Method Of Time Scales Research Articles

Dynamics of SMA micro-actuator in biomechanical system

In this paper the polynomial model of shape memory alloy is used to characterise properties of a micro-actuator which is applied as a new middle ear prosthesis. A two degrees of freedom model of the reconstructed middle ear is solve by means of multiple time scales method. The system has various behaviours near the primary resonance depending on ambient temperature. The special case when relative temperature θ = 1.0 characterises untypical resonance curve. Increasing temperature to the normal human body one the resonance curves are typical. Then the system has only one periodic solution if the excitation is not too strong.

Characteristics of Motor Development in Children with Autism Spectrum Disorder as Indicated by Movement Variability: Longitudinal Study Based on the Multiple Time Scale Method

Characteristics of Motor Development in Children with Autism Spectrum Disorder as Indicated by Movement Variability: Longitudinal Study Based on the Multiple Time Scale Method

Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

Abstract In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

Analytical solutions of a nonlinear two degrees of freedom model of a human middle ear with SMA prosthesis

A nonlinear two degrees of freedom system with shape memory element (SMA) is presented in the paper. Thermomechanical properties, shape memory effect and pseudoelasticity of the SMA joint, are modelled by phenomenological approach with the help of a fifth order polynomial approximation. The analytical solution of the mathematical model is obtained by means of the multiple time scales method. Next, a numerical study of a biomechanical system of human middle ear is performed. It has been demonstrated that for a selected rod type prothesis the cubic nonlinearity has the most essential effect on the system dynamics in the first order approximation, which converges with direct numerical simulations.

Multi-time scale energy management of wind farms based on comprehensive evaluation technology

A novel energy management of wind farms is proposed in this paper. Firstly, a novel comprehensive evaluation system is proposed to quantify economic properties of each wind farm to make the energy management more economical and reasonable. Then, a combination of multi time-scale schedule method is proposed to develop a novel energy management. The day-ahead schedule optimizes unit commitment of thermal power generators. The intraday schedule is established to optimize power generation plan for all thermal power generating units, hydroelectric generating sets and wind power plants. At last, the power generation plan can be timely revised in the process of on-line schedule. The paper concludes with simulations conducted on a real provincial integrated energy system in northeast China. Simulation results have validated the proposed model and corresponding solving algorithms.

Structured Projection-Based Model Reduction With Application to Stochastic Biochemical Networks

The chemical master equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason, simpler approximations to the CME have been proposed. In this paper, we focus on one such model, the linear noise approximation (LNA). Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced-order LNA converges to the full-order model in the mean square sense. Using this as motivation, we derive a network structure-preserving reduction algorithm based on structured projections. We discuss when these structured projections exist and we present convex optimization algorithms that describe how such projections can be computed. The algorithms are then applied to a linearized stochastic LNA model of the yeast glycolysis pathway.

On the upscaling of process-based models in deltaic applications

Process-based numerical models are increasingly used to study the evolution of marine and terrestrial depositional environments. Whilst a detailed description of small-scale processes provides an accurate representation of reality, application on geological timescales is restrained by the associated increase in computational time. In order to reduce the computational time, a number of acceleration methods are combined and evaluated for a schematic supply-driven delta (static base level) and an accommodation-driven delta (variable base level). The performance of the combined acceleration methods is evaluated by comparing the morphological indicators such as distributary channel networking and delta volumes derived from the model predictions for various levels of acceleration. The results of the accelerated models are compared to the outcomes from a series of simulations to capture autogenic variability. Autogenic variability is quantified by re-running identical models on an initial bathymetry with 1cm added noise. The overall results show that the variability of the accelerated models fall within the autogenic variability range, suggesting that the application of acceleration methods does not significantly affect the simulated delta evolution. The Time-scale compression method (the acceleration method introduced in this paper) results in an increased computational efficiency of 75% without adversely affecting the simulated delta evolution compared to a base case. The combination of the Time-scale compression method with the existing acceleration methods has the potential to extend the application range of process-based models towards geologic timescales.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with ZN symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Effects of neutral surface deviation on nonlinear resonance of embedded temperature-dependent functionally graded nanobeams

In this paper, forced vibration of functionally graded (FG) nanobeams resting on the nonlinear elastic foundations are investigated based on the nonlocal strain gradient theory. The material parameters of FG nanobeams are assumed to be temperature-dependent and change continuously along the thickness direction according to the power-law function (PFGM) or sigmoid function (SFGM). Based on the Euler–Bernoulli beam theory and von-Kármán geometric nonlinearity, the governing equations of motion are derived by considering the deviation between the geometrical and physical neutral surfaces. Closed-form approximate solution for nonlinear forced vibration of a FG nanobeam is derived by using multiple time scale method. The results show that decrease of non-homogeneity index and material length scale parameter, or increase of temperature variation and nonlocal parameter will increase the resonance frequencies of FG nanobeams. The effect of the in-coincidence of physical and geometrical neutral surfaces on the nonlinear resonance of the nanobeams could not be ignored, especially for SFGM nanobeams with larger non-homogeneity index and stronger size effects, embedded in a softer medium with obvious temperature variation.

Analytical solution and energy harvesting from nonlinear vibration of an asymmetric bimorph piezoelectric plate and optimizing the plate parameters by genetic algorithm

In this article, harvesting of electrical power from nonlinear vibration of an asymmetric bimorph piezoelectric plate is presented based on the classical plate theory with von Kármán strain–displacement nonlinear relations in the presence of temperature change effect. Two piezoelectric layers with different thicknesses cover top and bottom layers of a substructure. The structure has been excited under harmonic transverse forces in case of primary resonance. Two coupled ordinary differential equations for displacement and voltage have been derived and solved via multiple time scales method. The voltage equation has been defined by electric displacement and Gauss’s law. Analytic relations for voltage and harvested electrical power have been derived. The analytic relation for power is based on different parameters of the plate such as thicknesses of the layers, dimensions of plate, load resistance, frequency of harmonic excitation, and mechanical properties of structure. The parameters are optimized using genetic algorithm method with consideration of power relation as cost function. To harvest the maximum energy from the plate, the thicknesses of two piezoelectric layers, load resistance, and detuning parameter have been optimized. To illustrate the effectiveness of the optimization, results are depicted in three different simulations.

A Delayed Virus Infection Model with Cell-to-Cell Transmission and CTL Immune Response

In this paper, a delayed virus infection model with cell-to-cell transmission and CTL immune response is investigated. In the model, time delay is incorporated into the CTL response. By constructing Lyapunov functionals, global dynamical properties of the two boundary equilibria are established. Our results show that time delay in the CTL response process may lead to sustained oscillation. To further investigate the nature of the oscillation, we apply the method of multiple time scales to calculate the normal form on the center manifold of the model. At the end of the paper, numerical simulations are carried out, which support our theoretical results.

Time-frequency analysis of surface EMG signals for maximum energy localization during gait

The purpose of this work is to assess the maximum energy localization in time-frequency domain of the surface EMG signal of the main lower-limb muscles usually involved in able-bodied walking. The maximum energy localization in time-frequency domain has been identified by means of Continuous Wavelet Transform (CWT), a time-scale analysis method for multiresolution decomposition of continuous-time signals. WT coefficients allowed to reconstruct the scalogram function, providing an estimate of the local time-frequency energy density of a signal. Then, localization of maximum energy density has been identified as the interval in time-frequency where the scalogram is exceeding the 72% of the peak value of energy density in both time and frequency domain. Results showed that the localization of maximum signal energy in time coincided with the region of maximum muscle recruitment during walking. A common frequency band of maximum information content was identified for all muscles between 70 and 160 Hz. These findings could be suitable for both supporting the use of WT for sEMG analysis and providing clinical indications on muscle recruitment during walking.

Resonantly interacting non-linear waves in a van der Waals gas

The present paper uses the method of multiple time scales to derive the asymptotic solution of system of one-dimensional quasilinear hyperbolic equations for the generalized geometry in van der Waals gas. The transport equation for the amplitude of resonantly interacting high frequency waves propagating into non-ideal gas is derived. Further, we discuss the cases when the initial data for the wave amplitude is of 2π periodicity. The evolutionary behavior of non-resonant wave modes culminating into shock wave and its location are examined in van der Waals fluid.

Dynamic analysis of nonlinear variable frequency water supply system with time delay

In this paper, we study the mathematical model about variable frequency water supply system in the process of applying glue to particleboard. Based on the original linear ordinary differential model, the effects of time delay and the nonlinear factor are considered. Then, we obtain the delayed nonlinear differential equation associated with variable frequency water supply system. Further, we consider the existence and stability of the equilibria and the existence of several types of bifurcations in this functional differential equation. Next, we derive the normal forms of Hopf bifurcation and Bogdanov–Takens bifurcation by using the multiple time scales method and the center manifold reduction method, respectively, and analyze the classifications of local dynamics. Finally, by using Matlab software, we obtain numerical simulations with estimated values of parameters and show the existence of stable equilibrium, stable periodic-1, periodic-2, and periodic-4 solutions, and a complex chaotic attractor from a sequence of period-doubling bifurcations.

Global positioning system processing methods for GPS passive coherent location

This study addresses processing methods for the use of the global positioning system (GPS) as a signal of opportunity in a multistatic passive coherent location (PCL) system. The signal properties of the GPS signal are designed for position estimation, which makes it particularly suited for GPS PCL applications. The signal specifications are examined and the potential limitations of a proposed system are explored. Conventional GPS processing techniques are implemented in the framework of multistatic GPS PCL. GPS specific methods are developed for target position estimation of a multistatic PCL system in a three-dimensional plane. The PCL system has comparable performance metrics to conventional GPS positioning. Two methods are developed utilising measurements available in a conventional GPS system. The first involves a short time scale, which is in the order of milliseconds. The second involves a long time scale method, which is on the order of seconds. Simulation and analysis are performed to verify the methods. Experimental validation was also conducted using a hardware in the loop approach, as well as, an active radar calibrator.

Adaptive controller for a strength testbed for aircraft structures

The problem of control system design for a strength testbed of aircraft structures is considered. A method for calculating the parameters of a proportional-integral controller (control algorithm) using the time-scale separation method for the testbed taking into account the dead time effect in the control loop is presented. An adaptive control algorithm structure is proposed which limits the amplitude of high-frequency oscillations in the control system with a change in the direction of motion of the rod of the hydraulic cylinders and provides the desired accuracy and quality of transients at all stages of structural loading history. The results of tests of the developed control system with the adaptive control algorithm on an experimental strength testbed for aircraft structures are given.

Nonlinear longitudinal forced vibration of a rod undergoing finite strain

Rods are one of significant engineering’s structures and vibration analysis of a rod because of extended application of it in engineering is very important. Due to large amplitude or to excitations at frequencies close to their resonance frequencies, these structural elements can experience large amplitude, hence nonlinear vibration. Therefore, understanding of longitudinal nonlinear vibration of rods with different boundary conditions and large amplitude is very useful to reach an appropriate designing. In this paper, vibration of a rod with different boundary conditions undergoing finite strain, without simplification in strain–displacement equation, is investigated. For obtaining governing equation, Green–Lagrange strain, structural damping and Hamilton principle are used and then Galerkin method is employed to convert nonlinear partial differential equation to nonlinear ordinary differential equation. In spite of many papers that only use of cubic term for nonlinearity, the governing equation has quadratic and cubic terms. At the first, free vibration equations are solved with multiple time scales method and for verifying the accuracy of this method, the results are compared with results of Runge–Kutta numerical method, which have good accuracy. Then, forced vibration is investigated in the cases of primary resonance and hard excitation including sub-harmonic and super-harmonic resonances. Analytical expressions for frequency responses are derived, and the effects of different parameters including nonlinear coefficients, damping coefficient and external excitation are discussed.

Nonlinear harmonic vibration analysis of fluid-conveying piezoelectric-layered nanotubes

Abstract Nonlinear harmonic vibration of a piezoelectric-layered nanotube conveying fluid flow is investigated. The mathematical modeling of the structure is developed by means of the nonlocal theory and energy approach. The piezoelectric layer is assumed to be slender and the fluid flows through the nanotube at a uniform velocity. The forced vibration of the system is resulted from an external loading and hence, the parametric excitation is analyzed. Three different scenarios for its resonance conditions, known as the primary, parametric, and the simultaneous primary-parametric resonances, employing a strong perturbation technique known as the multiple time-scales method, are investigated. The effects of the variation of different parameters, such as the applied voltage, piezoelectric layer, nonlocal parameter and the fluid flow velocity, on both the frequency-amplitude relationship and the frequency response of the system are studied. Finally, a detailed discussion on the numerical results obtained were fully presented.

Acoustic Communications: Through soils, sands, water, and tissue

This talk will cover several experimental results and the challenges that arise in applying the basic concept of acoustic communications to vastly different media. Specifically, results obtained from state-of-the-art ultrasonic communications over distances of 100 m at data rates in excess of 1Mbps will be described, along with the unique challenges that such high data rates impose of any subsea applications, for which traditional Doppler compensation techniques are wholly inadequate. A sample-by-sample time-scale projection method was developed for streaming video applications for subsea operations. Over much shorter distance scales, even more acoustic bandwidth is available, and data races in excess of 300 MB/s have been achieved. Difficulties in such applications arise due to the nonlinearities excited in both the medium and potentially the transducers owing to the extremely wide bandwidths of operation. For potential biomedical applications, acoustic communication methods have been successfully used to transmit data in excess of 30 Mb/s through animal tissue. Challenges in such applications include no only nonlinearity and Doppler compensation, but also reverberation and scattering off bone and other materials. A final application that will be discussed is the use of acoustic communications methods for through-soils and through-sands experiments with application to various geotechnical projects. Attenuation, coupling, and excitation pose substantive challenges for such applications.

Stability characteristics of periodic streaming fluids in porous media

We study the linear stability of a three-layer flow of immiscible liquids located in a periodic normal electric field. We consider certain porous media assumed to be uniform, homogeneous, and isotropic. We analytically and numerically simulate the system of linear evolution equations of such a medium. The linearized problem leads to a system of two Mathieu equations with complex coefficients of the damping terms. We study the effects of the streaming velocity, permeability of the porous medium, and the electrical properties of the flow of a thin layer (film) of liquid on the flow instability. We consider several special cases of such systems. As a special case, we consider a uniform electric field and solve the transition curve equations up to the second order in a small dimensionless parameter. We show that the dielectric constant ratio and also the electric field play a destabilizing role in the stability criteria, while the porosity has a dual effect on the wave motion. In the case of an alternating electric field and a periodic velocity, we use the method of multiple time scales to calculate approximate solutions and analyze the stability criteria in the nonresonance and resonance cases; we also obtain transition curves in these cases. We show that an increase in the velocity and the electric field promote oscillations and hence have a destabilizing effect.