underlying optimisation problem. The feedback law for the control input of the nonlinear dynamical system is designed by exact linearisation of a dynamical formulation of a first-order optimality condition. For the problem formulation and the stability analysis of the nonlinear closed-loop feedback system, the notion of V-detectability is considered. An application to energy-optimal feed-forward torque control for different types of synchronous machines is presented, which demonstrates the usefulness of the method. In this regard, anisotropic permanent magnet synchronous machines and electrically excited synchronous machines are covered.

Effective dynamic properties of multi-segment beam lattices: a dynamic stiffness formulation

Effective dynamic properties of multi-segment beam lattices: a dynamic stiffness formulation

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

Dynamic stiffness formulation for vibration characteristics analysis of bi-dimensional functionally graded annular plate of variational thickness

In silico study of the mechanisms of hypoxia and contractile dysfunction during ischemia and reperfusion of hiPSC cardiomyocytes.

Interconnected mechanisms of ischemia and reperfusion (IR) has increased the interest in IR in vitro experiments using human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). We developed a whole-cell computational model of hiPSC-CMs including the electromechanics, a metabolite-sensitive sarcoplasmic reticulum Ca2+-ATPase (SERCA) and an oxygen dynamics formulation to investigate IR mechanisms. Moreover, we simulated the effect and action mechanism of levosimendan, which recently showed promising anti-arrhythmic effects in hiPSC-CMs in hypoxia. The model was validated using hiPSC-CM and in vitro animal data. The role of SERCA in causing relaxation dysfunction in IR was anticipated to be comparable to its function in sepsis-induced heart failure. Drug simulations showed that levosimendan counteracts the relaxation dysfunction by utilizing a particular Ca2+-sensitizing mechanism involving Ca2+-bound troponin C and Ca2+ flux to the myofilament, rather than inhibiting SERCA phosphorylation. The model demonstrates extensive characterization and promise for drug development, making it suitable for evaluating IR therapy strategies based on the changing levels of cardiac metabolites, oxygen and molecular pathways.

Dynamic Manipulation and Stiffness Modulation of Cooperative Continuum Robots: Theory and Experiment

Abstract Cooperative continuum robots (CCRs) are composed of multiple coupled continuum arms to cooperatively conduct manipulation tasks. They can highly enhance the performance of individual continuum arms by providing extra stiffness, leading to increased accuracy, payload capacity, and dynamic stability of the robot. This study aimed to investigate the stiffness analysis of tendon-driven supportive-type CCRs (S-CCRs). For this purpose, first, a generalized framework for the dynamic mathematical formulation and numerical solution of S-CCRs was proposed, their dynamic response to complex scenarios was obtained, and the accuracy of the model was experimentally evaluated. Then, the capability of stiffness modulation of S-CCRs was studied. Tendon-driven S-CCRs are potentially capable of changing the stiffness with structural configuration, providing active stiffness control at the design level. Hence, in this study, the effects of the connection point location/angle of the supportive arms to the operative arm, as well as the imposed tendon limitations of the supportive arm on the stiffness of the robot, and consequently on the dynamic payload manipulation, were studied and practical solutions were proposed to develop a simple but effective stiffness control mechanism. This study showed that a typical S-CCR can increase its stiffness, just by a modular connector design up to 84% during manipulation, bringing a novel opportunity for stiffness modulation of CCRs.

Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media

Travelling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrödinger equation arising as the envelope equation. We are interested in a rigorous existence proof of such solutions for a nonlinear wave equation with spatially periodic coefficients. Such solutions are quasi-periodic in a reference frame co-moving with the envelope. We use spatial dynamics, invariant manifolds, and near-identity transformations to construct such solutions on large domains in time and space. Although the spectrum of the linearised equations in the spatial dynamics formulation contains infinitely many eigenvalues on the imaginary axis or in the worst case the complete imaginary axis, a small denominator problem is avoided when the solutions are localised on a finite spatial domain with small tails in far fields.

Dynamic stiffness formulations for exact modal and dynamic response analysis of three-dimensional acoustic cavities in cylindrical coordinates

Exact dynamic stiffness (DS) models for three-dimensional (3D) cavities in cylindrical coordinates under any classical acoustic boundary conditions (BCs) are proposed in this paper. The paper first derives the exact general solutions that satisfy the governing differential equations. Then, these general solutions are used to develop the DS matrices for 3D cavities in cylindrical coordinates by substituting them into the acoustic pressure and normal velocity BCs. Subsequently, the Wittrick–Williams algorithm, along with the analytical expressions of the j0 count for various shaped cavities, is applied to compute natural frequencies. Finally, reliable and efficient techniques for dynamic response solution are employed. The DSM provides benchmark solutions for various 3D cavities. The convergence, universality, and efficiency of the proposed method in modal and response analysis are illustrated by comparing the results obtained using the DSM and FEM. The calculation time when using the DSM is only 0.1% of that when using the commercial finite element method, while maintaining the same accuracy. This research not only provides an effective technique for analyzing the cylindrical acoustic pressure field in engineering, but also establishes a foundation for the analysis of structural–acoustic coupling in tubular structures.

Lyra cosmologies with the dynamical system perspective

In this study, we revisit the homogeneous and isotropic, spatially curved model in the Lyra geometry framework. We apply the dynamical system approach to study the Universe evolution in model. The present cosmic dynamical system formulation is independent of the model parameter which yields the Universe expansion phases dominated by the stiff fluid, radiation, dark matter and dark energy. These expansion phases in the Lyra model are consistent with the General relativity model. In addition, the displacement vector field of the Lyra geometry model will give rise to the stiff matter dominated phase during early times of the Universe evolution. The cosmographic parameters, EoS parameter and statefinder diagnostic have been utilized in the dynamical system to illustrate the cosmic evolution of the Universe. The numerical solution technique is used to illustrate graphical behaviors of the cosmological parameters. On the basis of dynamical system and numerical analysis, we exhibit that the model explains accelerating universe expansion with transition from the decelerating phase and it will lead to the Λ cold dark matter (ΛCDM) model in the near future.

Use of patellofemoral digital twins for patellar tracking and treatment prediction: comparison of 3D models and contact detection algorithms.

Introduction: Poor patellar tracking can result in painful contact pressures, patella subluxation, or dislocation. The use of musculoskeletal models and simulations in orthopedic surgeries allows for objective predictions of post-treatment function, empowering clinicians to explore diverse treatment options for patients. Although a promising approach for managing knee surgeries, the high computational cost of the Finite Element Method hampers its clinical usability. In anticipation of minimal elastic deformations in the involved bodies, the exploration of the Multibody Dynamics approach emerged as a viable solution, providing a computationally efficient methodology to address clinical concerns related to the knee joint. Methods: This work, with a focus on high-performance computing, achieved the simulation of the patellofemoral joint through rigid-body multibody dynamics formulations. A comparison was made between two collision detection algorithms employed in the simulation of contact between the patellar and femoral implants: a generic mesh-to-mesh collision detection algorithm, which identifies potential collisions between bodies by checking for proximity or overlap between their discretized mesh surface elements, and an analytical contact algorithm, which uses a mathematical model to provide closed-form solutions for specific contact problems, but cannot handle arbitrary geometries. In addition, different digital twins (3D model geometries) of the femoral implant were compared. Results: Computational efficiency was considered, and histories of position, orientation, and contact force of the patella during the motion were compared with experimental measurements obtained from a sensorized 3D-printed test bench under pathological and treatment scenarios. The best results were achieved through a purely analytical contact detection algorithm, allowing for clinical usability and optimization of clinical outcomes.

Modeling and experimental validation of twin lip balanced vane pump considering micromotions, contact mechanics, and lubricating interfaces

This paper presents a model formulation for balanced twin lip vane pumps and an experimental activity to validate the model. The simulation model begins with a geometrical module that preprocesses the CAD drawings of a given unit. The model then performs a fluid dynamic analysis using a lumped-parameter formulation to solve for the pressures inside properly defined control volumes within the unit. The fluid dynamic model is solved simultaneously with a motion module that evaluates the planar motions of the vanes using Newton’s law of motion and with a lubricating interface solver based on the Reynolds equation. Contact dynamics formulations and elastohydrodynamic relations are applied at the vane locations in contact with the cam ring. The comparison with experimental results highlights a good match in volumetric and hydromechanical efficiencies. The measured outlet pressure ripple matches the simulated one for all tested speeds and pressures. The paper also shows a breakdown of the distribution of volumetric and power losses arising from various components of the machine. The proposed methodology is computationally inexpensive, so it can be used in future design and optimization studies aimed at improving the performance of such units.

Strong posterior contraction rates via Wasserstein dynamics

AbstractIn Bayesian statistics, posterior contraction rates (PCRs) quantify the speed at which the posterior distribution concentrates on arbitrarily small neighborhoods of a true model, in a suitable way, as the sample size goes to infinity. In this paper, we develop a new approach to PCRs, with respect to strong norm distances on parameter spaces of functions. Critical to our approach is the combination of a local Lipschitz-continuity for the posterior distribution with a dynamic formulation of the Wasserstein distance, which allows to set forth an interesting connection between PCRs and some classical problems arising in mathematical analysis, probability and statistics, e.g., Laplace methods for approximating integrals, Sanov’s large deviation principles in the Wasserstein distance, rates of convergence of mean Glivenko–Cantelli theorems, and estimates of weighted Poincaré–Wirtinger constants. We first present a theorem on PCRs for a model in the regular infinite-dimensional exponential family, which exploits sufficient statistics of the model, and then extend such a theorem to a general dominated model. These results rely on the development of novel techniques to evaluate Laplace integrals and weighted Poincaré–Wirtinger constants in infinite-dimension, which are of independent interest. The proposed approach is applied to the regular parametric model, the multinomial model, the finite-dimensional and the infinite-dimensional logistic-Gaussian model and the infinite-dimensional linear regression. In general, our approach leads to optimal PCRs in finite-dimensional models, whereas for infinite-dimensional models it is shown explicitly how the prior distribution affect PCRs.

Dynamic stiffness method and CUF-based component-wise theories applied to free vibration analysis of solid beams, thin-walled structures and reinforced panels

In this paper, an exact dynamic stiffness formulation using higher-order theories with displacement variables only is presented and subsequently used to investigate the free vibration characteristics of solid beams, thin-walled structures and reinforced panel structures. In essence, higher-order displacement fields are developed by using the Carrera unified formulation (CUF), and by discretizing the cross-section kinematics with bilinear, cubic and fourth-order Lagrange polynomials. In particular, the component-wise (CW) approach based on Lagrange expansion is applied in which the solid part and thin-walled part are considered as two independent components that can be assembled. The principle of virtual displacements is used to derive the governing differential equations and the associated natural boundary conditions. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The explicit terms of the dynamic stiffness matrices are also presented. The Wittrick–Williams algorithm of the dynamic stiffness method (DSM) is applied with the explicit expressions of the J0 count for beam elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. The accuracy and efficiency of the proposed methodology are extensively assessed for different solid beams, thin-walled structures and reinforced panels and the results are compared with those appearing in published literature and also checked by 3D finite element (FE) solutions.

Mechanical properties and deformation mechanisms of single crystal Mg micropillars subjected to high-strain-rate C-axis compression

The mechanical properties and deformation mechanisms of single crystal magnesium under c-axis quasi-static and high-strain rate compressions are investigated through in situ scanning electron microscope (SEM) experiments and post-mortem transmission electron microscope (TEM) characterization. The findings revealed that ductility and high rates of hardening are preserved for pillars as large as 15 μm. Furthermore, rate effects result in a mild increase in flow stress with plastic deformations controlled primarily by the slip of <a+c> type dislocations. Importantly and in contrast to other literature reports, plastic deformation occurs in the absence of twining. As the strain increases and plastic deformation exceeds about 4%, crystal rotation activates basal slip, <a> type dislocations, resulting in a more rate independent flow stress. TEM observation on micropillars compressed at a strain rate of 250/s, revealed the activation of {112‾2‾}<1‾1‾23> slip systems and high mobility of screw dislocations as major contributors to plastic strains in excess of 10% without fracture. These findings are relevant to the design of lightweight materials used in transportation systems, e.g., selection of material grain size. Moreover, the experimental data here reported provides the materials science community with a unique opportunity to validate discrete dislocation dynamics (DDD) formulations employed in multiscale design of materials.

New geometric formulation for libration dynamics and suppression of partial space elevator by fuzzy logic and thrust vectoring control

This study proposes a new control strategy for mitigating the libration in a partial space elevator (PSE). First, a libration-free or coupling-free analytical speed function is derived by assuming no in-plane and out-of-plane libration in the cargo transportation phase. Subsequently, a thrust is applied at the PSE's end body to counter any libration during this phase. A new set of geometric measures - bending and departure angles - are introduced to characterize the libration motion in PSE's dynamic equation. Based on these measures, two separate proportional-derivative (PD) stabilizing feedback laws are proposed. These PD laws individually control the bending and departure angles by thrust at the end body to suppress the libration that deviates from the libration-free trajectory. Due to the dynamic coupling between the bending and departure modes, they dominate alternatively. Accordingly, a novel fuzzy logic control law is proposed to switch between two PD controls based on the state of these two angles. Finally, a thrust vectoring control is proposed to combine in-plane and out-of-plane thrusting into a single actuation control. The asymptotic stability of the proposed control scheme is proved by Lyapunov's stability theory. Comprehensive numerical analyses demonstrate the effectiveness of the new geometric representation of the libration and the proposed new control strategy, highlighting their ability to suppress libration with bounded control inputs efficiently.