Mass-spring-damper Research Articles

Detachment waves in frictional contact: I — A two-mass system

This work studies a mathematical model for the motion of a two mass–spring–damper system with friction, and has a two-fold purpose. The first is to start a mathematical study of the way detachment or slip waves, when the system transits from stick to slip motion, propagate in discrete and continuous systems. The introduction of friction changes the problems into systems of differential set-valued inclusions, which are mathematically interesting, but rather complex. The second is to use such a ‘simple’ system as an example of a very general existence and uniqueness theorem for systems described by set-valued pseudomonotone operators, Kuttler and Shillor (1999) and Andrews et al. (2020).

Effect of Spring-Mass-Damper Pedestrian Models on the Performance of Low-Frequency or Lightweight Glazed Floors

For structural design purposes, human-induced loads on pedestrian systems can be described by several simplified (i.e., deterministic equivalent-force models) or more complex computational approaches. Among others, the Spring-Mass-Damper (SMD), Single Degree of Freedom (SDOF) model has been elaborated by several researchers to describe single pedestrians (or groups) in the form of equivalent body mass m, spring stiffness k and damping coefficient c. For all these literature SMD formulations, it is proved that the biodynamic features of walking pedestrians can be realistically reproduced, with high computational efficiency for vibration serviceability assessment of those pedestrian systems mostly sensitive to human-induced loads (i.e., with vibration frequency f1 < 8 Hz). Besides, the same SMD proposals are characterized by mostly different theoretical and experimental assumptions for calibration. On the practical side, strongly different SMD input parameters can thus be obtained for a given pedestrian. This paper focuses on a selection of literature on SMD models, especially on their dynamic effects on different structural floor systems. Four different floors are explored (F#1 and F#2 made of concrete, F#3 and F#4 of glass), with high- or low-frequency, and/or high- (>1/130th) or low- (1/4th) mass ratio, compared to the occupant. Normal walking scenarios with frequency in the range fp = 1.5–2 Hz are taken into account for a total of 100 dynamic simulations. The quantitative comparison of typical structural performance indicators for vibration serviceability assessment (i.e., acceleration peak, RMS, CREST) shows significant sensitivity to input SMD assumptions. Most importantly, the sensitivity of structural behaviours is observed for low-frequency systems, as expected, but also for low-mass structures, which (as in the case of glazed floor solutions) can be characterized by the use of lightweight modular units with relatively high vibration frequency. As such, major attention can be required for their vibrational analysis and assessment.

Design and Optimization of a Rack and Pinion Type WEC Using an Auxiliary Vibrating System

Research on wave energy converters with Rack and pinion type Power Take-Off (PTO) has been increasing over the last few years. A few control methods are used to optimize the performance of the said Wave Energy Converters (WECs). This paper presents a novel auxiliary vibrating system that can be implemented to improve the power input to a wave energy converter with a rack and pinion type PTO in regular waves. The design of the WEC system includes a floater, a double rack and pinion arrangement, a vibrating system, and a Mechanical Motion Rectifier (MMR) consisting of two one-way bearings that can convert the bidirectional wave motion to a unidirectional rotation of the output shaft. Once the waves move the floater upwards, this compresses the vibrating system which absorbs some of the energy and then the vibrating system helps the floater return to its original position by releasing the stored energy. The vibrating system also serves as a control method for limiting rack movement, so the impact of the waves is not detrimental to the system. This article aims to approximate the optimized power input to the system and investigate whether the implementation of a novel vibrating system improves the system power input. Allowing the WEC’s natural frequency to reach the wave’s natural frequency is important as it allows for maximum power absorption. The use of vibration systems to tune the WEC’s natural frequency close to the waves’ is novel and serves as the main factor in choosing this research. The WEC was modeled as 2 spring mass damper systems. Then the characteristic equations of the systems were extracted from the equations of motion and solved analytically to obtain the responses. One-factor-at-a-time (OFAT) method together with two different algorithms (Genetic and Multi-Start algorithms) from MATLAB code were used to optimize the response. The optimized power input to the system was then approximated. For system one, the maximum amplitude of the response was seen at a system mass of 500 kg and stiffness in the range of 100<k<240 N/m. The same was achieved for system two at a system mass of 500 kg and stiffness in the range of 100<k<138. The effect of the stiffness and mass on the response and input power has also been discussed.

Neural-network-based fluid–structure interaction applied to vortex-induced vibration

In this paper, a fluid–structure interaction (FSI) solver with neural-network-based fluid-flow prediction is proposed. This concept is applied to the problem of vortex-induced vibration of a cylinder. The majority of studies that are concerned with fluid-flow prediction using neural networks solve problems with fixed boundary. In this paper, a convolutional neural network (CNN) is used to predict unsteady incompressible laminar flow with moving boundary. A deformable non-Cartesian grid, which traces the boundary of the fluid domain, is used in this paper. The CNN is trained for oscillating cylinder with various frequencies and amplitudes. The dynamics of the elastically-mounted cylinder is modelled using a linear spring–mass–damper model and solved by an implicit differential scheme. The results show that the CNN-based FSI solver is capable of capturing the so-called lock-in phenomenon for the problem of vortex-induced vibration of a cylinder and the quantitative behaviour is similar to the results of the CFD-based FSI solver. Moreover, the CNN-based FSI solver is two orders of magnitude faster than the CFD-based FSI solver and the speedup is expected to be even greater on larger problems.

Exponential input-to-state stability for neutral stochastic delay differential equations with Lévy noise and Markovian switching

This paper mainly focuses on the pth ()-moment input-to-state stability (ISS) of neutral stochastic delay differential equations (NSDDEs) with Lévy noise and Markovian switching. By using the generalized integral inequality and the Lyapunov function methodology, the ISS, integral input-to-state stability (iISS), and stochastic input-to-state stability (SISS) of such equations are obtained. When the input signal is a constant signal and a zero signal, the pth ()-moment ISS reduces to the pth ()-moment practical exponential stability and the pth ()-moment exponential stability, respectively. Finally, an example of the mass–spring–damping (MSD) model under the stochastic perturbation is given to verify the validity of the results.

Equivalent Dynamic of Liquid Sloshing Coupled with Mass Transfer During On-Orbit Refueling

During an on-orbit refueling mission, the liquid fuel partially filling in the tanks will slosh and produce coupled motion with the servicer-to-client transfer, which may bring dangers to the spacecraft and even lead to attitude divergence. To effectively simulate the motion and the inertia of liquid fuel in a cylindrical tank during refueling, equivalent dynamic modeling of liquid fuel sloshing coupled with mass transfer is developed in this paper. A spring–mass–damper model with time-varying elastic and damping coefficients is implemented in the axial direction to equal the motion of the liquid mass center, while a pendulum model with time-varying pendulum length is adopted in the radial direction. An equivalent liquid elliptical cylinder is developed to approximate the inertia of dispersed liquid while sloshing. A series of computational fluid dynamics simulations are carried out to observe the liquid behaviors in the fuel tanks and to verify the proposed equivalent dynamic model. Finally, three-dimensional sloshing is theoretically and numerically analyzed.

Spring–Mass–Damper-Based Platooning Logic for Automated Vehicles

This paper applies a classical physics-based model to control platooning autonomous vehicles (AVs) in a commercial traffic simulation software. In the spring–mass–damper (SMD) model, each vehicle is assumed as a mass coupled with its preceding vehicle with a spring and a damper: the spring constant and damper coefficient control spacing and speed adoption between vehicles. Limitations on the platooning-oriented communication range and number of vehicles in each platoon are applied to the model to reflect real-world circumstances and avoid overlengthened platoons. The SMD model controls both intra-platoon and inter-platoon interactions. Initial evaluation of the model reveals that it does not cause a negative spacing error between AVs in a harsh deceleration scenario, guaranteeing safety. Besides that, the SMD model produces a smaller positive average spacing error than the VISSIM built-in platooning module, which prevents maximum throughput drop. The simulation result for a regular highway section reveals that the proposed platooning algorithm increases the maximum throughput by 10%, 29%, and 63% under 10%, 50%, and full market penetration rate (MPR) of AVs, respectively, with a 0.5 s response time. A merging section with different volume combinations on the main section and merging section and different MPRs of AVs is also modeled to test inter-platoon spacing policy effectiveness in accommodating merging vehicles. Travel time reductions of 20% and 4% are gained under a low MPR of AVs on the main lane and merging lane, respectively. Meanwhile, a more noticeable travel time reduction is observed in both main lane and merging lanes and under all volume combinations in higher AV MPRs.

Pseudo-Hamiltonian neural networks with state-dependent external forces

Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conserving. We introduce a pseudo-Hamiltonian formulation that is a generalization of the Hamiltonian formulation via the port-Hamiltonian formulation, and show that pseudo-Hamiltonian neural network models can be used to learn external forces acting on a system. We argue that this property is particularly useful when the external forces are state dependent, in which case it is the pseudo-Hamiltonian structure that facilitates the separation of internal and external forces. Numerical results are provided for a forced and damped mass–spring system and a tank system of higher complexity, and a symmetric fourth-order integration scheme is introduced for improved training on sparse and noisy data.

SVD enabled data augmentation for machine learning based surrogate modeling of non-linear structures

The computationally expensive estimation of engineering demand parameters (EDPs) via finite element (FE) models, while considering earthquake and material parameter uncertainty limits the use of the Performance Based Earthquake Engineering framework. Attempts have been made to substitute FE models with surrogate models, however, most of these models are a function of building parameters only. This necessitates re-training for earthquakes not previously seen by the surrogate. In this paper, the authors propose a machine learning based surrogate model framework, which considers both these uncertainties in order to predict for unseen earthquakes. Accordingly, earthquakes are characterized by their projections on an orthonormal basis, computed using SVD of a representative ground motion suite. This enables one to generate varieties of earthquakes by randomly sampling these weights and multiplying them with the basis, resulting in a large data set that is needed to train machine learning models. The weights along with the constitutive parameters serve as inputs to a machine learning model with EDPs as the desired output. Four competing machine learning models were tested and it was observed that a deep neural network (DNN) gave the most accurate prediction. The framework is validated by using it to successfully predict the peak response of one-story and three-story shear frame buildings represented using nonlinear spring–mass–damper systems, subjected to unseen far-field ground motions.

Quantized filtering for networked Takagi–Sugeno fuzzy systems with multipath data packet dropouts

This paper concerns the mixed and passivity‐based filtering problem for networked nonlinear systems with randomly occurring parameter uncertainties, multipath data packet dropouts, time‐varying delay, and quantization effects. The discrete‐time nonlinear plant considered in this paper is modeled as a Takagi–Sugeno fuzzy system with plant rules. The data missing phenomenon is considered in both measurement and performance output signals due to the unreliable nature of communication links. Further, to reduce the network bandwidth utilization, the measurement quantization is also employed for both the outputs before transmitting through the communication channel. Also, additive filter gain fluctuation is taken into account to reflect the imprecision in filter implementation. Stochastic variables obeying the Bernoulli distribution are incorporated in the model description to characterize the random occurrence of parameter uncertainties and data packet dropouts. A set of sufficient conditions assuring the stochastic stability of the filtering error system with mixed and passivity performance is derived according to Lyapunov stability theory. Finally, three numerical examples including mass–spring–damper and tunnel diode circuit model are established to establish the validity of the developed filter design algorithm.

Implementation of the SMC control strategy to an active horizontal seat suspension system

This article discusses an application of the sliding mode control (SMC) in active suspension systems, with particular focus on its use in the mass-spring-damper (MSD) systems. The article highlights advantages of the SMC over traditional control methods, such as improved robustness and insensitivity to parameter variations. The use of active elements in the MSD systems, such as the permanent magnet synchronous motor (PMSM), is also discussed. The article presents the mathematical modeling of the MSD system and the development of the sliding mode controller. Simulation tests are conducted to evaluate the performance of the system, and the results are presented by means of the power spectral density and transmission function. The article concludes that although chattering effect occurs in the proposed control system and the desired force is well reproduced in a horizontal seat suspension, a slight delay of the system response is presented. The results of this study suggest that the proposed SMC control strategy is a promising solution for improving the ride comfort and stability of seat suspension systems.

Long short-term memory (LSTM) model-based reinforcement learning for nonlinear mass spring damper system control

The Neural Networks (NN) model which is incorporated in the control system design has been studied, and the results show better performance than the mathematical model approach. However, some studies consider that only offline NN model learning and does not use the online NN model learning directly on the control system. As a result, the controller's performance decreases due to changes in the system environment from time to time. The Reinforcement Learning (RL) method has been investigated intensively, especially Model-based RL (Mb-RL) to predict system dynamics. It has been investigated and performs well in making the system more robust to environmental changes by enabling online learning. This paper proposes online learning of local dynamics using the Mb-RL method by utilizing Long Short-Term Memory (LSTM) model. We consider Model Predictive Control (MPC) scheme as an agent of the Mb-RL method to control the regulatory trajectory objectives with a random shooting policy to search for the minimum objective function. A nonlinear Mass Spring Damper (NMSD) system with parameter-varying linear inertia is used to demonstrate the effectiveness of the proposed method. The simulation results show that the system can effectively control high-oscillating nonlinear systems with good performance.

Identifying Lebesgue-sampled Continuous-time Impulse Response Models: A Kernel-based Approach*

Control applications are increasingly sampled non-equidistantly in time, including in motion control, networked control, resource-aware control, and event-triggered control. Some of these applications use measurement devices that sample equidistantly in the amplitude domain. The aim of this paper is to develop a non-parametric estimator of the impulse response of continuous-time systems based on such sampling strategy, known as Lebesgue-sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the output intersample behavior, which ultimately leads to more accurate models and more efficient output sampling compared to the standard approach. The efficacy of this method is demonstrated through a mass-spring damper case study.

Event-triggered integral sliding mode control for uncertain networked linear control systems with quantization.

In this paper, the integral sliding mode (ISM, SM) controller is designed to address the problem of implementing non-periodic sampled data for a class of networked linear systems with matched and unmatched uncertainties. Due to the redesigned gain of the nominal controller, the feedback control used by the nominal controller guarantees the asymptotic stability of the uncertain networked linear system. The discontinuous control uses intermittent control based on the reaching law to achieve the finite-time reachability of practical SM band. Based on the defined measurement error, the event-triggered (ET) condition can be derived, and furthermore, it guarantees a sufficient condition for the existence of the actual SM. On this basis, a quantization scheme is added to further decrease the network transmission burden of the linear system. No Zeno behavior occurs in the system owing to the existence of a positive lower bound of inter-event time. Compared with the conventional integral sliding mode control (ISMC, SMC), the proposed control law can not only relieve the network burden, but also decrease the transmission energy loss. Finally, simulation results of a numerical example and a mass-spring damping system demonstrate the effectiveness of the proposed method.

Optimization of engine and transmission mounting system for a V6 front wheel drive vehicle

Engine mounts helps to attach power train with the frame of the vehicle. The engine mounts help to keep the power- train in its position with the SUV chassis as vehicle experiences several torque loads and inertial loads. The mounting system helps in controlling the motion of the engine and transmission unit, preventing it from physical contact with other components of the vehicle system from sudden impact due to vibrations. The power train Mounting system helps in several ways to keep the engine and transmission unit firmly in its position during vehicle motion and helps in better drivability. Engine along with transmission unit con– tributes 25% of total weight of vehicle, it is important to isolate noise and vibration generated in the engine entering into the vehicle cabin, as power train is the source of vibration in the vehicle. So, it is important to study and investigate rigid body mode shapes for the engine and transmission unit for particular position of mounting unit and spring stiffness. This paper investigates the engine mounting system location and spring stiffness for a vertically mounted v8 engine. The engine and transmission unit mounted on vehicle chassis by elastomeric bushings. The bushing acts as spring mass damper system, helping in isolation of vibration and noise entering into cabin also prevents physical contact of engine with other critical vehicle components. Design of experiments approach is used to study effects of design variables. By varying mount location and stiffness rates the effects of these variable on the power train mounting system is studied and appropriate mounting location and stiffness rates is suggested to improve overall NVH performance of the power train.

Fixed-time leader-following consensus of multi-agent systems with intermittent control

In this article, the intermittent-based fixed-time (IBFT) consensus matter is researched for nonlinear multi-agent systems (MASs). By designing a novel IBFT control protocol, the follower can achieve consensus with the leader’s state within a settling time. To deal with the fixed-time (FT) consensus matter, a new differential inequality is proposed, which provides a way to analyze the IBFT stability. Some properties are given to ensure the FT consensus of the nonlinear MASs. Furthermore, we extend our results to the directed communication situation of agents. The FT leader-following consensus problem with directed topology via intermittent control is solved as well. The settling time achieved is relative to the protocol parameters and independent of the initial states. Three examples demonstrate the feasibility and effectiveness of the suggested control protocols, including two application examples, the Chua’s circuit system, a spring-mass-damper (SMD) system, and one numerical example.

Active Modeling and Control of the Ring-Shaped Pneumatic Actuator: An Experimental Study

A soft ring-shaped pneumatic actuator (RPA) that contracts radially plays a key role in biomimicking the contractions of the digestive system. However, the modeling and control of the RPA are still challenging due to the nonlinearity, hysteresis, and unique structure. In this article, we present an active-model-enhanced control (AMEC) scheme for the precise contraction control of the RPA. First, a generalized mass–spring–damper model is proposed to describe the dynamics of the RPA focusing on the midpoint of the inner wall. Based on the proposed model, the AMEC scheme is developed to enhance a proportional–integral–derivative (PID) controller in terms of tracking a reference trajectory. In this scheme, the modeling errors of the generalized mass–spring–damper model are estimated by an active modeling algorithm, which is integrated into the PID controller to eliminate the effect of the modeling errors. Finally, experiments are conducted to validate the proposed modeling and control scheme. The results indicate that the modeling errors are estimated by the active modeling algorithm with an acceptable estimation error. The tracking error of the AMEC is 52.7% smaller than that of the PID controller. The proposed modeling and control methods for the RPA lay a solid foundation for its biomimetic application.

Vibration Extraction for Melting Plastic Hydraulic Injection System with Stick Slip Vibration Analysis

IntroductionA hydraulic power injection machine is designed to use a driving screw to inject melted plastic into a specified mold. This machine can be found at an automotive spare parts factory. The cantilever-style heavy-duty screw injector is supported by one roller and secured at the end. An obvious need for vibration analysis on the roller support is essential. A mass spring damper model is proposed for deeply investigating the friction induced vibration mechanism for this injection system to well understand and analyze its vibration behavior.PurposeA mechanical mode of two degrees-of-freedom (DOF) is designed to improve research on the dynamic features of the Plastic Hydraulic Injection System (PHIS) mechanism.Materials and methodsExperimental investigation and analysis of this mechanism are explored to obtain the instability speed and critical stick slip (SS) speed. The numerical imitation results of this work will help with the design and development of the PHIS mechanism.ConclusionThe stability of the system and SS behavior are next examined by determining the critical variability speediness and critical SS speed. A simulation study is carried out to evaluate the effect of various parameters of the system on its stability and on the behavior of the SS motion.

Physics‐based deep neural network model to guide electrospinning polyurethane fibers

AbstractElectrospinning is an inexpensive room‐temperature method of producing nanofibers from polymer granules. While it is quite easy to produce electrospun nanofibers, it is very difficult to control properties of the resulting fibers without conducting laborious trial‐and‐error experiments. In this work, a mass‐spring‐damper (MSD) model was used to simulate formation of electrospun fibers for different combinations of electrospinning conditions such as voltage, needle‐to‐collector distance, and polymer concentration. The sparse data from the CPU‐intensive MSD model were then used in developing a deep neural network (DNN) model that could guide the electrospinning experiment toward producing fibers with a desired diameter. The accuracy of the MSD‐DNN hybrid model was examined via comparison with experimental data obtained by electrospinning polyurethane fibers.

Simulation and Experimental Verification of Dynamic Characteristics on Gas Foil Thrust Bearings Based on Multi-Physics Three-Dimensional Computer Aided Engineering Methods

This paper presents a method to simulate the dynamic operating characteristics of a gas foil thrust bearing based on linear elastic support and constant ambient temperature to mimic the transient structure–fluid interactions. In the physical model, the top and bump foils are simply represented by an infinite number of Hookean springs attached to a solid wall with a small amount of deformation, whereas the gas film in the bearing is under quasi-steady lubrication flow conditions with hydrodynamic pressure distributed on the little-deformed top foil. A three-dimensional multi-physics model in a cylindrical coordinate system is established via a commercial computer-aided engineering software package to predict the nominal dynamic characteristics of the gas foil thrust bearing. To verify the multi-physics model, an experimental bench was built in-house to measure the thrust force on the support of the bearing. With the pertinent bearing parameters being entered into the package, the simulations agree well with the experimental thrust forces. As a further step, a simulation model of a clamped-rotor gas foil thrust bearing design was thoroughly investigated under nominal operating conditions, resulting in predictions of underdamped oscillations in rotor motions. The phenomenon could be described using a linear mass–spring–damper model that is dependent on the gas film thickness. The stiffness and damping coefficients could serve as a base reference for rotor dynamics analysis. This concludes the potential development of a digital twin for gas foil thrust bearing systems.