Forces In Time Domain Research Articles

Nonlinear Time-Domain Theory for the Simulation of Moored Floating Body Motion

Nonlinear wave loads can induce low-frequency and high-frequency resonance motions of a moored platform in deep water. For the analysis of the nonlinear response of an offshore platform under the action of irregular waves, the most widely used method in practice is the Cummins method, in which the second-order exciting forces in the time domain are computed by a two-term Volterra series model based on incident waves, first-order body motion response, and quadratic transfer functions (QTFs). QTFs are bichromatic waves acting on a body and are computed in the frequency domain in advance. For moving bodies, QTFs are related to the first-order body response, which is to be determined in the simulation process of body motion response but is unknown in the computation procedure of QTFs. In solving this problem, Teng and Cong (2017) proposed a method to divide the QTFs into different components, which are unrelated to the body response. With the application of the new QTF components, a modified Cummins method can be developed for the simulation of the nonlinear response of a moored floating platform. This paper presents a review of the theory.

Time domain force identification based on adaptive ℓq regularization

Traditional time domain force identification methods require prior knowledge about the force profile to apply the appropriate regularization term. Generally speaking, ℓ1 and ℓ2 regularization are applied for sparse-type and continuous-type forces respectively. However, prior knowledge about the force type may be unavailable in engineering practice. It is then necessary to incorporate the determination of q (as in ℓq regularization) into the identification process. In this paper, we propose two methods to address the problem: the joint and marginal posterior modes of the force history. The identification problem is formulated within the Bayesian framework. The force history, precision parameters, and q are all treated as unknown random parameters, and estimated based on vibration measurements only. The proposed methods are numerically validated on a mass–spring system, an engineering-scale support structure and experimentally validated on a cantilever beam. It is shown that the proposed methods by considering the data-driven determination of q could adapt to the force profile and consistently provide satisfactory results.

Multi-body Dynamic Analysis of Wind Power Gearbox

Using multi-body dynamics theory, we establish a multi-body system model of a 1.5WM wind power gearbox. Based on Hertz contact theory, The meshing force calculation method of gear meshing transmission is presented. This paper makes a simulation study about the time domain characteristics and frequency spectrum characteristics of meshing forces in planetary transmission, analysis the variation curves with time of dynamic load coefficients of multistage planetary transmission. The results show that the contact force in time domain has obvious dynamic characteristics when planetary gear transmission and its frequency domain showed modulation phenomenon. The carrier is the gear meshing frequency and modulation wave frequency is gear rotation frequency.

A hierarchical Bayesian method for vibration-based time domain force reconstruction problems

Traditional force reconstruction techniques require prior knowledge on the force nature to determine the regularization term. When such information is unavailable, the inappropriate term is easily chosen and the reconstruction result becomes unsatisfactory. In this paper, we propose a novel method to automatically determine the appropriate q as in ℓq regularization and reconstruct the force history. The method incorporates all to-be-determined variables such as the force history, precision parameters and q into a hierarchical Bayesian formulation. The posterior distributions of variables are evaluated by a Metropolis-within-Gibbs sampler. The point estimates of variables and their uncertainties are given. Simulations of a cantilever beam and a space truss under various loading conditions validate the proposed method in providing adaptive determination of q and better reconstruction performance than existing Bayesian methods.

A Novel Anti-Swing Positioning Controller for Two Dimensional Bridge Crane via Dynamic Sliding Mode Variable Structure

To improve the control performance of anti-swinging and the orientation of two-dimensional bridge crane, a novel dynamic sliding mode variable structure control algorithm is presented here. The proposed controller can ensure global stability through improved design of sliding surface for the drive control force, and obtain the continuous driving control force in time domain, by using the Sigmoid function for switching function to suppress chattering. Experimental results demonstrated that it is effective on chattering suppression, swing reduction, and robust with various load qualities and friction resistances.

Analysis and Optimization of the Vibration and Noise of a Double Planetary Gear Power Coupling Mechanism

As the key component of a hybrid electric vehicle (HEV), the dynamic performance of the power coupling mechanism is found to have a significant effect upon the vibration and noise of the whole vehicle. In this paper, a dynamic model with rigid and flexible bodies of a double planetary gear power coupling mechanism is established. Then, the characteristics of the bearing constraining forces in time domain and frequency domain are simulated and analysed. At the same time, the finite element model of the housing of the power coupling mechanism is established. Then, the vibration response of the housing is analysed under the excitation of the bearing constraining forces, and the vibration displacement of the housing surface is obtained. Furthermore, based on the vibration displacement of the housing surface, a prediction model of housing radiating noise is established. Then, the radiating noise characteristics of the housing and the acoustic contribution of each panel are analysed. Finally, the free damping structure and new stiffener structure are adopted to optimize the rear end cover of the housing. The optimization model based on the vibration acceleration of the rear end cover surface is established by applying K‐S function and response surface method. Then, the optimization model is solved by applying the sequential quadratic programming to obtain the optimal structure of the housing. The optimization results demonstrate that the acoustic power level after optimization is decreased by 3.94 dB, 3.92 dB, 5.59 dB, and 2.84 dB at frequencies of 770 Hz, 870 Hz, 1650 Hz, and 2480 Hz, respectively. Therefore, the optimization effect of the housing structure is obvious, and this can be the theoretical basis and reference for reducing the vibration and noise of the power coupling mechanism.

Generalized Grouping Regularization for Time Domain Force Reconstruction Problems

Grouping regularization has received attention in recent studies because it offers flexibility and better noise immunity than traditional methods. In this paper, we propose the generalized grouping regularization (GGR). With different parameter settings, GGR provides localization ability, adaptive basis selection ability, and at the same time reconstruct forces in low signal-to-noise ratio (SNR) conditions. And with specific parameter settings, the proposed method degenerates to traditional Tikhonov regularization and compressed sensing. GGR is supposed to serve as the general regularization scheme for time domain force reconstruction problems. A cantilever beam simulation shows its superiority.

Identification of structural stiffness and excitation forces in time domain using noncontact vision-based displacement measurement

The emerging noncontact vision-based displacement sensor system offers a promising alternative to the conventional sensors for quantitative structural integrity assessment. Significant advantages of the noncontact vision-based sensor include its low cost, ease of operation, and flexibility to extract structural displacement responses at multiple points. This study aims to link the measured displacement data to the quantification of the structural health condition, by validating the feasibility of simultaneous identification of structural stiffness and unknown excitation forces in time domain using output-only vision-based displacement measurement. Numerical analysis are first carried out to investigate the accuracy, convergence and robustness of identified results to different noise levels, sensor numbers, and initial estimates of structural parameters. Then, experiment on a laboratory scaled beam structure is conducted. Results show that the global stiffness of the beam specimen as well as external hammer excitation forces can be successfully and accurately identified from displacement measurement at two points using one camera. The proposed output-only time-domain identification procedure utilizing vision-based displacement measurement represents a low-cost method for either periodic or long-term bridge performance assessment.

An improved state space method for force identification based on function interpolation in the presence of large noise

The conventional state space method for force identification has the disadvantage of large discretization error with a low sampling frequency. This paper presents an improved method based on the function interpolation of the external force in time domain. Two types of the interpolation functions are investigated, one is the linear interpolation, and the other type is the sigmoid curve interpolation. Gauss integration method is used for integration computation. Numerical studies show that both of the improved methods based on the two types of interpolation function are more accurate especially when the sampling is long and/or with a low sampling frequency. In addition, the proposed method is also extended for the case of high noise level. The key idea is to divide the time step of measured responses into several smaller time steps to form an overdetermined equation of the inverse force identification. Then, the least square algorithm is adopted, which helps to reduce the effect of the high random noise to improve the accuracy of identified solution.

Faxén form of time-domain force on a sphere in unsteady spatially varying viscous compressible flows

An explicit expression for the time-dependent force on a stationary, finite-sized spherical particle located in an unsteady inhomogeneous ambient flow is presented. The force expression accounts for both viscous and compressible effects. Towards this end, a time-harmonic plane travelling wave of a given frequency propagating in a viscous compressible flow over a sphere is considered. Linearized compressible Navier–Stokes equations are solved to obtain an analytical expression for the force exerted on the particle in the frequency domain. The force obtained in the Laplace space due to a travelling wave of a given frequency and wavenumber is then generalized to any arbitrary incoming flow. This is achieved by relating the radial and tangential velocity components in the Laplace space to the surface-averaged radial velocity and volume-averaged velocity vectors respectively in the time space. Moreover an expression relating the surface-averaged radial velocity and volume-averaged velocity vector has been provided. The total force is written as a summation of the undisturbed and disturbed force (quasi-steady, inviscid-unsteady and viscous-unsteady) contributions. The force contributions thus obtained are expressed as comprising of two parts – that arising due to spatial variation in the ambient flow and the other arising due to temporal variation. The current formulation is applicable to inhomogeneous ambient flows, however in the limit of negligible Reynolds and Mach numbers. The results are applicable even for particles of sizes larger than the acoustic wavelength. The accuracy of the explicit time-domain force expression is first tested by computing the force on an 80 mm diameter particle due to a weak planar expansion fan. Extension of this formulation when nonlinear effects become important is also proposed and tested by considering strong expansion fans. The results thus obtained are compared against corresponding axisymmetric numerical simulations.

An analytical model of grinding force based on time-varying dynamic behavior

This paper presents a time-domain force analytical model of cylindrical grinding process, which focuses on the time-varying dynamic behaviors caused by unstable machining process. This model analyzes the dynamic behaviors between the wheel and workpiece as the contact length and the maximum undeformed chip thickness change. It contains the grinding force affected by spindle run-out and vibration and especially focuses on the variation of grinding force which is affected by grinding parameters. In order to ensure the accuracy and computational efficiency of this model, the on-line detection results of grinding process have been adopted into the force analytical model. Through this model, explanations of different grinding parameter combinations are provided for grinding mechanism observed from the simulated results. Therefore, this model is validated by comparing the simulated results with the experimental results.

A Mixed Shooting – Harmonic Balance Method for Unilaterally Constrained Mechanical Systems

Abstract In this paper we present a mixed shooting – harmonic balance method for large linear mechanical systems on which local nonlinearities are imposed. The standard harmonic balance method (HBM), which approximates the periodic solution in frequency domain, is very popular as it is well suited for large systems with many degrees of freedom. However, it suffers from the fact that local nonlinearities cannot be evaluated directly in the frequency domain. The standard HBM performs an inverse Fourier transform, then calculates the nonlinear force in time domain and subsequently the Fourier coefficients of the nonlinear force. The disadvantage of the HBM is that strong nonlinearities are poorly represented by a truncated Fourier series. In contrast, the shooting method operates in time-domain and relies on numerical time-simulation. Set-valued force laws such as dry friction or other strong nonlinearities can be dealt with if an appropriate numerical integrator is available. The shooting method, however, becomes infeasible if the system has many states. The proposed mixed shooting-HBM approach combines the best of both worlds.

Parametrically excited vibrations of marine riser under random wave forces and earthquake

This article presents theoretical studies for parametrically excited vibrations of marine riser of the floating production, drilling, storage, and offloading system under random wave forces and earthquake excitation. The equation of motion of the riser is obtained by a mathematical method utilizing Euler beam theory and Galerkin method. The trigonometric series method is used to formulate random wave force and earthquake excitation in time domain. The dynamic analysis, spectral response analysis, and key parameters’ sensitivity analysis are conducted for the riser system. Parameter studies are conducted for the effects of wave and earthquake parameters and structural parameters on dynamics response of the riser system. The results from this study can provide valuable recommendations for the design and construction of the parametrically excited marine riser system under random wave forces and earthquake excitation and can promote widely practical application of the deep water riser in complicated environmental conditions.

Plasmonic trapping and tuning of a gold nanoparticle dimer.

We demonstrate theoretically the trapping and manipulating of a gold nanoparticle dimer, using surface plasmon excited by a focused linearly-polarized laser beam on a silver film. We use both finite-difference time-domain force analysis and Maxwell stress tensor to show that the gold nanoparticle dimer can be trapped by a virtual probe pair. A formula is derived to represent the plasmonic field, suggesting that the gap between the two gold nanoparticles in the dimer can be controlled, for example, by tuning the excitation-laser wavelength. We further test our theory by successfully trapping nanoparticle dimers formed by nanospheres and nanorods. The controllable gap in between the nanoparticles can lead to tunable localized surface plasmon resonances, and this may find new exciting applications in plasmonic sensing or in lab-on-a-chip devices.

Force modeling for incisions into various tissues with MRF haptic master

This study proposes a new model to predict the reaction force that occurs in incisions during robot-assisted minimally invasive surgery. The reaction force is fed back to the manipulator by a magneto-rheological fluid (MRF) haptic master, which is featured by a bi-directional clutch actuator. The reaction force feedback provides similar sensations to laparotomy that cannot be provided by a conventional master for surgery. This advantage shortens the training period for robot-assisted minimally invasive surgery and can improve the accuracy of operations. The reaction force modeling of incisions can be utilized in a surgical simulator that provides a virtual reaction force. In this work, in order to model the reaction force during incisions, the energy aspect of the incision process is adopted and analyzed. Each mode of the incision process is classified by the tendency of the energy change, and modeled for realistic real-time application. The reaction force model uses actual reaction force information with three types of actual tissues: hard tissue, medium tissue, and soft tissue. This modeled force is realized by the MRF haptic master through an algorithm based on the position and velocity of a scalpel using two different control methods: an open-loop algorithm and a closed-loop algorithm. The reaction forces obtained from the proposed model are compared with a desired force in time domain.

非線形バネ要素を含む剛体リンク機構により支持される構造物の過渡応答への非線形バネ特性の影響

The demands for comfort vehicle are getting increased in these years. On the other hand, the demands for the weight reduction for low fuel consumption are also increasing. In order to achieve these demands, the most efficient way is to reduce the input to the vehicle body. For reducing the input from road surface to the vehicle body, the suspension plays very important roles. So far, many literatures written about reduction of the input by the suspension have been reported. However, there are less papers written about the influence of nonlinear restoring force of the suspension component such as the shock absorber and the suspension bush. Typically, time domain behavior like harshness has large displacement. Therefore, the influence of the nonlinear restoring forces is not negligible. In this paper, the influence of the nonlinear restoring force in time domain is presented. For simplicity, two dimensional model which consists of rigid links connected by the nonlinear springs and elastic beam is used. On the model, the restoring force characteristic of an actual suspension bush is taken into account to set the range of the design space for the nonlinear restoring force of springs. The instantaneous maximum beam energy is maximized and minimized in order to show the influence of the nonlinear restoring force of springs. The maximization and minimization are conducted using local optimization method by the use of the sensitivity with respect to the nonlinear restoring force coefficient. Besides, the mechanism of the change of the instantaneous maximum beam energy is discussed from the point of view of energy flow. Finally, the influence in different input characteristics is investigated by changing the speed passing over a protrusion.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen’s theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov’s stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Dynamic Ice Force Analysis on a Conical Structure Based on Direct Observation and Measurement

In order to study dynamic ice force induced by ice-structure interaction, we adopted the most reliable method to directly measure ice force on full-scale structure. This paper mainly demonstrates the qualitative description on the basic model for dynamic ice forces based on direct measurement on the jackets with ice-breaking cone in the Bohai Sea. Temporal variations of ice force are recorded by the ice load panels, and corresponding ice failure processes on conical structures are recorded by video camera. It is found that, when an ice sheet acts on the upward narrow cone, bending failure occurs and broken ice pieces are completely cleared up by the side of the cone. The basic form of dynamic ice force in time domain is a series of impulse signals with minimum load of zero.

Mooring system influence on the efficiency of wave energy converters

The paper presents an analysis of the mooring system effects on the dynamics of an arbitrary floating wave energy converter (WEC) and on the efficiency of the device. The mooring system dynamics are calculated by a finite differences method, which accounts for the lines’ physical characteristics such as mass and stiffness, as well as for the hydrodynamic inertial and damping characteristics. A method is proposed and applied to consider the inertial, damping and stiffness effects of the mooring system on the WEC’s linear dynamics. An identification method is used to determine the linear mooring system coefficients from pre-calculated nonlinear time domain forces of the mooring system on the floater (the importance of nonlinear effects is assessed as well). Finally the mooring system dynamics is represented by additional inertial, damping and stiffness matrices which are added to the ones of the WEC. The influence of the mooring system on the WEC dynamics and efficiency is assessed in terms of wave induced motions and absorbed power. Results are presented for the transfer functions, statistics in selected stationary sea states and the expected annual absorbed energy. A wave scatter diagram representative of the Portuguese Pilot Zone is used for the annual predictions.

Explicit form of an implicit method for inverse force identification

Abstract Most existing time domain force identification methods are based on the state space method, which has the disadvantage of large discretization error with a low sampling frequency or a long sampling duration. This work transforms the conventional implicit Newmark-β algorithm into an explicit form for the solution of the Ax=b equations, which is an equivalent transformation, and it exhibits the same characteristics of Newmark-β algorithm as an implicit method. The accuracy of this method for the dynamic force identification is illustrated with two shear-frame buildings and a planar truss structure. Numerical results are compared with reference analytical responses. The new method gives more accurate identified force time histories compared with those from the conventional state space method for multiple sinusoidal and white noise excitations with 10% measurement noise in the responses.