Spring Damper System Research Articles

Hydrokinetic energy conversion by two rough tandem-cylinders in flow induced motions: Effect of spacing and stiffness

Flow Induced Motions (FIMs) of rigid circular cylinders, and particularly VIV (Vortex Induced Vibrations) and galloping, are induced by alternating lift. The VIVACE (VIV for Aquatic Clean Energy) Converter uses single or multiple cylinders, in tandem, on elastic end-supports, in synergistic FIM, to convert MHK energy to electricity. Selectively distributed surface roughness is applied to enhance FIM and increase efficiency. In this paper, two cylinders are used in tandem with center-to-center spacing of 1.57, 2.0 and 2.57 diameters, harnessing damping ratio 0.00<ζ < 0.24, for Reynolds number 30,000 ≤ Re ≤ 120,000. The virtual spring-damping system Vck in the Marine Renewable Energy Laboratory (MRELab) enables embedded computer-controlled change of viscous-damping and spring-stiffness for fast and mathematically correct oscillator realization, without including the hydrodynamic force in the closed control loop. Experimental results for oscillatory response, energy harvesting, and efficiency are presented and the envelope of optimal power is derived. All the experiments were conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) For the tested cylinder spacing, two cylinders harness power is between 2.56 and 13.49 times the power of a single cylinder, the efficiency of two cylinders is between 2.0 and 6.68 of a single cylinder. (2) The MHK power harnessed by the upstream cylinder is increased by up to 100%, affected by the downstream cylinder. (3) The MHK power harnessed by the downstream cylinder and its FIM are affected to a lesser extent by the interaction. (4) VIVACE can harness energy from flows as slow as 0.4 m/s with no upper limit in flow velocity. (5) Close spacing and high spring stiffness yield highest harnessed power. (6) The optimal harnessed power shifts to softer springs as spacing increases.

Parameter sensitivity of an in-plane gap closing electrostatic energy harvester with end-stop impacts

Conventionally modeled as spring–damper system, the end-stops in vibration energy harvesters set a limit to the displacement of the proof mass at sufficiently high excitation levels. In some studies, it is seen that the end-stop parameters needed adjustment to fit the simulations to the measurements at particular operating condition. In this article, the discrepancy between the simulation and measurement results on varying the operating condition is investigated in detail. A check on sensitivity of an electrostatic in-plane gap closing energy harvester to the parameters end-stop stiffness, end-stop damping, and end-stop position at various biases and excitation levels is performed. The simulations at 3-V bias and root mean square (RMS) acceleration amplitude 0.6 g show a remarkable variation of 30 Hz in up-sweep jump-down frequency on varying end-stop position by 0.12 µm. The simulation results also show a significant increase in sensitivity of up-sweep jump-down frequency to end-stop damping on increasing excitation level at fixed bias. The article also discusses the sensitivity in jump frequencies to perturbations in the excitation signal due to the presence of noise, where the jump-down frequency becomes smaller as the noise level increases. The trajectories studied at 8-V bias and RMS acceleration amplitude 0.6 g with different end-stop parameters show a strong influence of the end-stop model parameters on the motion of the proof mass. A lumped model of the device is fitted to the measurements for a whole range of operating conditions with one fixed set of model parameter, where asymmetric end-stop positions and their effect on the device behavior are shown to be crucial. The results presented in this article show that in order to reproduce and analyze the measured behavior of the harvester over a range of operating conditions, very fine details in the model are significant.

Damped Vibrations of Hydraulic Cylinder with a Spring-damper System in Supports

The description of the damped vibrations of hydraulic cylinder has been presented in this paper. The dissipation of vibration energy was caused by different kinds of damping on vibrations of hydraulic cylinder. Damping in adopted model is a result, of taken into account internal damping of viscoelastic material of beams that modelled the system, external viscous damping and constructional damping of supports. In this paper, the problem of transverse and longitudinal damped vibration of hydraulic cylinder was formulated and solved. The influence on the damped vibration frequency and the degree of vibration amplitude decay of damping coefficient and spring rigidity coefficient were presented.

Basilar Membrane Vibration in Time Domain Predicted by Fluid–Structure Interaction Model in Pre- and Post-stapedotomy State

A three dimensional, Fluid–Structure Interaction model of the uncoiled cochlea was built and calculated in the time domain in pre- and post-stapedotomy states. The model predicted the basilar membrane vibration amplitude and pressure waves magnitude in both states.Additionally, the model was analyzed in terms of the dynamics response of the cochlea. It was show, using Short Time Fourier Trnsform, that the sounds, thus hearing, may be unsteady phenomenas. The results of the FSI cochlea model were compared with one dimensional mass–spring–damper system.

Output feedback fault-tolerant control by a set-theoretic description of T–S fuzzy systems

This paper is concerned with the observer-based output feedback fault-tolerant control problem for T–S fuzzy systems. By constructing a set-theoretic description of fuzzy systems, the equivalence class theory in set theory is applied for designing observer and controller for less conservative results. Firstly, we designed the observer to get the information of the actuator faults in the system. Then, we use this information to design the fault-tolerant controller to compensate for the effect of faults and guarantee stability of the system. Finally, a simple nonlinear mass–spring–damper system is presented to illustrate the effectiveness of the proposed approach.

Modeling and dynamic behavior analysis of a coupled multi-cable double drum winding hoister with flexible guides

In this paper, a comprehensive model is derived to analyze the dynamic behavior of a multi-cable double drum winding mining hoister with flexible guides by using Hamilton principle. Each cable which consists of an inclined section and a varying length vertical section is modeled as an axially moving string with coupled transverse-longitudinal nonlinear vibration. The coupling between different cables is described through the dynamic and kinematic equations of the conveyance. The time-varying equal moment of inertia of drums is obtained by considering the varying mass of cables winding on drums. The model of flexible guides which was always approximated as a spring-damping system is modeled as a tensioned string with fixed ends in this paper. The dynamic characteristics of flexible guides are considered in the interaction between the conveyance and the flexible guides via calculating the lateral displacement of the conveyance corner and reaction forces from flexible guides. The dynamic behavior of the multi-cable double drum winding hoister with unbalance factors, the conveyance eccentricity and the drum radius inconformity, are analyzed by simulation. Some design principles are proposed to restrict the inconformity of dynamic tension between cables.

Twisting sliding mode control with adaptation: Lyapunov design, methodology and application

A novel adaptive-gain twisting controller that is robust to the bounded disturbances with the unknown boundaries is proposed. The control algorithm is derived using the Lyapunov function technique. It is shown that an ideal or real second order sliding mode is established, and the adaptation algorithm does not overestimate the control gain. The efficacy of the proposed adaptive twisting control is experimentally verified on a mass–spring–damper system.

Nonlinear piecewise restoring force in hydrokinetic power conversion using flow induced motions of single cylinder

Flow Induced Motions (FIMs) of a single, rigid, circular cylinder with piecewise continuous restoring force are investigated for Reynolds number 24,000≤Re≤120,000 with damping, and different piecewise functions as parameters. Selective roughness is applied to enhance FIM and increase the hydrokinetic energy captured by the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) Converter at higher Reynolds numbers. The second generation of virtual spring-damping system Vck, developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of viscous-damping and spring-stiffness for fast and precise oscillator modeling. Experimental results for amplitude response, frequency response, energy harvesting, and efficiency are presented and discussed. All experiments were conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinear piecewise spring Converter can harness energy from flows as slow as 0.275m/s with no upper limit. (2) In galloping, the nonlinear spring Converter has up to 76% better performance than its linear spring counterpart. (3) The FIM response is predominantly periodic for all nonlinear spring functions used. (4) Optimal power harnessing is achieved by changing the nonlinear piecewise spring function and the linear viscous damping. (5) VIVACE exhibits local maxima in power conversion at the end of the upper branch in VIV and the highest velocity reached in galloping. (6) The efficiency optima though are at the beginning of the VIV initial branch and at the beginning of galloping.

Simplifications in modelling of dynamical response of coupled electro-mechanical system

The choice of a most suitable model of an electro-mechanical system depends on many variables, such as a scale of the system, type and frequency range of its operation, or power requirements. The article focuses on the model of the electromagnetic element used in passive regime (no feedback loops are assumed) and a general lumped parameter model (a conventional mass–spring–damper system coupled to an electric circuit consisting of a resistance, an inductance and a capacitance) is compared with its simplified version, where the full RLC circuit is replaced with its RL simplification, i.e. the capacitance of the electric system is neglected and just its inductance and the resistance are considered. From the comparison of dynamical responses of these systems, the range of applicability of a simplified model is assessed for free as well as forced vibration.

Subspace identification with constraints on the impulse response

ABSTRACTSubspace identification methods may produce unreliable model estimates when a small number of noisy measurements are available. In such cases, the accuracy of the estimated parameters can be improved by using prior knowledge about the system. The prior knowledge considered in this paper is constraints on the impulse response. It is motivated by the availability of information about the steady-state gain, overshoot and rise time of the system, which in turn can be expressed as constraints on the impulse response. The method proposed has two steps: (1) estimation of the impulse response with linear equality and inequality constraints, and (2) realisation of the estimated impulse response. The problem on Step 1 is shown to be a convex quadratic programming problem. In the case of prior knowledge expressed as equality constraints, the problem on Step 1 admits a closed-form solution. In the general case of equality and inequality constraints, the solution is computed by standard numerical optimisation methods. We illustrate the performance of the method on a mass–spring–damper system.

Displacement model of the giant magnetostrictive actuator with strong bias magnetic field at low frequency

A giant magnetostrictive actuator is designed with strong bias magnetic field. The influence of the strong bias field is introduced, and the corresponding exciting input signal is selected. Magnetic reluctance estimation, approximate linearity between the strain and magnetic field, and a mass–spring–damper system assumption are employed to analyze the actuator’s displacement with low-frequency signal input. An experimental system is designed, and properties of the proposed actuator are tested. With the help of square wave test, appropriate direction of exciting signal for the magnetostrictive actuator is determined. With the help of sinusoidal wave test, the established model is validated and the relationship between the maximum value of the displacement and of the current is analyzed. With exciting frequency lower than 200 Hz, the errors between the calculating and testing results are within 1.0 m, which validates the model.

Effect of mass-ratio, damping, and stiffness on optimal hydrokinetic energy conversion of a single, rough cylinder in flow induced motions

Flow Induced Motions (FIMs) of a single, rigid, circular cylinder with end-springs are investigated for Reynolds number 30,000 ≤ Re ≤ 120,000 with mass ratio, damping, and stiffness as parameters. Selective roughness is applied to enhance FIM and increase the hydrokinetic energy captured by the VIVACE (Vortex Induced Vibration for Aquatic Clean Energy) Converter at higher Reynolds numbers. The second generation of virtual spring-damping system Vck, recently developed in the Marine Renewable Energy Laboratory (MRELab), enables embedded computer-controlled change of viscous-damping and spring-stiffness for fast and precise oscillator modeling. Experimental results for amplitude response, frequency response, energy harvesting, and efficiency are presented and discussed. All experiments were conducted in the Low Turbulence Free Surface Water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are: (1) The oscillator can harness energy from flows as slow as 0.3946 m/s with no upper limit. (2) Increasing the spring stiffness, shifts the VIV synchronization range to higher flow velocities, resulting in reduced gap between VIV and galloping, where the harnessed power drops. (3) In galloping, the harnessed power increases with the mass ratio. (4) Local optima in energy conversion efficiency appear at the beginning of the VIV upper branch and at the beginning of galloping. (5) Local optima in power appear at the end VIV upper branch and at the beginning of galloping.

Linear extended state observer based sliding mode disturbance decoupling control for nonlinear multivariable systems with uncertainty

In this paper, the sliding mode dynamic disturbance decoupling tracking control method based on the linear extended state observer (LESO) is proposed for a class of square multivariable nonlinear uncertain system. The model plant contains the known linear dynamics, the unknown nonlinear dynamics and the internal and external disturbances, and the various input-output pairs are interacted. The system states are not available for measurement. An improved LESO is developed. The leading feature which is different from the typical ESO lies in that its extended state does not contain the known linear dynamics. The improved LESO can guarantee the error variables to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. So this ball radius can be arbitrarily as small as desired by tuning design parameters. And we give a simple method by which the gain parameters of LESO can be computed easily. This estimation to the total disturbance of the original system is introduced into the sliding mode control design to complete disturbance rejection and decoupling. Rigorous stability analysis shows that the system output can track the desired signal closely. Finally, a class of mass–spring–damper system is taken to make the numerical simulation analysis to illustrate the effectiveness of the proposed control method.

Dynamic response of a cable-stayed bridge subjected to a moving vehicle load

In this work, the dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a moving vehicle load, is studied. The vehicle is modeled as a mass–spring–damper system moving at a constant velocity, which is assumed to keep contact with the deck beam at all times. Convective velocity and acceleration terms associated with the moving vehicle as it traverses along the vibrating deck beam are taken into consideration, as well as geometric nonlinearities of stay cables. The nonlinear response of the cable-stayed bridge is obtained by solving nonlinear and linear partial differential equations which govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality relations of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear cable-stayed bridge model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is calculated using the Runge–Kutta–Fehlberg method in MATLAB. Convergence of the dynamic response from the Galerkin method is investigated for two cases in which the velocities or masses of the moving vehicle are different. Results show that an accurate calculation of the dynamic response of the cable-stayed bridge needs use of a large number of modes of the linearized undamped cable-stayed bridge model, and needs many more modes for the deck beam than stay cables. Moreover, effects of the velocity and mass of the moving vehicle and the convective terms on the dynamic response of the cable-stayed bridge are studied with convergent Galerkin truncation.

Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers

This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.

Adaptive fuzzy output‐feedback control for switched uncertain non‐linear systems

The problem of adaptive fuzzy output-feedback control for a class of switched uncertain non-linear systems without the measurements of the system states is discussed. By utilising fuzzy logic systems to approximate unknown non-linear functions, an adaptive fuzzy control technique for the problem under study is provided by exploiting the average dwell time method and the backstepping technique. To reduce the conservativeness caused by adoption of a common observer for all subsystems, a switched observer for switched systems is designed. It is proved that the proposed controllers of subsystems can guarantee the semiglobally uniformly ultimately bounded for all the closed-loop signals under a class of switching signals with average dwell time, while the output tracking error can converge to a small neighbourhood of the origin. The effectiveness of the proposed control scheme is illustrated by its application to a switched RLC circuit and a mass–spring–damper system.

Efficient and Accurate Calculation of Discrete Frequency Response Functions and Impulse Response Functions

Modal properties of a structure can be identified by experimental modal analysis (EMA). Discrete frequency response functions (FRFs) and impulse response functions (IRFs) between response and excitation series are bases for EMA. In the calculation of a discrete FRF, the discrete Fourier transform (DFT) is applied to both response and excitation series, and a transformed series in the DFT is virtually extended to have an infinite length and be periodic with a period equal to the length of the series; the resulting periodicity can be physically incorrect in some cases, which depends on an excitation technique used. An efficient and accurate methodology for calculating discrete FRFs and IRFs is proposed here, by which fewer spectral lines are needed and accuracies of resulting FRFs and IRFs can be maintained. The relationship between an IRF from the proposed methodology and that from the least-squares (LS) method is shown. A coherence function extended from a new type of coherence functions is used to evaluate qualities of FRFs and IRFs from the proposed methodology in the frequency domain. The extended coherence function can yield meaningful values even with response and excitation series of one sampling period. Based on the extended coherence function, a fitting index is used to evaluate overall qualities of the FRFs and IRFs. The proposed methodology was numerically and experimentally applied to a two degrees-of-freedom (2DOF) mass–spring–damper system and an aluminum plate to estimate their FRFs and IRFs, respectively. In the numerical example, FRFs and IRFs from the proposed methodology agree well with theoretical ones. In the experimental example, an FRF and its associated IRF from the proposed methodology with a random impact series agreed well with benchmark ones from a single impact test.

Numerical investigation of Linear Particle Chain impact dampers with friction

Impact dampers were first introduced in 1934 and the research and development on improving their performance and configuration is still ongoing to date. In this paper, the recently developed Linear Particle Chain (LPC) impact damper is experimentally and numerically studied. The damper was attached to a single-degree-of-freedom structure represented by a spring damper system and released from an initial position. A SOLIDWORKS model for the damper has been developed and numerically simulated using the finite element approach. The Coulomb friction model of the colliding masses is added to the overall structure. The response of the system was analyzed and compared to the experimental results. The simulation model showed a faster decay when the number of balls in the LPC impact damper was increased and when different mass ratios were used which is in agreement with the experimental results.

A new method for sudden mechanical perturbation with axial load, to assess postural control in sitting and standing

Sudden application of load along a sagittal or coronal axis has been used to study trunk stiffness, but not axial (vertical) load. This study introduces a new method for sudden-release axial load perturbation. Prima facie validity was supported by comparison with standard mechanical systems. We report the response of the human body to axial perturbation in sitting and standing and within-day repeatability of measures. Load of 20% of body weight was released from light contact onto the shoulders of 22 healthy participants (10 males). Force input was measured via force transducers at shoulders, output via a force plate below the participant, and kinematics via 3-D motion capture. System identification was used to fit data from the time of load release to time of peak load–displacement, fitting with a 2nd-order mass–spring–damper system with a delay term. At peak load–displacement, the mean (SD) effective stiffness measured with this device for participants in sitting was 12.0(3.4)N/mm, and in standing was 13.3(4.2)N/mm. Peak force output exceeded input by 44.8 (10.0)% in sitting and by 30.4(7.9)% in standing. Intra-class correlation coefficients for within-day repeatability of axial stiffness were 0.58 (CI: −0.03 to 0.83) in sitting and 0.82(0.57–0.93) in standing. Despite greater degrees of freedom in standing than sitting, standing involved lesser time, downward displacement, peak output force and was more repeatable in defending upright postural control against the same axial loads. This method provides a foundation for future studies of neuromuscular control with axial perturbation.

On the Improved Nonlinear Tracking Differentiator based Nonlinear PID Controller Design

This paper presents a new improved nonlinear tracking differentiator (INTD) with hyperbolic tangent function in the state space system. The stability and convergence of the INTD are thoroughly investigated and proved. Through the error analysis, the proposed INTD can extract differentiation of any piecewise smooth nonlinear signal to reach a high accuracy. the INTD has the required filtering features and can cope with th nonlinearities caused by the niose. Through simulations, the INTD is implemented as signal derivative generator for the closed loop feedback control system with a nolinear PID controller for the nonlinear Mass Spring Damper system and showed that it could achieve the signal tracking and differentiation faster with a minimum mean square error.