Mass Spring Damper System Research Articles

Prognosis and Health Management using Energy Activity.

Abstract Accurate detection of faults in a dynamic system is very beneficial as this information can be used in a wide variety of ways by the machine operators or designers. This advantage becomes many folds when regarding the future condition i.e. time to failure, named remaining useful life, is available in addition to that of the present condition. Thus, prognosis is one of the most useful tools to improve the working of a machine as many critical decisions can be made. Prognosis can be critical for applications that risk loss of life and property. In this paper, a hybrid method, utilizing bond graph and artificial intelligence, is proposed for system health estimation (SHE) and prognosis. The Bond Graph model is used to calculate Energy Activity, which is used as a common metric for both SHE and prognosis. The proposed method is checked by simulation on a spring mass damper system undergoing a fault.

Wave Analysis and Control of Single/Multiple Cascade-Connected Damped Mass-Spring Systems

Wave Analysis and Control of Single/Multiple Cascade-Connected Damped Mass-Spring Systems

Longitudinal motion control for vehicle platooning in mixed traffic based on virtual mass-spring-damper theory

This paper proposes a novel control method based on the virtual mass-spring-damper (MSD) theory to improve the platoon's system safety in mixed traffic flows consisting of connected and automated vehicles (CAVs) and human-driven vehicles (HDVs). To validate the proposed control method, two kinds of mixed platoons composed of five CAVs and one HDV are modelled and simulated by using CarSim and Matlab/Simulink. The simulation results demonstrate that when the HDV is at the head of the platoon, the maximum spacing error is 1.73 m; while the HDV is in the middle of the platoon, it increases to 3.59 m. Meanwhile, the inter-vehicle spacing errors do not amplify as they propagate along the platoon. Therefore, by selecting the appropriate stiffness constants and damping coefficients of the virtual MSD system according to platoon forms, the proposed control method can effectively ensure the stability and improve the safety of the mixed vehicular platoon.

Longitudinal motion control for vehicle platooning in mixed traffic based on virtual mass-spring-damper theory

This paper proposes a novel control method based on the virtual mass-spring-damper (MSD) theory to improve the platoon's system safety in mixed traffic flows consisting of connected and automated vehicles (CAVs) and human-driven vehicles (HDVs). To validate the proposed control method, two kinds of mixed platoons composed of five CAVs and one HDV are modelled and simulated by using CarSim and Matlab/Simulink. The simulation results demonstrate that when the HDV is at the head of the platoon, the maximum spacing error is 1.73 m; while the HDV is in the middle of the platoon, it increases to 3.59 m. Meanwhile, the inter-vehicle spacing errors do not amplify as they propagate along the platoon. Therefore, by selecting the appropriate stiffness constants and damping coefficients of the virtual MSD system according to platoon forms, the proposed control method can effectively ensure the stability and improve the safety of the mixed vehicular platoon.

Robust tracking control for mechanical systems using only position measurements

A discontinuous control law is presented to solve the tracking problem for a class of second-order nonlinear systems and fully actuated n degrees of freedom (nDOF) mechanical systems. Moreover, the control algorithm can compensate for viscous friction, Coulomb friction, and bounded external perturbations. Only position measurements are available for feedback. In this way, this proposal does not require to measure or estimate another signal but the position of the mechanical system to achieve the tracking control objective, this is, the controller does not need velocity measurements as feedback; this constitutes the main contribution of the present approach. In the stability analysis, a strict Lyapunov function and its conditions are studied to prove asymptotic stability for second-order systems and Lagrangian systems. In a mass–spring–damper system is tested the closed-loop performance through numerical simulations. Also, simulations and real-time experiments are carried out in a (2DOF) Scara robot. As a result, the proposed discontinuous algorithm is proved to be suitable to solve the tracking problem, and also that the equilibrium points of the closed-loop system are globally stable.

Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems

In this article, variational iteration algorithm I with an auxiliary parameter is used for simple and damped mass–spring systems that undergo forced vibrations and transverse vibration of uniform and variable beams with simply supported analytical treatment. In addition, common vibration problems are classified and the values of Lagrange multipliers are identified for each type of problem. Examples are given at the end, which shows that this modification demonstrated the high efficiency and attained very good agreement in illustrated models and might be promptly reached out to other nonlinear differential and partial differential equations.

Vehicle–bridge interaction analysis by the state-space method and symplectic orthogonality

The dynamic properties of bridges can be extracted from the dynamic responses of the vehicles passing on these bridges. This paper proposes a method for the vehicle–bridge interaction analysis of continuous beam bridges with different spans and variable cross sections using numerical methods that are high in computational efficiency. Herein, the vehicle is simplified as a spring–damper–mass system and coupled to the bridge by its interactional force in the governing equations based on the Timoshenko beam theory. According to the symplectic orthogonality of the state vectors, the orthogonality of the mode shapes of the Timoshenko beams is proved, and the dynamic responses of the continuous beam bridges with different spans and variable cross sections can be solved by the mode superposition method. More complicated factors, such as harmonic load on vehicles, noise in measurement, and roughness of pavements, can also be conveniently taken into account. Finally, the proposed method is demonstrated using some numerical examples and applied to a real bridge. The results indicate that the method is convenient, efficient, and precise for engineering applications.

Modeling and stability analysis methods of neutrosophic transfer functions

Uncertainty is inherent property in actual control systems because parameters in actual control systems are no constants and changeable under some environments. Therefore, actual systems imply their indeterminate parameters, which can affect the control behavior and performance. Then, a neutrosophic number (NN) presented by Smarandache is very easy expressing determinate and/or indeterminate information because a NN p = c + dI is composed of its determinate term c and its indeterminate term dI for c, d ∈ R (R is all real numbers), where the symbol “I” denotes indeterminacy. Unfortunately, all uncertain modeling and analysis of practical control systems in existing literature do not provide any concept of NN models and analysis methods till now. Hence, this study firstly proposes a neutrosophic modeling method and defines a neutrosophic transfer function and a neutrosophic characteristic equation. Then, two stability analysis methods of neutrosophic linear systems are established based on the bounded range of all possible characteristic roots and the neutrosophic Routh stability criterion. Finally, the proposed methods are used for two practical examples on the RLC circuit and mass–spring–damper systems with NN parameters. The analysis results demonstrate the effectiveness and feasibility of the proposed methods.

Random Response of Spring–Damper–Mass–Belt System with Coulomb Friction

Purpose A randomly excited spring–damper–mass system placed on a uniformly moving belt is investigated with the consideration of the Coulomb friction between the system and the belt. The system response is analytically studied. The physical essence of friction and the influences of the belt speed, the friction amplitude and the excitation intensity on the random responses are discussed in detail.

Robustness Analysis of MIMO Mechatronic Systems in the Frequency Domain

A new and general method of robustness analysis for linear dynamic systems containing both electrical and mechanical components is proposed in this paper. The method is based on the convex optimization theory and, therefore, it is accurate, efficient, and scales well with the number of unknown variables. The method is applied to two examples: a piezoelectric harvester (single-input single-output case) and a double mass–spring–damper system (multiple-input multiple-output (MIMO) case). In both cases, upper and lower bounds of the magnitude response are computed and compared to the Monte Carlo method. The results show that parametric variation affect strongly the performance output, uncertainty must be taken into account for a robust design, and that the proposed method is a great improvement to the existing method in the literature.

The Existence and Uniqueness of Initial-Boundary Value Problems of the Fractional Caputo-Fabrizio Differential Equations

In this paper, the existence and uniqueness problem of the initial and boundary value problems of the linear fractional Caputo-Fabrizio differential equation of order $\sigma \in (1,2]$ have been investigated. By using the Laplace transform of the fractional derivative, the fractional differential equations turn into the classical differential equation of integer order. Also, the existence and uniqueness of nonlinear boundary value problem of the fractional Caputo-Fabrizio differential equation has been proved. An application to mass spring damper system for this new fractional derivative has also been presented in details.

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphicalb-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

송전철탑 하중설계를 위한 복수 경간 송전선의 갤로핑 시뮬레이션

When wind load acts on the Power Transmission Line (PTL) with asymmetric cross section from icing and snowing, the generated vibration is termed ‘galloping phenomenon’. Since galloping phenomenon triggers short circuits or ground faults of the PTL, various galloping studies are being conducted, at home and abroad. However, galloping analysis is performed for single span in most cases, while actual PTL comprises multiple spans. In this study, PTL is modeled as a mass-springdamper system, using a multi-body dynamics analysis program, RecurDyn. To analyze dynamic analysis of the PTL, damping coefficient is derived, by using the free vibration experiment of the PTL and Rayleigh damping theory. Through flow analysis, the galloping occurrence condition was identified, and galloping simulation was performed, by modeling the wind load. The effect of galloping on the stress applied to the pylon, was analyzed by flexible modeling the pylon between spans. As a result, approximately 150% of stress is applied to the pylon, so the galloping phenomenon should be considered when designing the pylon.

Effects of the Reynolds number and structural damping on vortex-induced vibrations of elastically-mounted rigid cylinder

In this work, analyses of the damping ratio and turbulence effects on three-dimensional vortex-induced vibrations of a two degrees-of-freedom elastically mounted rigid cylinder are carried out. Simulations are conducted for damping ratios of ζ=0.5, 2.5, 5.0 and 10.0% for flows covering Reynolds numbers in the three TrSL flow regimes, in the range of Re=7.5×102 to 1.3 × 105. Variation of the response amplitudes, phase angles, force coefficients and frequency ratios by the damping ratios and Reynolds number are investigated using the classically damped spring-mass system equations programmed inside the CFD software Fluent. New results are obtained for very-high Reynolds numbers and different damping ratios. New conclusions are drawn from the mechanical responses using surface interpolation of 240 data-points, which allows the investigation of the trends of a given response variable ξ based on the Ay*vs.ζ(m*+CA)vs.ξ three-dimensional plot proposed by the authors. A new mechanism of elongation of the upper branch extension based on the universal reduced damping, Su, during the TrSL3 regime is described.

An analytical perspective about structural damage identification based on transmissibility function

Transmissibility functions have been widely applied into the field of structural health monitoring, especially for damage detection. However, due to the existence of few analytical research works to conceive the significance of damage onset, the inherent mechanism of damage identification based on transmissibility function has not yet been clearly and deeply evaluated. In this article, an analytical approach has been investigated to demonstrate how to localize damage components caused by mass and stiffness change in terms of multiple-degree-of-freedom mass–spring–damper system, based on the inherent analysis between the transmissibility functions for any two consecutive masses. This study also points out the importance of the system input: various input location may lead to different recognized damage regions. Related simulation case studies and laboratory activities are carried out, proving the effectiveness and accuracy of the proposed approach.

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.

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.