Nonlinear Force-velocity Research Articles

Coupled SPH–FEM Modeling of Tsunami-Borne Large Debris Flow and Impact on Coastal Structures

Field surveys in recent tsunami events document the catastrophic effects of large waterborne debris on coastal infrastructure. Despite the availability of experimental studies, numerical studies investigating these effects are very limited due to the need to simulate different domains (fluid, solid), complex turbulent flows and multi-physics interactions. This study presents a coupled SPH–FEM modeling approach that simulates the fluid with particles, and the flume, the debris and the structure with mesh-based finite elements. The interaction between the fluid and solid bodies is captured via node-to-solid contacts, while the interaction of the debris with the flume and the structure is defined via a two-way segment-based contact. The modeling approach is validated using available large-scale experiments in the literature, in which a restrained shipping container is transported by a tsunami bore inland until it impacts a vertical column. Comparison of the experimental data with the two-dimensional numerical simulations reveals that the SPH–FEM models can predict (i) the non-linear transformation of the tsunami wave as it propagates towards the coast, (ii) the debris–fluid interaction and (iii) the impact on a coastal structure, with reasonable accuracy. Following the validation of the models, a limited investigation was conducted, which demonstrated the generation of significant debris pitching that led to a non-normal impact on the column with a reduced contact area and impact force. While the exact level of debris pitching is highly dependent on the tsunami characteristics and the initial water depth, it could potentially result in a non-linear force–velocity trend that has not been considered to date, highlighting the need for further investigation preferably with three-dimensional models.

Experimental and Numerical Studies of Dynamic Behaviors of a Hydraulic Power Take-Off Cylinder Using Spectral Representation Method

Hydraulic cylinders are generally used as power take-off (PTO) mechanisms in wave energy converters (WECs). The dynamic behavior of its PTO force, which integrates friction and pressure forces, is a difficult constraint to include in an analytical or in a numerical model. In this paper, the PTO force characteristics of a hydraulic cylinder are experimentally and numerically investigated under different magnitudes of controlled excitation force. In order to characterize the dynamic behaviors of PTO force, the displacement, acceleration, and pressure in the cylinder chamber for given excitation forces are measured. The pressure force is calculated using the measured value of the pressure, and the friction force is calculated based on the equation of motion using measured values of the pressure, excitation force, and acceleration of the piston. Experimental results show clearly a strong nonlinear force–velocity characteristics, including stochastic and hysteretic behaviors. To model the hysteretic behavior, the modified LuGre model is used for the friction force and a new approach is proposed for the pressure force. To model the stochastic behavior of the friction and pressure forces, the spectral representation method is used. The systematically comparison between measured and simulated results shows that the numerical model captures most of dynamic behaviors of PTO force.

Experimental studies on use of toggle brace mechanism fitted with magnetorheological dampers for seismic performance enhancement of three-storey steel moment-resisting frame model

The supplemental passive and semi-active dampers such as viscous fluid dampers and magnetorheological (MR) dampers normally placed in either Chevron or Toggle brace are increasingly used to provide enhanced seismic protection for new/retrofit existing buildings and bridges. The experimental nonlinear force–velocity relationships of MR dampers at different current inputs are fitted to fractional velocity power law. A three-storey quarter length scale steel moment-resisting frame model with two MR dampers fixed in upper toggle brace mechanism placed at ground floor level is designed and fabricated to study its seismic response characteristics. The natural frequencies and corresponding damping ratios of the model with MR damper at different current inputs are found. A procedure for modeling of MR dampers as nonlinear viscous fluid dampers is described. A methodology to find effective damping of the structural model is developed, using the formulations for nonlinear viscous fluid dampers given in literature. The methodology developed is used for finding the effective damping of structural model fitted with MR dampers in upper toggle bracing mechanism in different storeys of frame model. The model is subjected to two types of seismic excitations, and from studies of responses, it is found that the reduction in responses because of provision of MR dampers are to be quite significant. Copyright © 2011 John Wiley & Sons, Ltd.

Robust transport by multiple motors with nonlinear force–velocity relations and stochastic load sharing

Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force–velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the ‘tug-of-war’ of the multiple opposing motors.

Semi-Active Fuzzy Control of MR Damper on Structures by Genetic Algorithm

AbstractThe magnetorheological (MR) damper is a new device proposed for structural protection. It is filled with MR fluid that can be changed, when exposed to a magnetic field, regularly from free flowing liquid, linear viscous one to semi-solid. A phenomenological model based on the Bouc-Wen hysteresis model is adopted to predict both the force-displacement behavior and the complex nonlinear force-velocity response. The theory of fuzzy control is adopted here to determine the command voltage of MR dampers, but the applying of fuzzy control rules has always to deal with the classic problem of optimization. And due to the structural responses of analysis results, it can be confirmed that the reducing effects have an obviously improvement after an optimization by genetic algorithm.

Multiple-Motor-Based Transport

Intra-cellular transport via processive molecular motors plays an important role in maintaining cell structure and function. In many cases, cargoes move distances longer than expected for single motors; there is significant evidence that this increased travel is in part due to multiple motors working together to move cargoes. However, while we understand much about the function of single motors both experimentally and theoretically, our understanding of how multiple motors work together to move cargoes is less developed. We start with a Monte-Carlo model of single motor to theoretically investigate how multiple motors work together. We have investigated the effect of non-linear force-velocity curves and stochastic load sharing on multiple motor transport using stochastic model. We are particularly interested in cargo transport by a few molecular motors which is motivated by in-vivo results that only a few motors are engaged to transport cargo. Predictions for average travel distances and mean velocities obtained from stochastic model are significantly different from those predicted using steady-state model. Our theoretical study of multiple motor transport using stochastic model also shows that single-motor force-velocity curve plays an important role in determining the ensemble function when only a few motors are engaged.

Measurement Of The Protein Friction Between The Yeast Kinesin-8 Kip3p And Microtubules

Several proteins have been shown to undergo 'one-dimensional' diffusion along the surface of microtubules. Diffusion is thought to enhance the rate of targeting of proteins to the microtubule end for the depolymerizing kinesin-13 and the polymerase XMAP215, or to increase the processivity of kinesin-1 and dynein. According to the Einstein-Smolukowski relation, the diffusion coefficient, D, is related to the friction coefficient, gamma, according to D = kT/gamma. This relation, however, has not been experimentally tested for individual bio-molecules. We measured both the diffusional and frictional properties of single yeast kinesin-8 motor proteins, Kip3p, interacting with microtubule filaments in the ADP state. Using single molecule fluorescence we found that that the diffusion coefficient was 5400±1400 nm2/s with an average lifetime on the microtubule lattice of 8 s. Using an optical trap to drag a microsphere coated with Kip3p along microtubules, we measured a single molecule drag coefficient of 790±230 nNs/m at low speeds. Thus we verified the Einstein-Smolukowski relation. For larger speeds and drag forces, we measured a non-linear force-velocity relation which was well fit by a model in which Kip3p is diffusing in a periodic potential with an 8-nm periodicity and a barrier height between binding sites of 14±2 kT. This finding of an 8-nm periodicity is supported by an analysis of the positional fluctuations. Our measurements are a step towards resolving the molecular mechanism underlying protein friction an important parameter for active protein locomotion limiting the efficiency.

Synthesis of a semi-active suspension seat for attenuation of Whole-Body Vibration and shock

In this study, two semi-active control algorithms are synthesised on the basis of the measured nonlinear force-velocity properties of a Magneto-Rheological (MR) damper, including the current-dependent hysteresis and post yield saturation. The control algorithms employ the well-known sky-hook control condition function, suspension travel limits and a modulation function to compensate for the switching discontinuities. The results show that the proposed semi-active control synthesis could help achieve improved shock isolation while retaining adequate control of continuous WBV. A Hardware-In-the-Loop (HIL) test and simulation platform are developed for tuning of the proposed semi-active controllers and validation of the analytical formulations.

Development and Relative Assessments of Models for Characterizing the Current Dependent Hysteresis Properties of Magnetorheological Fluid Dampers

Magnetorheological (MR) dampers exhibit hysteretic and nonlinear force— velocity characteristics, which are strongly dependent upon the nature of the excitation and applied current. A number of reported models for characterizing such hysteretic and nonlinear force—velocity properties are reviewed in view of their applicability for predicting the hysteretic damping force under varying applied current and excitation conditions. It is concluded that the vast majority of these models lack consideration of damping force dependence upon the control current, and the frequency and magnitude of excitation. An independent current function is proposed that could enhance the current-dependent damping force prediction ability of the selected models, when integrated with the hysteretic force function. The parameters of the resulting modified models are identified on the basis of the measured data acquired for a MR-damper under wide ranges of excitation amplitudes and frequencies, and applied currents. These include modified linear biviscous, polynomial, extended Bouc—Wen and generalized sigmoid function models. The validity of modified models and the proposed current function is examined by comparing the model results with measured data under different currents and excitation conditions. The results show that the integration of the proposed current function could significantly enhance the performance of all models in predicting the current-dependent hysteretic damping force. The relative error analyses reveal that modified Bouc—Wen and sigmoid function models can provide reasonably good characterization of nonlinear and hysteretic MR-damping force over a range of current and excitation conditions considered in the study.

The theoretical limits to the power output of a muscle-tendon complex with inertial and gravitational loads.

When a muscle delivers power to an inertial load through a spring, the peak power can exceed the maximum that the muscle alone could produce. Using normalized differential equations relating dimensionless quantities we show, by solving the equations either analytically or numerically, that one dimensionless constant (Xi), representing the inertial load, is sufficient to specify the behaviour during shortening of a muscle-tendon complex with linear force-velocity and force-extension properties. In the presence of gravity, an additional constant (Gamma), representing the gravitational acceleration, is required. Nonlinear force-velocity and force-extension relationships each introduce an additional constant, representing their curvature. In the absence of gravity the power output delivered to an inertial load is limited to approximately 1.4 times the maximum power of the muscle alone, and when gravity is present the power delivered is limited to approximately twice the power of muscle alone. These limits are found for the purely inertial load at Xi ca. 1 and with gravity acting at XiGamma = 0.5 with Xi arbitrarily small. The effects of nonlinear muscle and tendon properties tend to cancel each other out and do not produce large deviations from these optima. A lever system of constant ratio between muscle and load does not alter these limits. Cams and catches are required to exceed these limits and attain the high power outputs sometimes observed during explosive animal movement.

On influence of kinematics to equivalent linear damping of helicopter blade hydraulic damper

An analytical model of hydraulic damper was presented in forward flight accounting for pitch/flap/lag kinematic coupling and its nonlinear force-velocity curve. The fourth order Runge-Kutta was applied to calculate the damper axial velocity in time domain. Fourier series based moving block analysis was applied to calculate equivalent linear damping in terms of transient responses of damper axial velocity. Results indicate that equivalent linear damping will be significantly reduced if pitch/flap/lag kinematic coupling introduced for notional model and flight conditions.

Cause of kinematic differences during centrifugal and centripetal saccades

Measurements of eye movements have shown that centrifugal movements (i.e. away from the primary position) have a lower maximum velocity and a longer duration than centripetal movements (i.e. toward the primary position) of the same size. In 1988 Pelisson proposed that these kinematic differences might be caused by differences in the neural command signals, oculomotor mechanics or a combination of the two. By using the result of muscle force measurements that were made in recent years (Orbit TM1.8 Gaze mechanics simulation, Eidactics, San Francisco, 1999) we simulated the muscle forces during centrifugal and centripetal saccades. Based on these simulations we show that the cause of the kinematic differences between the centrifugal and centripetal saccades is the non-linear force–velocity relationship (i.e. muscle viscosity) of the muscles.

Damping actions of the neuromuscular system with inertial loads: soleus muscle of the decerebrate cat.

A transient perturbation applied to a limb held in a given posture can induce oscillations. To restore the initial posture, the neuromuscular system must provide damping, which is the dissipation of the mechanical energy imparted by such a perturbation. Despite their importance, damping properties of the neuromuscular system have been poorly characterized. Accordingly, this paper describes the damping characteristics of the neuromuscular system interacting with inertial loads. To quantitatively examine damping, we coupled simulated inertial loads to surgically isolated, reflexively active soleus muscles in decerebrate cats. A simulated force impulse was applied to the load, causing a muscle stretch, which elicited a reflex response. The resulting deviation from the initial position gave rise to oscillations, which decayed progressively. Damping provided by the neuromuscular system was then calculated from the load kinetics. To help interpret our experimental results, we compared our kinetic measurements with those of an analogous linear viscoelastic system and found that the experimental damping properties differed in two respects. First, the amount of damping was greater for large oscillation amplitudes than for small (damping is independent of amplitude in a linear system). Second, plots of force against length during the induced movements showed that damping was greater for shortening than lengthening movements, reflecting greater effective viscosity during shortening. This again is different from the behavior of a linear system, in which damping effects would be symmetrical. This asymmetric and nonlinear damping behavior appears to be related to both the intrinsic nonlinear mechanical properties of the soleus muscle and to stretch reflex properties. The muscle nonlinearities include a change in muscle force-generating capacity induced by forced lengthening, akin to muscle yield, and the nonlinear force-velocity property of muscle, which is different for lengthening versus shortening. Stretch reflex responses are also known to be asymmetric and amplitude dependent. The finding that damping is greater for larger amplitude motion represents a form of automatic gain adjustment to a larger perturbation. In contrast, because of reduced damping at small amplitudes, smaller oscillations would tend to persist, perhaps contributing to normal or "physiological" tremor. This lack of damping for small amplitudes may represent an acceptable compromise for postural regulation in that there is substantial damping for larger movements, where energy dissipation is more critical. Finally, the directional asymmetry in energy dissipation provided by muscle and reflex properties must be reflected in the neural mechanisms for a stable posture.

A comparison of static and dynamic characteristics between rectus eye muscle and linear muscle model predictions

The characteristics of a muscle model are analyzed using rectus eye muscle parameter values and compared to rectus eye muscle data. The muscle is modeled as a viscoelastic parallel combination connected to a parallel combination of active state tension generator, viscosity element, and length tension elastic element. Each of the elements is linear and their existence is supported with physiological evidence. The static and dynamic properties of the muscle model are compared to rectus eye muscle data. The length-tension characteristics of the model are in good agreement with the data within the operating region of the muscle. With the muscle model incorporated into a lever system to match the isotonic experiment paradigm, simulation results for this linear system yield a nonlinear force-velocity curve. Moreover, the family of force-velocity curves generated with different stimulus rates reported in the literature match the predictions of the model without parametric changes. The results of this paper are important in studies involving the oculomotor plant and oculomotor neural networks. Additionally, these results may be applicable to other muscles.