Mass-spring-damper Research Articles

Exploring submergence impact on flow-induced motion energy-harvesting with circular-triangular prisms

AbstractRecent advancements in energy-harvesting have utilized Flow-Induced Motion (FIM) as a renewable source, diverging from past efforts aimed at minimizing FIM's adverse effects. This study introduces kinetic energy converters using alternating lift technology (ALT), employing a prism with a Circular-Triangular (Cir-Tria) shape, coupled with a spring and damper, to generate energy. Utilizing computational fluid dynamics in OpenFOAM for Reynolds numbers between 2 × 103 and 13 × 103 and varying submergence depth ratio from 0.98 to 5.91, this research employs a moving computational grid, two-dimensional incompressible Navier–Stokes equations, the k-omega Shear Stress Transport (SST) turbulence model, the Volume of Fluid, VOF, two-phase model, and the cylinder mass–spring–damper equation. Findings show that approaching the flow surface negatively impacts the FIM response due to the interaction of vortices from the flow surface and the prism’s upper shear layer. This interaction weakens and neutralizes the upper vortices, altering the flow structure around the prism and the governing FIM phenomena. Proximity to the free surface significantly affects FIM responses, with a notable decrease in vibration amplitude and energy conversion as the submergence depth ratio increases from 0.98 to 5.91. Maximum system efficiency of 1.4% is observed in the VIV initial branch at infinite submergence (single-phase flow). Beyond a submergence depth ratio of 5.91, FIM amplitude and energy conversion flatten, indicating negligible free surface effects.

The effect of small internal and dashpot damping on a trapped mode of a semi-infinite string

The effect of small internal and dashpot damping on a trapped mode of a 1D-waveguide, that is, a semi-infinite string on a Winkler elastic foundation, has been investigated. At the edge of the string a mass–spring–damper system is attached. The string is assumed to have an internal damping. Four models for the internal damping are considered: air damping, Kelvin–Voigt damping, local Kelvin–Voigt damping, and damping related to time hysteresis. Depending on the internal damping and the parameters in the formulated problem, it will be shown that the amplitude of a trapped mode of the string can decrease or increase with time.

Discrete element method simulation of high-speed vehicle collisions with road barrier systems

AbstractThe behavior of road or perimeter protection barriers under vehicle impact are usually investigated based on crash tests and finite element (FE) numerical approaches, which are ether expensive or time-consuming. Several studies have proposed to reduce the computation time of the numerical analysis by substituting the complex FE models of vehicles using simplified mass–spring–damper system models. However, these models have drawbacks since consideration of different vehicle impact angles is difficult and they are unable to correctly simulate the risk of high-speed vehicle collision running over the barrier. In this paper, a new approach is proposed to simulate the collision of vehicles with barriers based on the discrete element method (DEM). Here, to save computation time only a handful of 3D non-spherical particles are used to represent the barrier and vehicle. These particles are generated based on the super-quadric function, which is capable of generating a variety of shapes needed for the model. The contact detection and evaluation are carried out based on discrete function representation of the particles with uniform sampling. The bond between two discrete elements is defined using a nonlinear cohesive beam model since the distance between the elements is relatively large. The simulation results obtained based on this approach are more accurate and complete than the simplified mass–spring models and computationally more efficient than the FE model.

Operator splitting for coupled linear port-Hamiltonian systems

Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms preserve the dissipative structure of the overall system and are convergent of second order. Numerical results for coupled mass–spring–damper chains illustrate the computational efficiency of the splitting methods compared to a straight-forward application of the implicit midpoint rule to the overall system.

Understanding wave energy converters dynamics: High-fidelity modeling and validation of a moored floating body

In ocean engineering, one of the most challenging phenomena to replicate is the interaction between waves and a moored floating body. Accurately evaluating such systems is essential for minimizing uncertainties, mitigating risks, and advancing technologies like wave energy converters. For this purpose, this study aims to develop a high-fidelity numerical model capable of reducing reliance on costly experimental campaigns during the device design phases. The model integrates a fluid dynamics module based on the Navier–Stokes equations, implemented in Star CCm+, with a mooring model utilizing a mass–spring–damper system, specifically MoorDyn. The primary objective is to introduce this coupled approach and demonstrate its efficacy through validation against experimental data from two distinct wave energy converters: ISWEC and PeWEC. The validation process encompasses comprehensive comparisons between simulated and observed kinematic behavior, mooring tensions, and crucially, pressure loads. Results indicate that the model is able to faithfully predict the complex phenomena involving a moored floating body, affirming the accuracy and reliability of the proposed coupling methodology. The coupling developed is available online link, where a simplified case study is present to show how to compile the library and add it in the numerical model.

A Piecewise Particle Swarm Optimisation Modelling Method for Pneumatic Artificial Muscle Actuators

Pneumatic artificial muscles (PAMs) possess compliant properties desirable for certain applications such as prosthetics and robotic structures. However, this compliance along with their inherent nonlinear dynamics make them difficult to accurately model and as such accurately control under certain control architectures. Common approaches to this problem include measuring the actuator’s physical properties and approximating a model based on these parameters or using deep learning methods to train a model with the actuator’s behaviours. This paper introduces an optimisation-based modelling approach based on a particle swarm optimisation (PSO) algorithm using a mass–spring–damper approximation for the PAM, as well as a piecewise modelling method that accounts for nonlinear dynamics. The use of optimisation to estimate model parameters removes the need to measure physical properties, and the three-element approximation allows for fast model generation with low computational complexity and training data requirements. Through multiple tests comparing model behaviour with real PAM motion, the accuracy of these models is confirmed to be promising for future work. Dynamic nonlinearities are properly accounted for using the piecewise modelling method, including both hysteresis and disproportionate input/output relationship across the stroke length of the actuator. Compared with other PAM modelling techniques, this method has improved generation time, lower computational load requirements, and complexity and can be applied to actuators for which the phenomenological mass–spring–damper model is a good approximation.

The application and algorithm of fabric simulation in game industry

fabric simulation has emerged as a crucial aspect of computer graphics, particularly in applications such as film production, video games, and design. This paper provides a comprehensive review of fabric simulation methodologies, implementation techniques, and its diverse applications within the game industry. The fabric simulation algorithms are broken down into Fabric Modeling, Dynamic Simulation, and Collision Handling. The three common modeling strategies of Elasticity-Based Models, Particle-Based Models, and Mass-Spring Damper Models, are discussed in detail. Additionally, dynamic simulation strategies such as Position-Based Dynamics (PBD) and Extended Position-Based Dynamics (XPBD) are explored for their role in real-time simulations, particularly in the game industry. The paper also delves into collision handling algorithms, exploring the strategies for accurate collision detection and response. The application of fabric simulation in the game industry is highlighted, showcasing how it enhances realism and immersion by simulating fabric movement and interactions with the environment. The paper introduced various fabric simulation tools and systems within popular game engines like Unity 3D and Unreal Engine 5. Furthermore, optimization strategies, such as view-dependent adaptive simulation, are discussed to improve performance providing insight for future work.

The application and algorithm of fabric simulation in game industry

fabric simulation has emerged as a crucial aspect of computer graphics, particularly in applications such as film production, video games, and design. This paper provides a comprehensive review of fabric simulation methodologies, implementation techniques, and its diverse applications within the game industry. The fabric simulation algorithms are broken down into Fabric Modeling, Dynamic Simulation, and Collision Handling. The three common modeling strategies of Elasticity-Based Models, Particle-Based Models, and Mass-Spring Damper Models, are discussed in detail. Additionally, dynamic simulation strategies such as Position-Based Dynamics (PBD) and Extended Position-Based Dynamics (XPBD) are explored for their role in real-time simulations, particularly in the game industry. The paper also delves into collision handling algorithms, exploring the strategies for accurate collision detection and response. The application of fabric simulation in the game industry is highlighted, showcasing how it enhances realism and immersion by simulating fabric movement and interactions with the environment. The paper introduced various fabric simulation tools and systems within popular game engines like Unity 3D and Unreal Engine 5. Furthermore, optimization strategies, such as view-dependent adaptive simulation, are discussed to improve performance providing insight for future work.

A nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator

Compared with traditional actuators, the giant magnetostrictive actuator has the merits of fast response, high accuracy, and high reliability and has been widely applied. However, its performance is affected by the electromagnetic loss and the temperature, prestress, and magnetic coupling effect. In order to accurately analyze its performance, it is necessary to establish a nonlinear dynamic model including the electromagnetic loss and the magnetic–prestress–thermal coupling effect. First, based on the field separation approach, the magnetic fields generated by the eddy current loss and the anomalous loss are obtained and added to the Jiles–Atherton model. Second, the magnetostrictive model is given with the magnetic–prestress–thermal coupling effect. Finally, assuming the transmission of the giant magnetostrictive actuator as a mass–spring–damper system, a nonlinear dynamic hysteresis model with magnetic–prestress–thermal coupling effect and dynamic electromagnetic losses of a giant magnetostrictive actuator is developed. Based on this model, the output displacement curves of the giant magnetostrictive actuators under different driving currents and frequencies are given. The comparison with the experimental results shows that this model agrees well with the experiment.

Modeling damped spring vibration using python to train students' critical thinking and scientific reasoning

Programming has been carried out to model the vibration of a mass spring system with no damping and with damping variations using Python programming language coding. This research aims to simulate the simple harmonic vibration of a mass spring (without damping) and the vibration of a damped mass spring. The programming is designed after formulating the equations of motion of damped mass spring vibrations that behave as second-order differential equations and analyzing the numerical formulation of the Feynman-Newton algorithm arrangement. The method used is experimentation using python to simulate the vibration of the spring. Simulation by varying the damping constant (c = 0, c < √4mk, c = √4mk, and c > √4mk). The simulation results show various vibration graphs, namely simple harmonic vibration, under damped vibration, critically damped vibration, and over damped vibration. The shape of the vibration graph is influenced by the mass, spring constant, and damping constant. The greater the damping constant, the less the maximum speed of vibration. This research has succeeded in visualizing the simple harmonic vibration of a massless spring (without damping) and the vibration of a damped massless spring. This modeling can help the physics learning process in high school in understanding the concept of spring vibration to obtain critical reasoning in accordance with physical phenomena. Modeling of damped spring vibrations using Python can be used as a physics learning media on vibration material to train scientific and critical reasoning skills, and as a learning innovation because it is a new thing where the curriculum and high school learning in Indonesia are not used to being delivered.

Control of edgewise vibration of a pre-twisted rotating beam with shunted piezoelectric tuned mass damper

The edgewise vibration control of a pre-twisted beam, rotating in the vertical plane, is considered in this study. A piezoelectric tuned mass damper (PTMD) comprising a spring–mass–damper system and a piezoelectric transducer with its associated shunt circuit is considered the control device. A finite element formulation of the pre-twisted rotating beam with the attached PTMD is developed while considering the effect of centrifugal stiffening due to rotation and the effect of gravity force. The natural frequencies of the beam (without PTMD) obtained using the present formulation are corroborated by comparing them with the results derived from Ansys. A single PTMD attached at the tip end of the beam can effectively suppress the response of the beam subjected to a distributed load in the edgewise direction. The best values of resistance and inductance of the shunt circuit are obtained through a parametric study on the peak and root mean square value of the beam tip response. A qualitative difference in the uncontrolled as well as in the controlled responses can be noticed while considering the effect of the gravity load component in the edgewise direction. Further, it has been observed that the conventional Tuned Mass Damper (TMD) provides better control than the PTMD system for ideally tuned conditions, however, the control performance of TMD degrades rapidly as compared to the PTMD in the presence of detuning. This demonstrates the effectiveness of PTMD in a practical implementation where achieving the perfectly tuned condition is seldom realized. The control performance of PTMD marginally degrades when the beam is subjected to multi-directional excitation. Hence, the proposed control system has the potential for application in rotating beam-type structures, such as wind turbine blades.

Forecasting dynamics by an incomplete equation of motion and an auto-encoder Koopman operator

The governing equation of mass–spring–damper dynamics usually consists of a known structure and undetermined nonlinear components. This work proposes a physics-informed method to learn the unknown component by modeling its evolution with an auto-encoder Koopman operator. The Koopman operator is well known for its global linearization of dynamics and sensitivity to spectral modes. The undetermined component in an oscillatory equation of motion (EOM) is first reconstructed by a time-delay neural network whose inputs stack past sequences of observables and the control. Then, the evolution of the undetermined component is globally linearized and propagated by the Koopman operator in a latent space created by an auto-encoder neural network. Ultimately, observables at the future timestep are forecasted by timestepping the original EOM. Uniting an incomplete EOM and the Koopman operator, the proposed physics-informed Koopman neural ordinary differential equation (PiKNODE) method shows competitive edges compared with several black- and grey-box benchmarks in four synthetic and experimental case studies. Additionally, an anomaly-detection technique based on the Jensen–Shannon distance is proposed to boost the practicality of the PiKNODE for structural health monitoring.

Controlling chaotic vocal fold oscillations in the numerical production of vowel sounds

Lumped mass models have been studied in depth to unveil the complex nonlinear physics of phonation. Even in the case of simple symmetric models, slight changes in muscle restoring forces or excessive subglottal pressure can cause abnormal or even chaotic vocal fold oscillations. In a recent work, it was shown that it was possible to device a theoretical pacemaker for phonation that could render the chaotic motion regular again. This consisted of attaching an additional mass–spring–damper system to the vocal fold model, the damping of which could be adjusted according to an altering energy chaos control strategy. The chaos of phonation is low-dimensional and one may wonder whether it has a profound effect in voice production and, if so, whether the proposed phonation pacemaker could compensate for it. For this purpose, we compute the time evolution of the glottal volume velocity generated by normal, chaotic and controlled oscillations of the vocal folds and convolve it with the impulse response of magnetic resonance imaging (MRI) geometries of the human vocal tract, corresponding to the vowels /ɑ/, /i/ and /u/. The impulse response for each vowel is obtained from the solution of the wave equation by the finite element method, when a Gaussian pulse is prescribed as a boundary condition in the glottis of the vocal tract. It will be demonstrated that the chaotic vibration of the vocal folds severely distorts the vowel sounds and that the proposed control strategy is able to recover with high quality the vowels produced in normal phonation. Audiovisual files are provided to support the objective results of the phenomena in terms of spectral and time analysis of the train of glottal pulses generated by the vocal folds and the produced vowel sounds.

Reliability-based optimization of supported pendulum TMDs’ nonlinear track shape using Padé approximants

Supported Pendulum Tuned Mass Dampers (PTMDs) are vibration absorbers whose mass is constrained to oscillate along a curved path, enabling to use gravity as a restoring force. Through a proper track shape selection, they can adapt to the so-called Nonlinear Energy Sinks (NES) concept, consolidated for spring–mass–damper TMDs. Accordingly, NESs are recognized for their ability to resonate in a wide range of frequencies due to their nonlinear nature, becoming more effective when variations on the host structure’s natural frequencies occur. However, regardless of the recent advances in the last few years, gaps remain to be explored in the track shape optimization of supported PTMDs. For instance, a comprehensive literature review shows that Reliability-Based Design Optimization (RBDO) studies to determine the track shape of supported PTMDs cannot be found to the best of the author’s knowledge. Within this context, this paper proposes an original RBDO approach to define the track shape of supported PTMDs in buildings subjected to seismic excitation. For this purpose, a generic rational function with an arbitrary curvature, determined from the Padé approximation of the circle equation, is constructed to allow the PTMD’s path shape search. This procedure allows optimizing fewer parameters than required in Taylor series expansions while providing a wider range of alternatives for numerical optimization. Finally, an active-learning Kriging-based Efficient Global Optimization (EGO) procedure is employed to find the optimum solutions with few objective function evaluations. The application case consists of a typical soft story building subjected to seismic loadings. The optimal track differs from the circle equation, with a higher slope for moderate displacements.

Artificial intelligence-based position control: reinforcement learning approach in spring mass damper systems

This work examines the use of deep Reinforcement Learning (RL) in mass-spring system position control, providing a fresh viewpoint that goes beyond conventional control techniques. Mass-spring systems are widely used in many sectors and are basic models in control theory. The novel aspect of this approach is the thorough examination of the impact of several optimizer algorithms on the RL methodology, which reveals the optimal control tactics. The research applies a Deep Deterministic Policy Gradient (DDPG) algorithm for continuous action spaces, where the actor and critic networks are important components in assessing the agent’s performance. The RL agent is trained to follow a reference trajectory using the Simulink environment for system modeling. The study provides insights into the agent’s learning approach and performance optimization by evaluating the training process using force-time graphs, reward graphs, and Episode Manager charts. Furthermore, the effect of different combinations of optimizers on the control performance of the agent is examined. The outcomes highlight the importance of optimizer selection in the learning process by revealing significant variations in training times. As a result, a better understanding of the relationship between various optimizers and control performance is provided by this study’s novel application of reinforcement learning in mass-spring system control. The results raise the possibility of more potent methods for controlling complex systems and add to the expanding field of study at the interface of control theory and deep learning.

An analytical model of oscillating heat pipe performance

Concentrated heat dissipation poses formidable challenges across various domains, such as electronics, power generation, and aerospace applications. Oscillating Heat Pipes (OHPs), also known as Pulsating Heat Pipes (PHPs), have emerged as promising solutions due to their exceptional heat transfer capabilities and adaptability. Although OHPs have received significant research attention, their widespread adoption in industry has been hindered by the absence of reliable and cost-effective design tools. These tools are challenging to develop due to the complex nature of OHP operation, the multitude of design variables to consider, and the substantial computational resources required for computational modeling.In this study, previous OHP models based on first principles and spring–mass–damper analogies are combined with novel methods to create an analytical model that captures a much wider range of OHP phenomena than previous analytical models. The model predicts OHP heat transfer performance orders of magnitude faster than computational techniques and for a wider range of design parameters than experimental correlations. Furthermore, this model provides critical insights into the underlying principles governing OHP operation, including a theory for the onset and stabilization of circulation.The analytical model was compared to 185 experimental data in the literature and predicted the OHP temperature drop with a mean error of 16.6%. Additionally, the temperature drop was predicted within 30% for 84.5% of the data analyzed. The model’s analytical nature facilitates rapid solutions, enabling evaluations across a large design space that could be used to identify a small number of candidate designs for further experimental or computational evaluation.

Graph oscillators: Physics-guided graph modeling of mass–spring–damper systems for trajectory prediction and damage localization

Recognizing that a multiple-degree-of-freedom mass–spring–damper system can be viewed as a group of connected nodes, this paper presents a novel computational framework that learns such coupled oscillations by a graph, a mathematical structure describing pairwise connections between objects. Further reinforced by an incomplete equation of motion, distributed neural networks and an anti-symmetric coupling constraint, we can learn unknown coupling mechanisms (or nodal interactions in the language of graph models) using limited data. The proposed physics-data-hybrid method demonstrates a promising predictive capability even for unseen control inputs, outperforming three black-box and grey-box counterparts in synthetic and experimental studies. In addition to its predictive capability, the distributed parameterization of nodal interactions allows us to identify local anomalies by evaluating updates after short transfer learning. While limits of the current method exist, it displays the potential of a generalizable and interpretable meta-model for predicting nonlinear trajectories and identifying the system’s status.

A Dual Triggering Scheme to Adaptive Fuzzy Resilient Control of Switched Nonlinear Systems Against Mixed Attacks.

A dual event-triggered adaptive fuzzy resilient control scheme for a class of switched nonlinear systems with vanishing control gains under mixed attacks is proposed in this article. The scheme proposed achieves dual triggering in the channels of sensor-to-controller and controller-to-actuator by designing two new switching dynamic event-triggering mechanisms (ETMs). An adjustable positive lower bound of interevent times for each ETM is found to preclude Zeno behavior. Meanwhile, mixed attacks, that is, deception attacks on sampled state and controller data and dual random denial-of-service attacks on sampled switching signal data, are handled by constructing event-triggered adaptive fuzzy resilient controllers of subsystems. Compared with the existing works for switched systems with only single triggering, more complex asynchronous switching caused by dual triggering and mixed attacks and subsystem switching is addressed. Further, the obstacle caused by vanishing control gains at some points is eliminated by proposing an event-triggered state-dependent switching law and introducing vanishing control gains into a switching dynamic ETM. Finally, a mass-spring-damper system and a switched RLC circuit system are applied to verify the obtained result.

Study on Coupled Vibration of Human-plate System under Pedestrian Excitation

In the paper, in order to explore the influence of human-structure interaction (HSI) in the vertical direction on the dynamic response of floors due to human-induced excitation, the formula for the human-plate interaction system is deduced. The pedestrian is in turn modelled as moving force (MF), spring-mass-damper (SMD), and added mass-spring-mass-damper (MSMD). The floor is modelled using a formulation in modal coordinates. Aiming at the formula of human-plate interaction system, the state space method is used to get the instantaneous frequency and instantaneous damping ratio of the floor under walking excitation, and the acceleration responses can be obtained using the Runge-Kutta method. Furthermore, this work studies the influence of pedestrian mass and structural modal mass on structural vibration response. The results show that the floor frequency is observed to decrease and the damping ratio gives the opposite trend when the pedestrian enters the floor. The MF model overestimates the measured response, while the actual results can be well approximated by the results for SMD and MSMD models considering HIS. Accounting for increasing human mass and decreasing modal mass lead to significant increase in the dynamic properties and the structural response.

Physics-informed and black-box Identification of robotic actuator with a flexible joint

In robotics, precise models are critical for ensuring safety and functionality. However, acquiring a precise model characterizing a system’s dynamics can be challenging. One of the alternatives to address this issue is system Identification, which aims to obtain models through physical and experimental observations. In this manner, the developments in machine learning algorithms, such as neural networks, have significantly improved the modeling of complex and nonlinear phenomena. In this work, a mass-spring-damper (MSD) system and a low-cost original elastomer-based Series Elastic Actuators (eSEA) assembly are used to evaluate the performance of system Identification models. The black-box models selected are variations of the AutoRegressive Moving Average with eXogenous input (ARMAX) algorithm. The gray-box model aims to estimate the parameters of 4 friction models; the optimization is done utilizing physics-informed neural networks (PINNs). For both case studies, the PINNs outperformed the black-box models. In the didactic example, the parameters obtained are close to the ground truth, and the highest determinant coefficient obtained is 0.99. The friction model that best represents the robotic actuator is the LuGre model, with the parameters obtained using the PINNs, outperforming the best black-box model by lowering the mean absolute error (MAE) by 30.83%. With a determinant coefficient of 0.94, the model shows a high capacity for describing the multiple nonlinearities present in the system.