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Purpose: Energy harvesting has been extensively developed to scavenge energy from mechanical oscillations. Many investigations focus on the resonant issues which can activate large-amplitude responses in the region of the fundamental frequency. Hence, there are many ultra-low slowly changing excitation sources in the actual environment. To adapt to the slowly changing vibrational excitations, in this paper, we explore a novel bursting oscillations to collect energy induced by the low-frequency excitations. Methods: The slowly changing ambience excitation is proposed by a cosinoidal voltage source, and the nonlinear restoring force is realized using a nonlinear capacitor. A novel harvester of electromechanical device is developed, the electromechanical coupling equations are presented, and the bursting response is observed via numerical integration. Results: The superiority of the presented bursting energy harvester is contrasted with the resonance and nonresonance frequencies. Based on the method of fast–slow dynamical analysis method, the dynamical mechanism of bursting oscillations is revealed via the transformed phase diagram. Furthermore, the effects of system parameters on the bursting motion are discussed. [ABSTRACT FROM AUTHOR]

Forced vibration is investigated for two elastically connected cantilevers, under harmonic base excitation. One of the cantilevers is with a tip magnet repelled by a magnet fixed on the base. The cantilevers are uniform viscoelastic beams constituted by the Kelvin model. The system is formulated as a set of two linear partial differential equations with nonlinear boundary conditions. The method of multiple scales is developed to analyze the effects of internal resonances on the steady-state responses to external excitations in the nonlinear boundary problem of the partial differential equations. In the presence of 2:1 internal resonance, both the first and the second primary resonances are examined in detail. The analytical frequency–amplitude response relationships are derived from the solvability conditions. It is found that the frequency–amplitude response curves reveal typical nonlinear phenomena such as jumping and hysteresis in both primary resonances as well as saturation in the second primary resonance. The frequency–amplitude response curves may be converted from hardening-type single-jumping to double-jumpings, and further to softening-type single-jumping by adjusting the distance between two magnets. It is also found that the unstable parts of the frequency–amplitude response curves correspond to quasi-periodic motions. The finite difference scheme is proposed to discretize both the temporal and the spatial variables, and thus the numerical solutions can be calculated. The analytical results are supported by the numerical solutions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we are concerned with the wave equations in perforated domains with a homogeneous Neumann condition on the boundary of the holes. The multiscale asymptotic expansion of the solution for the problem are constructed and associated explicit convergence rates are obtained. A multiscale numerical method is introduced. Finally, we present some numerical results which support strongly the convergence theorem. [Copyright &y& Elsevier]

In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle's invariance principle, a criterion is established by constructing an effective control identification scheme and adjusting automatically the adaptive coupling strength. The proposed control law is applied to a complex community network which is periodically synchronized with different chaotic states. Numerical simulations are conducted to demonstrate the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, stability in parametric resonance of axially moving viscoelastic plates subjected to plane stresses is investigated. The plate material obeys the Kelvin–Voigt model in which the material time derivative is used. The generalized Hamilton principle is employed to obtain the governing equation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The governing equation can be regarded as a continuous gyroscopic system with small periodically parametric excitations and a damping term. The method of multiple scales is applied to the governing equation to establish the solvability conditions in principal and summation parametric resonances. The natural frequencies and modes of linear generating equation are numerically calculated based on the given boundary conditions. The necessary and sufficient condition of the stability is derived from the Routh–Hurwitz criterion. Some numerical examples are presented to demonstrate the effects of related parameters on the frequencies and the stability boundaries. The differential quadrature scheme is developed to solve numerically the linear generating system and the primitive equation model. The numerical calculations confirm the analytical results. [Copyright &y& Elsevier]

This study focuses on the steady-state periodic response of supercritically transporting viscoelastic beams. In the supercritical speed range, forced vibrations are investigated for traveling beams via the multiscale analysis with a numerical confirmation. The forced vibration is excited by the spatially uniform and temporally harmonic vibration of the supporting foundation. A nonlinear integro-partial-differential equation is used to deter-mine steady responses. The straight equilibrium configuration bifurcates in multiple equi-librium positions at supercritical translating speeds. The equation is cast in the standard form of continuous gyroscopic systems via introducing a coordinate transform for nontri-vial equilibrium configuration. The natural frequencies and modes of the supercritically traveling beams are analyzed via the Galerkin method for the linear standard form with space-dependent coefficients under the simply supported boundary conditions. Based on the natural frequencies and modes, the method of multiple scales is applied to the govern-ing equation to determine steady-state responses. To confirm results via the method of multiple scales, a finite difference scheme is developed to calculate steady-state response numerically. Quantitative comparisons demonstrate that the approximate analytical results have rather high precision. Numerical results are also presented to show the con-tributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode. [ABSTRACT FROM AUTHOR]

A backstepping approach is proposed for the synchronization of chain networks of multi-spatiotemporal chaotic systems with topologically equivalent structures. The synchronization of multi-spatiotemporal chaotic systems is implemented by adding the control only to a terminal node, and the controller is designed via a corresponding update law. The control law is applied to spatiotemporal Gray-Scott systems. Numerical results demonstrate the effectiveness and the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

Equilibria of axially moving beams are computationally investigated in the supercritical transport speed ranges. In the supercritical regime, the pattern of equilibria consists of the straight configuration and of non-trivial solutions that bifurcate with transport speed. The governing equations of coupled planar is reduced to a partial-differential equation and an integro-partial-differential equation of transverse vibration. The numerical schemes are respectively presented for the governing equations and the corresponding static equilibrium equation of coupled planar and the two governing equations of transverse motion for non-trivial equilibrium solutions via the finite difference method and differential quadrature method under the simple support boundary. A steel beam is treated as example to demonstrate the non-trivial equilibrium solutions of three nonlinear equations. Numerical results indicate that the three models predict qualitatively the same tendencies of the equilibrium with the changing parameters and the integro-partial-differential equation yields results quantitatively closer to those of the coupled equations. [ABSTRACT FROM AUTHOR]

The vibrations and stability are investigated for an axially moving rectangular antisymmetric cross-ply composite plate supported on simple supports. The partial differential equations governing the in-plane and out-of-plane displacements are derived by the balance of linear momentum. The natural frequencies for the in-plane and out-of-plane vibrations are calculated by both the Galerkin method and differential quadrature method. It can be found that natural frequencies of the in-plane vibrations are much higher than those in the out-of-plane case, which makes considering out-of-plane vibrations only is reasonable. The instability caused by divergence and flutter is discussed by studying the complex natural frequencies for constant axial moving velocity. For the axially accelerating. composite plate, the principal parametric and combination resonances are investigated by the method of multiple scales. The instability regions are discussed in the excitation frequency and excitation amplitude plane. Finally, the axial velocity at which the instability region reaches minimum is detected. [ABSTRACT FROM AUTHOR]

Abstract: In solid state physics, the most widely used techniques to calculate the electronic levels in nanostructures are the effective masses approximation (EMA) and its extension the multiband k · p method (see ). They have been particularly successful in the case of heterostructures (see, e.g. ). This paper discusses the multiscale analysis of the Schrödinger equation with rapidly oscillating coefficients. The new contributions obtained in this paper are the determination of the convergence rate for the approximate solutions, the definition of boundary layer solutions, and higher-order correctors. Consequently, a multiscale finite element method and some numerical results are presented. As one of the main results of this paper, we give a reasonable interpretation why the effective mass approximation is very accurate for calculating the band structures in semiconductor in the vicinity of Γ point, from the viewpoint of mathematics. [ABSTRACT FROM AUTHOR]

Abstract: Poling processes of ferroelectrics by an electric field in addition to a mechanical load transverse to poling direction is simulated by microstructural FEM based on the nonlinear constitutive model of . Observation of the evolution of domain switching shows that the compressive stress apparently enhances the degree of switching aligned with the poling direction. As a macroscopic response, the additional application of compressive stress significantly improves the electromechanical coupling effect. In the present numerical investigation, the enhancement of the coupling coefficient K 33 of BaTiO3 exceeds 10%. [Copyright &y& Elsevier]

Steady-state periodical response is investigated for planar vibration of axially moving viscoelastic beams subjected external transverse loads. A model of the coupled planar vibration is established by introducing a coordinate transform. The model can reduce to two nonlinear models of transverse vibration. The finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies. The effect of material parameters and excitation parameters on the amplitude of the steady-state responses are examined. Numerical results also indicate that the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters, and the two models of transverse vibration yield satisfactory results. [ABSTRACT FROM AUTHOR]

Abstract: Stability of an axially accelerating viscoelastic beam constituted by the standard linear solid model is investigated. The material time derivative is used in the viscoelastic constitutive relation. The instability condition is determined for combination and principal parametric resonances via the asymptotic analysis. The differential quadrature scheme is developed to solve numerically the partial differential equation governing transverse motion of axially accelerating viscoelastic beams. The stability boundaries are numerically located in the excitation amplitude and the excitation frequency plane. Numerical simulation demonstrates the effects of the stiffness, the viscosity and constant mean speed of beam. The numerical calculations validate the analytical results in the principal parametric resonance. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the elastomechanical problems of a honeycomb structure of composite materials. A multiscale finite element method and the postprocessing technique with high accuracy are presented. We will derive the proofs of all theoretical results. Finally, some numerical tests validate the theoretical results of this paper. [Copyright &y& Elsevier]

An implicit finite-element code is employed to study the internal grinding process of carbon steel Q235 cirque, and its temperature field and thermal deformation are obtained. The method of thermal load calculation is proposed, a 2D finite element model is developed, and analysis steps are introduced. The diameter of the cirque is 150 mm and that of the inner hole is 56.24 mm. By adopting the clamps of surface locating and three-jaw chuck, it is found that, during the grinding process, the workpiece is in an elastic–plastic state, far from thermal-softening state. The thermal deformation of the ground cirque is basically symmetrical in a diamond shape, but the deformations of the inner circle and the outer circle are not uniform, and the inner circle thermal deformation may be negative or positive. Such different thermal displacements will produce shape error and dimension error in the inner hole. Through comparison of the two clamping modes, it is found that the precision of the surface locating is better than the three-jaw chuck. The symmetrical property of the thermal deformation of the cirque and the comparison of two clamping modes indicate that the computation is valid. [ABSTRACT FROM AUTHOR]

Abstract: An asymptotic perturbation method is proposed to investigate stability of an axially accelerating viscoelastic beam. The material time derivative is used in the viscoelastic constitutive relation. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The stability condition can be determined via the asymptotic perturbation method. The differential quadrature scheme is developed to solve numerically the equation of axially accelerating viscoelastic beams with simple supports. The stability boundaries are numerically located in the summation parametric resonance and the principal parametric resonance. Numerical examples show the effects of the beam viscoelasticity and the mean axial speed. The numerical calculations validate the analytical results in the principal parametric resonance. [Copyright &y& Elsevier]

Abstract: In this paper, we discuss the multiscale computation of the eigenvalue problems for the elastic equations in composite materials. The multiscale finite element method for solving these problems is presented. Numerous numerical results validate the proposed method of this paper. [Copyright &y& Elsevier]

Abstract: Stability is investigated for an axially accelerating viscoelastic beam. The material time derivative is used in the viscoelastic constitutive relation, not simply the partial time derivative. The method of multiple scales is applied directly to the governing equation without discretization. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams constrained by simple supports with rotational springs in parametric resonance. The finite difference schemes are developed to solve numerically the equation of axially accelerating viscoelastic beams with fixed supports for the instability regions in the principal parametric resonance. The numerical calculations confirm the analytical results. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity. [Copyright &y& Elsevier]

Abstract: To deal with the uncertainties and randomness of defective percentage and shortages happened in the real-life situations, the order inventory model with a mixture of shortages and imperfect items is presented and investigated in the fuzzy environment. The objective function is established on the total inventory cost. Then, the economic order quantity is decided by optimizing the objective function by using the derivative method to find the minimal inventory cost. Finally, the numerical example is presented and the influence of the defective percentage on the presented model is studied. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the elliptic eigenvalue problem with the mixed boundary in a perforated domain. The higher-order asymptotic expansions of the eigenvalues and the eigenfunctions for the problem will be presented. We derive the rigorous justification of the convergence results. From this, a multiscale finite element method and some numerical examples are presented. [Copyright &y& Elsevier]

Abstract: In this paper, we employ the bifurcation theory of planar dynamical systems to study the smooth and nonsmooth traveling wave solutions of the generalized Degasperis-Procesi equationThe parameter condition under which peakons, compactons and periodic cusp wave solutions exist is given. The numerical simulation results show the consistence with the theoretical analysis at the same time. [Copyright &y& Elsevier]

Abstract: Nonlinear free transverse vibration of an axially moving beam is investigated. A partial-differential equation governing the transverse vibration is derived from the Newton''s second law. Under the assumption that the tension of beam can be replaced by the averaged tension over the beam, the partial-differential reduces to a widely used integro-partial-differential equation for nonlinear free transverse vibration. The method of multiple scales is applied directly to two equations to evaluate nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and to highlight the difference between two models. Two models yield the essentially same results for the weak nonlinearity, the small axial speed and the low mode, while the difference between two models increases with the nonlinear term, the axial speed, and the order of mode. [Copyright &y& Elsevier]