Mass Spring Damper System Research Articles

Formula omitted] model reduction for diffusively coupled second-order networks by convex-optimization

This paper provides an H2 optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input–output mapping of the original system but also preserves crucial structures, such as the second-order form, asymptotically stability, and diffusive couplings. To this end, an H2 optimal approach based on a convex relaxation is used to reduce the dimension, yielding a lower order asymptotically stable approximation of the original second-order network system. Then, a novel graph reconstruction approach is employed to convert the obtained model to a reduced system that is interpretable as an undirected diffusively coupled network. Finally, the effectiveness of the proposed method is illustrated via a large-scale networked mass–spring–damper system.

Validation using the in vivo experiment of the 3D model of the human ear using the equivalent mechanical impedance of the Mass-Spring-Damper System

The ear can be defined as the organ responsible for auditory perception. Its role among others is to amplify, transmit and convert an acoustic wave, presents in the environment, into an electrical pulse that can be interpreted by the brain via the auditory nerve. The conductive hearing loss is a major public health problem; it is related to a malfunction of the outer or middle ear leading to an interruption of the propagation of the sound wave within the hearing organ. Conductive deafness is caused by impulse noise which is present in a large number of professional sectors; many professions and/or sectors of activity are therefore concerned. There are two primary aims of this study: (1) to realize a 3D model of the human ear in order to characterize the impulse noise and evaluate its auditory risks in professional environments so as to identify the means of protecting the ear; (2) to carry out a comparison between the results obtained numerically using our 3D model and those obtained from experimental tests. The 3D model of the human ear was realized using the COMSOL multiphysics software. The structure–acoustic interaction between the auditory canal, which will be considered as the propagation field of the acoustic wave, and the structures of the ear (eardrum, skin, bone, cartilage) have been solved using the Finite Element Method (FEM). For the modeling, the ossicles, the cochlea and the middle ear were replaced by a Mass-Spring-Damper System (MSDS). The results obtained from the 3D modeling show that the maximum displacements of the eardrum are in the frequency range of [1700, 2600] Hz. A peak on the sound pressure gain results around 3000 Hz was observed. The change in the damping coefficient d has a strong influence on the displacement of the eardrum. A grow of the acoustic pressure honest the eardrum compared to that recorded at the entrance of the auditory canal is noted. These results were validated by the results of experiments carried out in vivo.

MODELING MASS-SPRING-DAMPER SYSTEM USING SCILAB

Modeling a system means developing a mathematical representation to simulate certain properties observed in real systems. These systems can range from a car suspension to the most complex robotics. In modern mechanical engineering, it is routine to model a physical dynamic system as a set of differential equations that will later be simulated using a computer. This systems can range from a car suspension to the most complex robotics. Use software for numerical analysis and qualitative analysis of dynamic systems in engineering and applied science education simplifies the analysis and analysis. In this paper, the dynamic behavior of massspring-damper system has been studied by mathematical equations in free software Scilab. Scilab is free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications. The resulting equations represent a generalization of the classical mass-spring-damper model; the proposed representation can be used to describe a wide variety of systems, which had not been addressed due to the limitations of the classical calculus. Software implementation of the model and calculations are performed in the Scilab environment. The massive use of software generated a great business. Although the reliability and effectiveness of commercial software is undeniable, their cost is not available to most researchers, students, and public universities. This paper clearly shows that Scilab is capable of handling such uncertainties with little effort. It should be noted that this paper is written with the intention of disseminate the ideas of how to use Scilab for teaching theory modelling, dynamic of machine or performing related research works.

Higher prices for specialty carbon blacks plus surcharges for European products

In this paper, we have applied an efficient shifted second kind Chebyshev wavelet method (S2KCWM) to vibrating dynamical models arising in mechanical systems such as vibration of circular membrane, damped spring mass system and ship oscillatory motions. To the best of our knowledge, until now there is no rigorous wavelet based solution has been reported for the vibrating dynamical models. The power of the manageable method is confirmed. The wavelet solutions are compared with numerical simulations by MATLAB. Good agreement between the solutions is presented in this paper. Some numerical examples are given to demonstrate the validity and applicability of the proposed method. Moreover the use of Chebyshev wavelets is found to be simple, efficient, flexible, convenient, less computation costs and computationally attractive.

Vortex-induced vibration of a sphere close to or piercing a free surface

Vortex-induced vibration (VIV) of an elastically mounted sphere placed close to or piercing a free surface (FS) was investigated numerically. The submergence depth ( $h$ ) was systematically varied between $1$ and $-$ 0.75 sphere diameters ( $D$ ) and the response simulated over the reduced velocity range $U^*\in [3.5,14]$ . The incompressible flow was coupled with the sphere motion modelled by a spring–mass–damper system, treating the free-surface boundary as a slip wall. In line with the previous experimental findings, as the submergence depth was decreased from $h^* = h/D =1$ , the maximum response amplitude of the fully submerged sphere decreased; however, as the sphere pierced the FS, the amplitude increased until $h^* = -0.375$ , and then decreased beyond that point. The fluctuating components of the lift and drag coefficients also followed the same pattern. The variation of the near-wake vortex dynamics over this submergence range was examined in detail to understand the effects of $h^*$ on the VIV response. It was found that $h^* = 1$ is a critical submergence depth, beyond which, as $h^*$ is decreased, the vortical structures in the wake vary significantly. For a fully submerged sphere, the influence of the stress-free condition on the VIV response was dominant over the kinematic constraint preventing flow through the surface. For piercing sphere cases, two previously unseen vortical recirculations were formed behind the sphere near times of maximal displacement, enhancing the VIV response. These were strongest at $h^* = -0.375$ , and much weaker for small submergence depths, explaining the observed response-amplitude variation.

Performance Evaluation of Pole Placement and Linear Quadratic Regulator Strategies Designed for Mass-Spring-Damper System Based on Simulated Annealing and Ant Colony Optimization

This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab software has been used for simulations and performance analysis. The results show the superiority of the state feedback based on the LQR controller in improving the system stability, reducing settling time, and reducing maximum overshoot. Furthermore, AC optimization shows significant advantages for optimizing the parameters of PP and LQR and reducing the fitness value in comparison with SA optimization

Study the Effects of Mass in a Simple Damped Harmonic Motion of a Mass-spring System Using Simulation

The effect of mass on the behavior of oscillatory systems in a damped spring-mass system was studied using simulation. It was found that the mass affects the amplitude and displacement in the case of an undamped oscillatory system. In critically damped systems, the mass affects the displacement exponentially, and the system doesn’t oscillate. In the case of an overdamped system, there is also no oscillatory motion, and an increase in the mass was not affected, since the system gets to rest very quickly. The study shows that simulation can be a very helpful tool to study the behavior of oscillatory physical systems. Keywords: Simple harmonic motion damped mass-Spring system, simulation

Fatigue Damage Monitoring of Wind Turbine Blades by Using the Kalman Filter

Fatigue damage accumulation needs to be monitored for extending the lifetime of horizontal axis wind turbines. To monitor accumulation of fatigue damage, this paper proposes a blade load and fatigue damage monitoring system consisting of physics models coupled with the Kalman filter (KF). The proposed monitoring system estimates bending moment distribution along the blade as a time series from 1 Hz data collected by a supervisory control and data acquisition (SCADA) system and from 20 Hz strain sensor data collected at the blade root. Static load is computed on the basis of blade element and momentum theory from SCADA data, whereas dynamic response of the blade is computed by assuming a mass–spring–damper system. The KF corrects the estimated moment distribution with moment measured at the blade root. The monitoring system is demonstrated and validated by installing it on a 2 MW floating downwind turbine and estimating strain and fatigue damage at the medium span position of the blades, where a strain sensor is installed. The validation results show that strain wave forms and fatigue damage estimated by the monitoring system with the KF are consistent with those computed from the strain measurement with sufficient accuracy for structural health monitoring.

An in-silico study of the effect of non-linear skin dynamics on skin-mounted accelerometer inference of skull motion

Accurate and precise analysis of head impact telemetry data is important for development of biomechanical models and methodologies to decrease the risk of traumatic brain injury. Systematic review suggests that much existing data lacks verification. Soft tissue artefact is a common problem that is not frequently addressed. This paper outlines a method of modelling the coupled, non-linear, skull-skin-sensor system. The model is based on a second order underdamped spring mass damper system that incorporates non-linear values to account for the complex dynamic nature of skin. MATLAB was used to simulate the estimated movement of a sensor mounted to the skin relative to measurements collected via a mouthguard sensor. The non-linear elastic and damping models were developed from descriptions in literature. The model assumed a sensor of 8 g, mounted behind the ear. Results were compared to a typical linear system. In small impacts, the linear and non-linear models provided similar accelerations to the skull. However, in large impacts, the acceleration of the sensor was estimated to be 158% greater than the skull acceleration when modelled non-linearly, while a linear model showed only a 0.7% increase. This implies that for small impacts, the nonlinearity of skin-skull dynamics is not an important characteristic for modelling. However, in large impacts, the non-linearity of the skin-skull dynamic can lead to drastic over-estimates of skull acceleration when using skin mounted accelerometers. In BriefThe system of an accelerometric sensor mounted to the skin is often used to assess the accelerations experienced by athletes during impacts. By developing a non-linear model of the skull-skin-sensor model, the importance of accounting for the non-linear nature of skin while taking telemetry measurements of head acceleration during impact is demonstrated.

Estimating the forcing function in a mechanical system by an inverse calibration method

This article proposes and demonstrates a calibration-based integral formulation for resolving the forcing function in a mass–spring–damper system, given either displacement or acceleration data. The proposed method is novel in the context of vibrations, being thoroughly studied in the field of heat transfer. The approach can be expanded and generalized further to multi-variable systems associated with machine parts, vehicle suspensions, translational and rotational systems, gear systems, etc. when mathematically described by a system of constant property, linear, time-invariant ordinary differential equations. The analytic approach and subsequent numerical reconstruction of the forcing function is based on resolving a parameter-free inverse formulation for the equation(s) of motion. The calibration approach is formulated in the frequency domain and takes advantage of several observations produced by the dimensionality reduction leading to an algebratized system involving an input–output relationship and a transfer function possessing all the system parameters. The transfer function is eliminated in lieu of experimental data, from a calibration effort, thus leading to a reduction of systematic errors. These parameter-free, reduced systematic error aspects are the distinct and novel advantages of the proposed method. A first-kind Volterra integral equation is formed containing only the unknown forcing function and experimental data. As with all ill-posed problems, regularization must be introduced for system stabilization. A future-time technique is instituted for forming a family of predictions based on the chosen regularization parameter. The optimal regularization parameter is estimated using a combination of phase–plane analysis and cross-correlation principles. Finally, a numerical simulation is performed verifying the proposed approach.

Nonlinear feedback self-excitation of modal oscillations in a class of under-actuated two degrees-of-freedom mechanical systems

Recently, scientists have utilized self-excited oscillations in many mechanical and micromechanical applications and accordingly, several experimental and theoretical research activities have been undertaken with the objective of artificially inducing self-excited oscillation in mechanical systems. This paper considers some theoretical aspects of generation of self-excited oscillation in a two degrees-of-freedom under-actuated spring–mass–damper system by centralized nonlinear feedback. The control force depends on the response of both masses. The proposed control law is slightly general in nature as it entails both collocated and non-collocated control as special cases. The response of the nonlinear feedback control is studied with the help of the method of averaging. The present study shows that by appropriately selecting the control gains it is possible to excite the desired mode(s) of oscillation irrespective of initial conditions. Even it is possible to excite dual mode oscillation having the characteristics of quasiperiodic oscillations. The theoretical analysis of the dynamics of the system with the control is validated by simulation results, performed in MATLAB Simulink.

Supplemental state observer‐based sliding mode control for a dynamic system

A supplemental state observer-based sliding mode control (SSOBSMC) for a dynamic system is proposed in this paper. First, a supplemental state vector is formulated including system output and supplemental output. A supplemental state observer (SSOB) is proposed to estimate the unavailable states. Furthermore, the SSOBSMC consisting of SSOB and sliding mode control (SMC) is proposed to perform state estimation and robust tracking control for the dynamic system with some unavailable states. To demonstrate the application of the proposed methods, a mass-spring-damper (MSD) system is used as an application example to perform numerically. From the simulation results, the SSOB shows a good ability for state estimation, while the SSOBSMC simultaneously demonstrates accuracy in state estimation ability as well as a robust tracking control performance for the non-linear MSD system. The major contributions of this paper are the proposed SSOB that can accurately estimate the unavailable states for the non-linear dynamic system with time-varying disturbances; and the SSOBSMC, which simultaneously displays accuracy in state estimation ability and robust tracking control performance.

Analysis of Forces generated in Human Body segments for Real time Space flight

Human body modelling for a space travel is a significant task to be considered for analyzing the forces generated on the human body segments. During the flight from earths atmosphere due to high escape velocity and acceleration, huge reaction forces will be generated on body segments which are beyond human capacitance. Recent studies evaluated the forces generated in various body segments by equipping external sensor vest or strips around the body parts where the application is limited for several on ground operations like hopping, sitting etc. and few studies analyzed the theoretical forces by modelling the human body as a second order spring mass damper system. The main objective of this work is to analyze the forces experienced by the human body segments for like Head, Neck, Upper Torso, Central Torso and Lower Torso for real time space flight data. The analysis is done on the anthropometric data of 50th percentile male US citizens available in literature by considering the human body as a second order spring mass damper system and the real time space flight parameters are taken from STS-121 space shuttle launched from Kennedy Space centre on July 4th 2006. The obtained resultant forces are plotted against the time of flight and it is observed that high forces are generated on Central Torso compared to remaining body parts and are varying with altitude of the vehicle.

Structural controllability of networked relative coupling systems

This paper studies the controllability of networked relative coupling systems (NRCSs), in which subsystems are of fixed high-order linear dynamics and coupled through relative variables depending on their neighbors, from a structural perspective. The purpose is to explore conditions for subsystem dynamics and network topologies under which for almost all weights of the subsystem interaction links, the corresponding numerical NRCSs are controllable, which is called structurally controllable. Three types of subsystem interaction fashions are considered: (1) each subsystem is single-input–single-output (SISO), (2) each subsystem is multiple-input–multiple-output (MIMO), and the weights for all channels between two subsystems are identical, and (3) each subsystem is MIMO, but different channels between two subsystems can be weighted differently. We show that all parameter-dependent modes of the NRCSs are generically controllable under some necessary connectivity conditions. We then derive necessary and/or sufficient conditions for structural controllability depending on subsystem dynamics and network topologies’ connectivity in a decoupled form for all the three interaction fashions. We also extend our results to handle certain subsystem heterogeneities and demonstrate their direct applications on some practical systems, including the mass–spring–damper system and the power network.

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Displacement amplification enhances rapid actuation of electromagnetic actuators: Drive with load of spring–mass–damper system

Displacement amplification affects the response time of actuators using electromagnetic attractive force. Although this force is widely used for actuation, it exhibits a tradeoff between thrust and stroke, because thrust depends on the gap between the electromagnet and armature, and increasing the gap (stroke) drastically degrades thrust. Displacement amplification has been proposed for actuators to mitigate this tradeoff by magnifying the gap motion to efficiently use large forces in small gaps. Although such an actuator is applicable to submillimeter stroke and fast motions, dynamic characteristics have not been studied enough for designing in practical usages. This paper reveals the effect of displacement amplification on the actuation time through both a simple dynamic model for basic theoretical discussion and a simulation including damping factor to gain a more practical perspective. We also propose a test bench to verify the analyses and compare experimental and simulation results. The experiments confirm shorter actuation time and thus improved performance by combining electromagnetic attractive force and displacement amplification with spring–mass–damper as load. In addition, the experimental and simulation results show that only characteristics of the magnetic circuit should be considered for deciding the amplification ratio in designing DAEAs.

Solution of the symmetric band partial inverse eigenvalue problem for the damped mass spring system

ABSTRACT The structured partial quadratic inverse eigenvalue problem (SPQIEP) is to construct the structured quadratic matrix polynomial using the partial eigendata. The structures arising in physical applications include symmetry, band (tridiagonal, diagonal, pentagonal) etc. The construction of the structured matrix polynomial is the most difficult aspect of this problem and the research on structured inverse eigenvalue problem is rare. In this paper, the symmetric band partial quadratic inverse eigenvalue problem (SBPQIEP) for the damped mass spring system is considered. This problem concerns in finding the symmetric band matrices , and C with bandwidth p from m ( ) prescribed eigenpairs so that the corresponding quadratic matrix polynomial has the given eigenpairs as its eigenvalues and eigenvectors. In general, SBPQIEP is very hard to solve due to the additional band structure constraint. We propose a novel method, based on the matrix-vectorization and Kronecker product of matrices for solving this problem. Furthermore, explicit expressions for general solutions are presented. Numerical experiments on a spring mass problem are presented to illustrate the applicability and the practical usefulness of the proposed method.

2D modeling of the human ear using the equivalent mechanical impedance

Several mass–spring–damper models have been developed to study the response of the human body parts. In such models, the lumped elements represent the mass of different body parts, and stiffness and damping properties of various tissues. The aim of this research is to develop a 2D axisymmetric model to simulate the motion of the human tympanic membrane. In this contribution we develop our model using a Comsol Multiphysics software to construct a 2D axisymmetric objects, the acoustic structure interaction between the ear canal (field of propagation of the acoustic wave) and the structure of ear (skin, cartilage, bone, tympanic membrane) was solved using finite elements analysis (FEA). A number of studies have investigated the motion of the human tympanic membrane attached to the ossicular chain and the middle ear cavity. In our model, the tympanic annular is assumed to be fixed and the loading of what comes behind the tympanic membrane as the ossicular chain, while middle ear cavity and cochlea were replaced by the equivalent mechanical impedance of a spring mass damper system. The obtained results demonstrate that the maximum displacements of the umbo are obtained at the frequency range of 0.9–2.6 kHz, the sound pressure gain had the shape of peak with a maximum at 2–3 kHz frequency range. The umbo displacement depends on the damping coefficient d, and the sound pressure at the tympanic membrane was enhanced compared to that at the ear canal entrance.

A new numeric–symbolic procedure for variational iteration method with application to the free vibration of generalized multi-span Timoshenko beam

In this article, a novel approach is introduced for the free vibration analysis of beams based upon the variational iteration method. The new approach uses a numeric–symbolic procedure that tackles the problem of increased execution time involved in symbolic integrations. This drawback is usually encountered in solving complicated free vibration problems such as stepped beams connected to lumped parameter subsystems. The proposed procedure is applied for free vibration analysis of a generalized multi-span Timoshenko beam connected to multiple lumped subsystems. Each subsystem is represented by a two-degree-of-freedom spring–mass–damper system. Several verification examples are presented where the results of the proposed numeric–symbolic variational iteration method are compared with the conventional symbolic approach symbolic variational iteration method in terms of execution time. Special attention is given to the verification of the new results against finite element modeling results and exact solutions where possible. Based on the presented results, it is shown that the new numeric–symbolic variational iteration method procedure efficiently reduces the time required for solving the free vibration problem while maintaining the high accuracy and robustness of the variational iteration method. The new procedure presented here may facilitate solving some engineering problems in which the conventional symbolic approach usually fails to solve owing to extensive memory requirements. The study contributes toward further improvements of the variational iteration method and its application to sophisticated dynamic systems.

Surface Prediction for Spatial Augmented Reality Applications

In spatial augmented reality applications, incorrect projection mapping may occur when projecting images onto moving non-rigid surfaces. This may detract from the user experience, as the image may not be perceived as originally intended. This is especially apparent when using low-cost projectors and cameras or when surfaces are moving quickly. In this paper, an algorithm is developed which predicts the motion of a non-rigid surface, so that when an image is being projected onto the surface, the projection “matches” the surface shape, while using low-cost equipment. Using an interconnected mass–spring–damper system to model the surface, the surface position is predicted using a Kalman filter-based algorithm, which also compensates for the processing delays and fast-moving surfaces. To accurately model real-world materials, the mass–spring system parameters are found using a system identification approach. When the prediction algorithm is implemented experimentally, in real-time, the results show convergent results in the sense that the surface predictions converge to the measured position of a non-rigid surface. The error results show that the algorithm is both accurate and robust and can currently be applied in spatial augmented reality applications.