Mass-spring-damper Research Articles

Simulation and Analysis of Two-Mass Suspension Modification Using MATLAB Programming

The designs of automotive suspension system are aiming to avoid vibration generated by road condition interference to the driver. This final project is about a quarter car modeling with simulation modeling and analysis of Two-Mass modeling. Both existing and new modeling are being compared with additional spring in the sprung mass system. MATLAB program is developed to analyze using a state space model. The program developed here can be used for analyzing models of cars and vehicles with 2DOF. The quarter car modelling is basically a mass spring damping system with the car serving as the mass, the suspension coil as the spring, and the shock absorber as the damper. The existing modeling is well-known model for simulating vehicle suspension performance. The spring performs the role of supporting the static weight of the vehicle while the damper helps in dissipating the vibrational energy and limiting the input from the road that is transmitted to the vehicle. The performance of modified modelling by adding extra spring in the sprung mass system provides more comfort to the driver. Later on this project there will be comparison graphic which the output is resulting on the higher level of damping system efficiency that leads to the riding quality.

Input-to-State Stabilization of Interval Type-2 Fuzzy Systems Subject to Cyberattacks: An Observer-Based Adaptive Sliding Mode Approach

This paper focuses on the sliding mode control (SMC) problem of interval type-2 (IT2) fuzzy systems subject to the unmeasurable state and cyberattacks. A key issue is how to design a state observer under the constraint that only the bounds of membership functions are known. To this end, this paper introduces two weighting factors to construct a new membership function. Besides, the concept of input-to-state stability (ISS) is utilized to deal with the residual term resulting from the cyberattacks and external disturbances. The sufficient condition is established such that the sliding mode dynamics and the estimated error dynamics are input-to-state stable. Furthermore, by online estimating the unknown parameters in upper bounds of cyberattacks and external disturbances, an adaptive sliding mode controller is synthesized such that the reachability of the prescribed sliding surface can be guaranteed and the effect of cyberattacks on the system performance can be effectively attenuated. Finally, the validity of the proposed method is illustrated by a mass–spring–damper system.

Conformity and stability analysis of a modified spring–mass–damper system dynamics-based car-following model

Modeling the dynamics of a traffic system involves using the principles of both physical and social sciences since it is composed of vehicles as well as drivers. A novel car-following model is proposed in this paper by incorporating the socio-psychological aspects of drivers into the dynamics of a purely physics-based spring–mass–damper mechanical system to represent the driver–vehicle longitudinal movements in a traffic stream. The crux of this model is that a traffic system can be viewed as various masses interacting with each other by means of springs and dampers attached between them. While the spring and damping constants represent the driver behavioral parameters, the mass component represents the vehicle characteristics. The proposed model when tested for its ability to capture the traffic system dynamics both at micro, driver, and macro, stream, levels behaved pragmatically. The stability analysis carried out using perturbation method also revealed that the proposed model is both locally and asymptotically stable.

Analysis of Modal Resonance Between PLL and DC-Link Voltage Control in Weak-Grid Tied VSCs

Weak ac grid operation is known to challenge the stability of voltage source converters (VSCs). This paper provides an interpretation for the cause of such instability in view of a particular modal resonance within VSC's control, i.e., the resonance between dc-link voltage control (DVC) and synchronizing control-phase-locked loop (PLL). To characterize this modal interaction, a two degrees-of-freedom mass–spring–damper model is first proposed. Subsequently, based on a multi-modal decomposition approach, the amount of interaction is quantified by the incremental damping and frequency drift superimposed on each individual mode. Analytical results indicate that when the natural frequencies of PLL and DVC mode are close, strong interaction will push the lower-frequency mode to move toward the decreased frequency and damping direction, while causing the higher-frequency mode to go the opposite. Moreover, weaker ac grid operation will amplify such frequency/damping excursion and, thus, will render the lower-frequency mode unstable. Further, when the ac voltage control (AVC) is disregarded, a dynamic stability margin is analytically derived, and operation beyond the margin will result in monotonic drift. With the inclusion of AVC, owing to its introduced additional negative damping, by contrast, instability will occur in the presence of oscillations. Both eigenvalue analysis and simulations are conducted to verify the results.

Large and Infinite Mass–Spring–Damper Networks

This paper introduces mechanical networks as a tool for modeling complex unidirectional vibrations. Networks of this type have branches containing massless linear springs and dampers, with masses at the nodes. Tree and ladder configurations are examples demonstrating that the overall dynamics of infinite systems can be represented using implicitly defined integro-differential operators. Results from the proposed models compare well to numerical results from finite systems, so this approach may have advantages over high-order differential equations.

On the Application of the Multiple Scales Method on Electrostatically Actuated Resonators

We investigate modeling the dynamics of an electrostatically actuated resonator using the perturbation method of multiple time scales (MTS). First, we discuss two approaches to treat the nonlinear parallel-plate electrostatic force in the equation of motion and their impact on the application of MTS: expanding the force in Taylor series and multiplying both sides of the equation with the denominator of the forcing term. Considering a spring–mass–damper system excited electrostatically near primary resonance, it is concluded that, with consistent truncation of higher-order terms, both techniques yield same modulation equations. Then, we consider the problem of an electrostatically actuated resonator under simultaneous superharmonic and primary resonance excitation and derive a comprehensive analytical solution using MTS. The results of the analytical solution are compared against the numerical results obtained by long-time integration of the equation of motion. It is demonstrated that along with the direct excitation components at the excitation frequency and twice of that, higher-order parametric terms should also be included. Finally, the contributions of primary and superharmonic resonance toward the overall response of the resonator are examined.

Analysis of controllers in suppressing the structural building vibration

Two degree of freedom (2 DOF) mass spring damper system is used in representing as building structure that dealing with the earthquake vibration. The real analytical input is used to the system that taken at El Centro earthquake that occurred in May 1940 with magnitude of 7.1 Mw. Two types of controller are presented in controlling the vibration which are fuzzy logic (FL) and sliding mode controller (SMC). The paper was aimed to improve the performance of building structure towards vibration based on proposed controllers. Fuzzy logic and sliding mode controller are widely known with robustness character. The mathematical model of two degree of freedom mass spring damper wasis derived to obtain the relationship between mass, spring, damper, force and actuator. Fuzzy logic and sliding mode controllers were implemented to 2 DOF system to suppress the earthquake vibration of two storeys building. Matlab/Simulink was used in designing the system and controllers to present the result of two storeys displacement time response and input control voltage for uncontrolled and controlled system. Then the data of earthquake disturbance was taken based on real seismic occurred at El Centro to make it as the force disturbance input to the building structure system. The controllers proposed would minimize the vibration that used in sample earthquake disturbance data. The simulation result was carried out by using Matlab/Simulink. The simulation result showed sliding mode controller was better controller than fuzzy logic. In specific, by using the controller, earthquake vibration can be reduced.

Disturbance-observer Based Adaptive Control for Second-order Nonlinear Systems Using Chattering-free Reaching Law

In this paper, an adaptive sliding mode control incorporating with a nonlinear disturbance observer is proposed for a class of second-order nonlinear systems with unknown parameters and matched lumped disturbance. A double hyperbolic reaching law with chattering-free characteristic is first constructed, and an adaptive sliding mode controller is designed to guarantee the satisfactory tracking performance and fast error convergence. The chattering problem is eliminated by means of the infinitely approaching equilibrium point instead of crossing it by employing two hyperbolic functions. In order to identify the unknown parameters accurately, an adaptive parametric update law is presented through constructing a set of auxiliary filtered variables. Then, a nonlinear disturbance observer is proposed to improve the tracking performance and compensate for the lumped disturbance including perturbations and uncertainties. The stability analysis is provided by the Lyapunov stability theory, and a numerical simulation on a mass-spring damper system is given to demonstrate the effectiveness of the proposed method.

Redesign and evaluation of an equation-based model reduction method in OpenModelica

Even in times of a continuously growing computational power and miniaturisation of computers and control devices, the demand for model reduction techniques persists. Detailed models of physical systems typically result in rather complex dynamic models. In the design process, when the design space has been narrowed down to a concrete design, it is often desirable to replace these detailed models by simpler ones. The reduced models are expected to run multitudes faster while preserving important properties of the original model required for control design and validation purposes. For evaluation purposes, the reduction method is applied to a simple sample model (two mass spring damper). The reduced model generated by the reduction algorithm is compared with the results of a theoretically derived reduced model. In the conclusions, deficits of the current implementation are discussed. Proposals for further improvements of the methodology for extended control design use cases are given in the outlook.

Sampled-Data Adaptive Output Feedback Fuzzy Stabilization for Switched Nonlinear Systems With Asynchronous Switching

This paper considers the problem of sampled-data adaptive output feedback fuzzy stabilization for switched uncertain nonlinear systems associated with asynchronous switching. A state observer is designed to estimate the unmeasured states and fuzzy logic systems are employed to deal with the unknown nonlinear terms. Sampled-data controller and novel switched adaptive laws are constructed based on the recursive design method and an average dwell time constraint is given to ensure that the closed-loop system is stable. The proposed scheme is employed in a mass–spring–damper system to demonstrate its effectiveness.

Event-Triggered ${H}_{\infty}$ Control for Uncertain Markov Jump Systems With Nonlinear Input

This paper investigates the robust event-triggered control scheme for discrete-time Markov jump systems with nonlinear input. An event-based strategy is addressed to reduce the data communication and improve the control efficiency. A Lyaounov function method is utilized to analysis the mean square stability and sufficient conditions are obtained in the form of linear matrix inequalities. Convex combination approach is utilized to handle nonlinear input while parameter uncertainty and external disturbances are both included and the robustness H ∞ performance is analyzed. Finally, a numerical example is shown to compare the different schemes and a mass spring damping system is given to illustrate the effectiveness of the provided method.

Nonlinear System Identification Using Temporal Convolutional Networks: A Silverbox Study

Identification of nonlinear systems is presented using a neural network variant known as the temporal convolutional network (TCN). The identification capabilities of TCNs and standard feedforward neural networks (FNNs) are benchmarked and compared using the Silverbox dataset: a publicly available dataset from a circuit equivalent to a nonlinear spring-mass damper. The TCN is found to have superior performance in simulation of the test portion of the dataset. In addition, published benchmark results are surveyed and compared to the TCN results. Analysis of existing results reveals testing variances that effect model performance, so guidelines for fair comparison of models on the Silverbox benchmark are presented.

The feasibility of predicting ground reaction forces during running from a trunk accelerometry driven mass-spring-damper model.

BackgroundMonitoring the external ground reaction forces (GRF) acting on the human body during running could help to understand how external loads influence tissue adaptation over time. Although mass-spring-damper (MSD) models have the potential to simulate the complex multi-segmental mechanics of the human body and predict GRF, these models currently require input from measured GRF limiting their application in field settings. Based on the hypothesis that the acceleration of the MSD-model’s upper mass primarily represents the acceleration of the trunk segment, this paper explored the feasibility of using measured trunk accelerometry to estimate the MSD-model parameters required to predict resultant GRF during running.MethodsTwenty male athletes ran at approach speeds between 2–5 m s−1. Resultant trunk accelerometry was used as a surrogate of the MSD-model upper mass acceleration to estimate the MSD-model parameters (ACCparam) required to predict resultant GRF. A purpose-built gradient descent optimisation routine was used where the MSD-model’s upper mass acceleration was fitted to the measured trunk accelerometer signal. Root mean squared errors (RMSE) were calculated to evaluate the accuracy of the trunk accelerometry fitting and GRF predictions. In addition, MSD-model parameters were estimated from fitting measured resultant GRF (GRFparam), to explore the difference between ACCparam and GRFparam.ResultsDespite a good match between the measured trunk accelerometry and the MSD-model’s upper mass acceleration (median RMSE between 0.16 and 0.22 g), poor GRF predictions (median RMSE between 6.68 and 12.77 N kg−1) were observed. In contrast, the MSD-model was able to replicate the measured GRF with high accuracy (median RMSE between 0.45 and 0.59 N kg−1) across running speeds from GRFparam. The ACCparam from measured trunk accelerometry under- or overestimated the GRFparam obtained from measured GRF, and generally demonstrated larger within parameter variations.DiscussionDespite the potential of obtaining a close fit between the MSD-model’s upper mass acceleration and the measured trunk accelerometry, the ACCparam estimated from this process were inadequate to predict resultant GRF waveforms during slow to moderate speed running. We therefore conclude that trunk-mounted accelerometry alone is inappropriate as input for the MSD-model to predict meaningful GRF waveforms. Further investigations are needed to continue to explore the feasibility of using body-worn micro sensor technology to drive simple human body models that would allow practitioners and researchers to estimate and monitor GRF waveforms in field settings.

Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure

Parametric studies on the optimization of baffles on vibration suppression of partially filled tanks coupled by structure have been widely conducted in literature. However, few studies focus on the effect of the position of the baffles on fluid flow stratification and dampening the motion. In the present study, a numerical investigation, an engineering analysis, and optimal design study were performed to determine the effect of external flow on circular obstacle baffles performance on suppressing the vibrations of coupled structure in a closed basin. The single degree of freedom model (mass–spring–damper) is used to model the structure that holds the tank. The coupled system is released from an initial displacement without a velocity. The governing mass, turbulent Navier–Stokes momentum, volume of fluid, and one degree of freedom structure equations are solved by the Pressure-Implicit with Splitting of Operators algorithm in fluids and Newmark method in structure. Based on a detailed study of transient structure motion coupled with sloshing dynamics, the optimal baffle location was achieved. Optimal position of the baffle and its width are systematically obtained with reference to the quiescent free surface.

Control of Connected and Autonomous Vehicles with Cut-in Movement using Spring Mass Damper System

This paper proposes a theoretical framework to control a platoon of connected and autonomous vehicles (CAVs) in the presence of cut-in movements. The control method is developed based on the spring–mass–damper (SMD) system concept and aims to improve the platoon efficiency and stability after a cut-in movement (e.g., lane change and merging from on-ramp). The method seeks to resolve a disturbance created by a cut-in vehicle by systematically setting two control parameters, spring constant and damping coefficient, of the SMD-based control model based on the prevailing traffic conditions. The control method is evaluated through a simulation based on the changes in speed and spacing, recovery time to reach the desired speed, disturbance propagation, and platoon flow. The simulation result shows that the control method can effectively reduce the disturbance caused by a cut-in movement and improve platoon flow.

Vibration analysis of steel–concrete composite floors when subjected to rhythmic human activities

The main objective of this research work is to investigate the dynamic structural response of floors, when subjected to rhythmic human activities (aerobics), based on experimental tests and numerical modelling. The focus of this investigation is to assess the human comfort of floors, initially, simulating the individuals by traditional “force only” models and after that the effect of the people–structure dynamic interaction is considered based on the modelling of SDOF biodynamic models (mass–spring–damper systems). This way, the analysed structural model is related to a steel–concrete composite building, which is composed of three floors, with dimensions of 20 × 20 m, total area of 1200 m2 (3 × 400 m2) and a ceiling height of 4 m. The numerical modelling of the structure was performed based on the use of the ANSYS computational program and utilising the Finite Element Method (FEM) simulations. Aiming to evaluate the human comfort of the investigated composite floors, the dynamic characteristics of the individuals (mass, damping and stiffness) were experimentally obtained to introduce them into the developed biodynamic modelling. Thus, the dynamic response of the investigated composite floors was evaluated in terms of the peak accelerations, RMS and VDV values, based on current human comfort criteria. The results found along this investigation have indicated significant reductions of the peak accelerations values, when the biodynamic systems were considered in comparison with the results provided by the “force only” models.

Modeling Human Difference Threshold in Perceiving Mechanical Properties From Force

We discuss an extension of the basic principles underlying the human haptic just noticeable difference (JND) in perceiving a manipulator's mechanical properties from force feedback. Two cases are studied: first, the JND in perceiving the stiffness of manipulators with various masses and, second, the JND in perceiving the damping of a combined mass–spring–damper system with varying stiffness and mass. The extended JND laws are obtained through mapping psychophysical findings to JND formulations based on frequency response functions. We first present two human-factor experiments in which subjects discriminated between different levels of manipulator stiffness/damping while moving the manipulator with a prescribed sinusoidal deflection. For the two testing cases, both JNDs violate Weber's law: Due to the increases in mass, the normalized stiffness JND (the Weber fraction) decreases as the reference stiffness level increases; the damping JND for a constant reference damping increases with higher combined responses of stiffness and mass. On the basis of weighting the frequency response magnitude of mechanical properties, we performed model identification that fit the experimental observations and extended the JND laws for the two testing cases. Our extended JND laws indicate that, first, the stiffness and mass affect the stiffness JND in the same way, the stiffness JND is a fixed proportion of the combined frequency response of stiffness and mass, and, second, the frequency response magnitude of the damping JND is a fixed proportion of the frequency response magnitude of the combined system (the mass–spring–damper system).

Numerical simulation of track settlements based on an iterative holistic approach

A track settlement algorithm implemented in a multibody simulation software (MBS) is presented. The purpose is to extend the capabilities of a railway track model so a ballast degradation analysis can be performed. The main idea is to implement a methodology that enables a simulation of the train/track interaction and its influence on the overall track settlement mechanism of a regular track section. For this purpose, the common moving track model widely used in MBS codes is changed to a model in which the track stands still. This is done by inserting, in a discrete way, a set of mass–spring–damper systems along the track. The new way in which the track is modelled allows us, in a more accurate way, to take into account different capabilities of the track model, such as track flexibility and damping conditions, discrete support conditions given by the sleeper distance, and the possibility of modelling each track component independently along the track section. In the novel methodology presented in this work, a settlement algorithm has been directly implemented in the MBS package. The latter makes it possible to simulate the track degradation process given by the settlement of the ballast layer. The process consists of two main phases. In the first one, the train/track interaction analysis is carried out. In the second one, the dynamic forces are obtained at the supports along the track, which are then taken and transformed, by applying a settlement law, into vertical displacements that in turn are applied as longitudinal level irregularities in the wheel/rail contact. The process is completed by linking the aforementioned phases in a cyclic mode, considering as many iterations as desired. This work presents an efficient and novel technique that makes MBS code capable of predicting the impact of the accumulated track settlement on the train/track interaction.

Investigation of nonlinear dynamic behavior of a capacitive carbon nano-tube based electromechanical switch considering van der Waals force

In this study, nonlinear dynamic behavior of a capacitive carbon nano-tube switch is investigated considering van der Waals (vdW) force. The carbon nano-tube is considered as a nano-beam and dynamic equation of motion for this switch is presented based on the Euler–Bernoulli beam model. In order to simplify the bifurcation analysis of the carbon nano-switch, dynamic equation based on the modified mass–damper–spring model has been extracted. The fixed points of the switch have been studied in the absence and presence of the electrostatic force. Global and local criterion for stability study of the nano switch is employed. In order to study the local stability of the fixed points, the associated eigenvalues were extracted and the stability of these points was identified. For studying global stability, motion trajectories of the switch with and without considering damping effect are provided and presented. Basin of attraction set and region of periodic set and dependency of them on the applied voltage, as well as the vdW force and damping effect are investigated. Critical values of the applied voltage and vdW parameter leading to qualitative changes in the nano switch behavior through a saddle node bifurcation are obtained.

Vehicle–bridge coupling dynamic response of sea-crossing railway bridge under correlated wind and wave conditions

The sea-crossing railway bridge is exposed to a high risk of wind and wave, which threatens the safety of the bridge and railway. A wind–wave–vehicle–bridge dynamic analysis model for sea-crossing railway bridge under wind and wave loadings is developed by extending the previous wind–vehicle–bridge model. The developed wind–wave–vehicle–bridge model involves multipoint fluctuating wind field, irregular wave field, finite element model of the bridge, and mass–spring–damper model of the vehicle. The correlation between wind and wave is considered by an empirical curve derived based on field measurement. Static, buffeting, and self-excited wind forces on the bridge and vehicle are considered with coefficients obtained from wind tunnel tests. The wave forces on the bridge are calculated by Morison equation including stretching modification. The governing equations of the wind–wave–vehicle–bridge model are solved in time domain by Newmark-β method to compute the dynamic response of bridge and vehicle. The dynamic response of bridge and vehicle is compared and discussed in both wind–wave–vehicle–bridge and wind–vehicle–bridge model. The performance of bridge and vehicle are finally evaluated. Studies of dynamic response under correlated wind and wave are found to be imperative for assessment of structural and vehicle safety and driving comfort of sea-crossing railway bridge.