Mass-spring-damper Research Articles

Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact

The present paper concerns low-velocity impact for nanocomposite sandwich truncated conical shells (NSTCS). Graphene platelets (GPLs)-reinforced as core layer is covered through magnetostrictive layers as face sheets. The supposed impacts are applied over the above face layer and further, the interaction among impactors as well as NSTCS is assumed utilizing novel equivalent three-degree-of-freedom (TDOF) with spring–mass–damper (SMD) model. For modeling the core layer and face sheets mathematically, higher-order shear deformation theory (HSDT) besides first-order shear deformation or Mindlin theory (FSDT) is utilized, respectively. To presume this sandwich structure much more realistic, the Kelvin–Voigt model will be used. According to Hamilton’s principle concerning continuity boundary conditions, the governing equations are obtained. Utilizing differential cubature (DC) as well as Bolotin procedures, the governing equations will be solved. In this work, different variables covering various boundary edges, Controller, cone’s semi vertex angle, damping,​ feedback gain, the proportion of core to face sheets thickness, dispersion kinds of GPLs and their volume percent, and their effects on low-velocity impact analysis of the sandwich structure will be investigated. To indicate the accuracy of applied theories as well as methods. the results are collated with another paper. It is found that increment of GPLs volume percent leads to rise the deflection as well as maximum contact force whereas contact duration is reduced.

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

Robust adaptive finite-time stabilization control for a class of nonlinear switched systems based on finite-time disturbance observer

The problem of adaptive global finite-time stabilization control for a class of nonlinear switched systems in the presence of external perturbations and arbitrary switchings has been addressed in this research study. The proposed scheme has been designed based on a finite-time estimation technique in which during the control procedure, unknown imposed perturbations are accurately estimated by means of the designed finite-time disturbance observer (FTDO). Due to the exact estimation of the external disturbances within a given finite time, the encountered complications and adversities from loss of information in the Lyapunov parameter estimation (LPE) methods have been solved which are caused by the persistent switchings in the system. Furthermore, a new solution for the problem of chattering phenomenon in nonlinear switched systems has been presented by utilizing the designed FTDO, which can counteract the malfunctioning responses of the system caused by external disturbances and unmodeled dynamics. In this paper, an acknowledged class of nonlinear switched systems has been taken into account which is in the general form of canonical structure. In addition, the established design strategy is formulated for the control of perturbed nonlinear switched systems with one and only input and assures that the system states through the finite-time convergence characteristic, reach the equilibrium point of origin. Finally, numerical simulations are carried out on a mass-spring-damper (MSD) dynamical system to indicate advantages and superior efficiency of the suggested method.

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.

The influence of human motion state on human-structure interaction

Under pedestrian load, significant vibration and comfort problems are easy to arise for large-span low-frequency structures so that human-structure interaction should be considered in the design. However, different human motion states have different human modal parameters, which makes the design more difficult. The Spring-Mass-Damper (SMD) model is used to conduct numerical simulation experiments on 6 box beams with different fundamental frequencies in 4 different human motion states, based on which the dynamic characteristics of the structure under 30 working conditions are compared and analyzed. It is recommended to use the modal parameters of the standing human body in the vibration comfort design, and use the modal parameters of the human body at normal walking speed for the design of the low-frequency structure.

Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers

Vortex-induced vibrations are one of the major factors in fatigue failure of power transmission lines and can be mitigated using vibration absorbers in the form of Stockbridge dampers. Since power transmission lines play an important role in modern infrastructure, a thorough understanding of the nonlinear dynamical interactions between conductors, dampers, and wind forces is crucial. Although different nonlinear models exist for conductor vibration with attached dampers or under wind force, no work combines all these nonlinearities in a single model and examines the dynamics of the conductor along with dampers. In an attempt to fill this gap, this work combines the nonlinearities from the mid-plane stretching of the conductor, equivalent cubic stiffness of the Stockbridge damper, and fluctuating lift force modeled as a Van der Pol oscillator in a single model to investigate the nonlinear vortex-induced vibrations. In this work, the conductor is modeled as a simply supported beam and the Stockbridge damper as a mass–spring–damper–mass system with a combination of cubic and linear stiffness. The governing equations of motion are solved analytically using the method of multiple scales for the case of primary resonance between the fluctuating lift-force and conductor. Analytical findings are further validated by comparing against the numerical integration of a reduced-order system, and the results show an excellent match. The analysis is extended by conducting a parametric study to investigate the effect of different system parameters on the frequency response curves. These findings are promising and further provide a direction to design an optimal vibration absorber.

Design and simulation of point absorber wave energy converter

The paper aims to design and simulation of a wave energy harvesting system commonly known as point absorber for Ennore port located in the coastal area of Chennai, India. The geographical condition of India, which is surrounded by the three sides with seas and ocean, has enormous opportunity for power production through wave energy harvesting system. The wave energy converter device is a two-body floating system and its both parts are connected by power take-off unit which acts as spring mass damper system. In this paper, the hydrodynamic diffraction, stability analysis, frequency, and time response analysis is carried out on ansys-aqwa. The numerical results are compared with the results obtained from the similar experiments for validation of CFD solver. Effects of the properties featuring wave characteristics including wave height and wave period of Ennore port on the energy conversion, Froude-Krylov and diffraction force, response amplitude operator (RAO) are studied. Based on the study, float diameter, draft, geometry, and varying damping coefficient for power generation are optimized. Finally, the optimally designed point absorber is simulated as per Indian ocean energy harvesting standard and mass of the system, heave dimension, diffraction forces, and pressure variations are computed.

Post-capture control of a tumbling space debris via tether tension

The Earth orbit is in a serious predicament caused by millions of space debris, and operational spacecraft are facing a risk of collision with those objects. The net capturing method has been considered as one of the most promising method to remove space debris objects. However, a tumbling target has a risk to slide toward the service satellite and collide with it after captured. To avoid this from happening, a control method must be designed for the combined system. This paper first presents the necessity of controlling the combined system right after the net capture. In another respect, the existing configurations of the combined system always include an additional mechanism to de-tumble the target which will dramatically complicate the design. Instead of using an additional mechanism, a novel control strategy is proposed to de-tumble the target only via the tether connecting to the service satellite and the target. Dynamics of the system is analyzed and flexibility of the tether is considered by employing the mass–spring–damper model. The control method includes three control modes to actively control the pose of the service satellite which significantly impacts the tether tension so that the target can be maintained a safe distance to the service satellite. Numerical simulations demonstrate that the proposed control strategy can be utilized to effectively de-tumble the target within a short period of time and mitigate the risk of collision with the service satellite.

Design of a Switching PID Controller for a Magnetically Actuated Mass Spring Damper

Design of a Switching PID Controller for a Magnetically Actuated Mass Spring Damper

Tunable Wave Energy Converter Using Variable Inertia Flywheel

Axisymmetric heaving point absorbers are popular wave energy converters because of their easy deployment and insensitivity to incident wave directions. These devices are designed ideally to resonate with the incident wave to achieve high power output. However, as the device resonant frequency deviates from the dominant frequency of ever-changing irregular waves, the performance drops drastically. To solve this problem and as a complement to existing measures, we propose a mechanism, named variable inertia flywheel, to directly manipulate the equivalent mass of the point absorber, thus altering the system resonance frequency and power absorption bandwidth. We use a flywheel with symmetrically placed mass spring dampers in a ballscrew-based power take-off system. With its variable inertia and mass amplification effect, we can economically and dynamically adapt the system equivalent mass and corresponding parameters with small mass spring dampers. Apart from the passive configuration, we also propose the semi-active and active configurations to further enhance the performance and broaden the functionality scope of the proposed power take-off system. Numerical studies have revealed the dynamics of variable inertia flywheel, and have validated its adaptivity to varying wave conditions and its potential for increasing power output of point absorbers in both regular and irregular waves.

Mass–spring–damper modeling and stability analysis of type-4 wind turbines connected into asymmetrical weak AC grid

Nowadays, grid codes of various countries have required that grid-connected wind turbines should possess the capability of negative sequence current control during asymmetrical grid condition. As for type-4 wind turbines, however, due to the existence of the negative sequence voltage, the interaction between the dc-link voltage control (DVC) and phase locked loop (PLL) of the grid-side converter is likely to cause small-signal instability when the impedance of the AC grid cannot be ignored. As a specific contribution, the paper establishes a detailed four degree-of-freedom mass–spring–damper model considering the couplings between the positive and negative sequence subsystems based on the theory of mechanical vibration, so as to characterize the modal interaction between the DVC and PLL. The model can be used to evaluate the influence of factors such as negative sequence voltage, grid impedance and control parameters on the system stability. Simulation studies were finally performed to verify the correctness of the proposed model and the analysis.

Dynamic characteristic of combined viscous and Coulomb damping under varying nature of material and coefficient of friction

Practically, most systems possess characteristics of both viscous damping and Coulomb damping. A model of combined viscous and Coulomb damping is analysed while taking into account the different nature of materials. Different material contact surfaces exhibit distinct coefficients of friction which has an effect on the displacement response of a vibratory system. The study involves analysis of a linear spring-mass damper system by varying its material parameters, taking frictional force into account. The response in terms of maximum displacement amplitude is examined while varying the values of coefficient of friction. Material parameters such as natural frequency (varied by mass and stiffness each), damping ratio and coefficient of friction are studied. The research is conducted using theory of combined viscous and dry friction damping and graphical observations are made to study the response in view of different surface contacts.

Robust $\mathcal {H}_{\infty }$-Based Control for Uncertain Stochastic Fuzzy Switched Time-Delay Systems via Integral Sliding Mode Strategy

In this article, we investigate the problems of robust exponential stabilization in mean square and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -based integral sliding mode controller design for uncertain stochastic Takagi–Sugeno (T-S) fuzzy switched time-delay systems with both matched and unmatched uncertainties under synchronous switching and asynchronous switching, respectively. In these systems, the control input is dependent on a switching signal. Under synchronous switching and asynchronous switching, sufficient conditions are developed to guarantee that the resulting closed-loop systems are robustly exponentially stable in mean square with a prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> -performance, respectively. The integral sliding mode surfaces and the sliding mode controllers are designed for the underlying systems under synchronous switching and asynchronous switching, respectively. By two examples stemming from the mass–spring–damper model and the single-link robot arm model under stochastic perturbation, the effectiveness of the results obtained is verified.

Investigation of transverse galloping in the presence of structural nonlinearities: theory and experiment

We formulate and experimentally validate a theoretical reduced-order model for the transverse galloping of nonlinear structures, namely a pair of identical, parallel-oriented cantilever beams whose free ends are attached to square prisms. We derive the structural nonlinearities from (a) a single-mode approximation of the nonlinear (truncated at cubic order) equation of motion, calculated for conservative cantilever beams augmented by a non-conservative aerodynamic force acting on a prism; and (b) phenomenological linear, quadratic, and cubic damping forces. We estimate the coefficients of the damping forces from the ring-down responses of the structures in still air. We analyze the deterministic dynamics of transverse galloping that stem from the aerodynamic force of the quasi-steady theory, and the stochastic effect of spectral line broadening that stem from turbulence-induced random fluctuations. Our findings clearly show that standard nonlinear macroscopic structures exhibit considerably different steady-state response curves than the universal curve of Parkinson obtained for linear mass–spring–damper structures. Importantly, the amplitudes of the oscillations are attenuated at high upstream velocities due to nonlinear damping, while the spectral line broadens due to turbulence-induced random fluctuations and an amplitude-to-phase noise conversion, which lowers the quality of the self-sustained oscillations. These two phenomena should be considered in the design of efficient transverse galloping-based energy harvesters—a rapidly growing field of research.

Numerical investigation of railway transition zones stiffened with auxiliary rails

Culverts and bridges are the most common areas on railway lines where abrupt changes of track stiffness can occur. Using auxiliary rails in the transition zone is one option for gradually increasing track stiffness. The study reported in this paper investigated this issue by means of finite-element modelling. A ballasted track with a concrete culvert on the Tehran–Isfahan high-speed railway line in Iran was modelled and the effect of installing auxiliary rails in the transition zone was investigated. The ballasted track and its components – including railpads, ballast and subgrade – were modelled as a series of mass–spring–damper systems, while the sleepers and culvert were simulated using Euler–Bernoulli beam elements. The dynamic behaviour of the track and its components was investigated by simulating loads moving at different speeds. The results indicated there was a reduced variation in rail deflections, track accelerations and railpad forces, demonstrating that auxiliary rails improve the dynamic performance and behaviour of transition zones.