Research on the flow stability and noise reduction characteristics of quasi-periodic elastic support skin

To enhance flow stability and reduce hydrodynamic noise caused by fluctuating pressure,a quasiperiodic elastic support skin composed of flexible walls and elastic support elements is proposed for fluid noise reduction.The arrangement of the elastic support element is determined by the equivalent periodic distance and quasi-periodic coefficient.In this paper,a dynamic model of skin in a fluid environment is established.The influence of equivalent periodic distance and quasi-periodic coefficient on flow stability is investigated.The results suggest that arranging the elastic support elements in accordance with the quasi-periodic law can effectively enhance flow stability.Meanwhile,the hydrodynamic noise calculation results demonstrate that the skin exhibits excellent noise reduction performance,with reductions of 10 dB in the streamwise direction,11 dB in the spanwise direction,and 10 dB in the normal direction.The results also demonstrate that the stability analysis method can serve as a diagnostic tool for flow fields and guide the design of noise reduction structures.

Mobility edges in one-dimensional finite-sized models with large quasi-periodic disorders

We study the one-dimensional tight-binding model with quasi-periodic disorders,where the quasi-period is tuned to be large compared to the system size.It is found that this type of model with large quasi-periodic disorders can also support the mobility edges,which is very similar to the models with slowly varying quasi-periodic disorders.The energy-matching method is employed to determine the locations of mobility edges in both types of models.These results of mobility edges are verified by numerical calculations in various examples.We also provide qualitative arguments to support the fact that large quasi-periodic disorders will lead to the existence of mobility edges.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

Improving Wilson-θ and Newmark-β Methods for Quasi-Periodic Solutions of Nonlinear Dynamical Systems

Quasi-periodic responses can appear in a wide variety of nonlinear dynamical systems. To the best of our knowledge, it has been a tough job for years to solve quasi-periodic solutions, even by numerical algorithms. Here in this paper, we will present effective and accurate algorithms for quasi-periodic solutions by improving Wilson-θ and Newmark-β methods, respectively. In both the two methods, routinely, the considered equations are rearranged in the form of incremental equilibrium equations with the coefficient matrixes being updated in each time step. In this study, the two methods are improved via a predictor-corrector algorithm without updating the coefficient matrixes, in which the predicted solution at one time point can be corrected to the true one at the next. Numerical examples show that, both the improved Wilson-θ and Newmark-β methods can provide much more accurate quasi-periodic solutions with a smaller amount of computational resources. With a simple way to adjust the convergence of the iterations, the improved methods can even solve some quasi-periodic systems effectively, for which the original methods cease to be valid.

Geometric Aspects of Quasi-Periodic Property of Dirichlet Functions

The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.

Studies of Optical Properties of Symmetrical Quasi-Periodic Photonic Crystals

Using the transfer matrix method approach (TMM), the present paper attempts to determine the optical properties of quasi-periodic symmetric one-dimensional photonic systems. In addition, it studies hybrid hetero-structure systems constructed by using periodic and quasi-periodic multilayer systems. The effect of symmetry applied to symmetric multilayer systems results in the appearance of optical windows at the photonic band gaps (PBG) of the system. The use of hybrid symmetric systems, at normal incidence in the visible range, show that the complete photonic band gap is the sum of bands from individual systems. The results show also that the width of the PBG depends on the parameters and nature of the built system.

Quasi-periodic events on structured earthquake models

There has been much interest in studying quasi-periodic events on earthquake models.Here we investigate quasiperiodic events in the avalanche time series on structured earthquake models by the analysis of the autocorrelation function and the fast Fourier transform.For random spatial earthquake models, quasi-periodic events are robust and we obtain a simple rule for a period that is proportional to the choice of unit time and the dissipation of the system.Moreover, computer simulations validate this rule for two-dimensional lattice models and cycle graphs, but our simulation results also show that small-world models, scale-free models, and random rule graphs do not have periodic phenomena.Although the periodicity of avalanche does not depend on the criticality of the system or the average degree of the system or the size of the system,there is evidence that it depends on the time series of the average force of the system.

Band structures of elastic waves in two-dimensional eight-fold solid–solid quasi-periodic phononic crystals

Combined with the supercell method, band structures of the anti-plane and in-plane modes of two-dimensional （2D） eight-fold solid-solid quasi-periodic phononic crystals （QPNCs） are calculated by using the finite element method. The influences of the supercell on the band structure and the wave localization phenomenon are discussed based on the modal distributions. The reason for the appearance of unphysical bands is analyzed. The influence of the incidence angle on the transmission spectrum is also discussed.

Stability and Robustness Analysis of an Adaptive Algorithm for Quasi-periodic Disturbances Rejection

Winding and web transport systems are subjected to quasi-periodic disturbances of the web tension due to the eccentricity and the non-circularity of the reel and rolls. The disturbances induced by the non-circularity and eccentricity of the rolls are quasi-periodic with a frequency that varies with their rotation speed. An adaptive method of rejection of these disturbances is proposed in this paper. It is based on a phase-locked loop structure that estimates simutaneously the phase and magnitude of the perturbation and then cancels it. This algorithm can be plugged in an existing industrial controller. The stability and robustness of the algorithm are also discussed. The ability of the algorithm to reject quasi-periodic disturbances with slowly varying frequencies is shown through simulation results.

Quasi-periodic Solutions of the General Nonlinear Beam Equations

In this paper, one-dimensional （1D） nonlinear beam equations of the form utt - uxx ＋ uxxxx ＋ mu = f （u） with Dirichlet boundary conditions are considered, where the nonlinearity f is an analytic, odd function and f（u） = O（u3）. It is proved that for all m ∈ （0, M＊] R （M＊ is a fixed large number）, but a set of small Lebesgue measure, the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.

Boundedness in Asymmetric Quasi-periodic Oscillations

In the paper, by applying the method of main integration, we show the boundedness of the quasi-periodic second order differential equation x′′+ ax;-bx;+φ（x） = p（t）, where a≠b are two positive constants and φ（s）, p（t） are real analytic functions. Moreover, the p（t） is quasi-periodic coefficient, whose frequency vectors are Diophantine. The results we obtained also imply that, under some conditions,the quasi-periodic oscillator has the Lagrange stability.

Reducibility of Periodic Quasi-Periodic Systems

In this work, the reducibility of quasi-periodic systems with strong parametric excitation is studied. We first applied a special case of Lyapunov-Perron (L-P) transformation for time periodic system known as the Lyapunov-Floquet (L-F) transformation to generate a dynamically equivalent system. Then, we used the quasi-periodicnear-identity transformation to reduce this dynamically equivalent system to a constant coefficient system by solving homological equations via harmonic balance. In this process, we obtained the reducibility/resonance conditions that needed to be satisfied to convert a quasi-periodic system in to a constant one. Assuming the reducibility is possible, we obtain the L-P transformation that can transform original quasi-periodic system into a system with constant coefficients. Two examples are presented that show the application of this approach.

QUASI-PERIODIC WAVES AND QUASI-SOLITARY WAVES IN STRATIFIED FLUID OF SLOWLY VARYING DEPTH

The nonlinear waves in a stratified fluid of slowly varying depth are investigated in this paper.The model considered here consists of a two-layer incompressible constant-density inviscid fluid confined by a slightly uneven bottom and a horizontal rigid wall.The Korteweg-de Vries(KdV)equation with varying coefficients is derived with the aid of the reductive perturbation method.By using the method of multiple scales,the approximate solutions of this equation are obtained.It is found that the unevenness of bottom may lead to the generation of socalled quasi-periodic waves and quasi-solitary waves,whose periods,propagation velocities and wave profiles vary slowly.The relations of the period of quasi-periodic waves and of the amplitude,propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented.The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.

材料特性对输送脉动流体的粘弹性轴向功能梯度管非线性动力行为的影响

The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very complex.And the dynamic behavior will induce the failure of the pipes,and research of vibration and stability of pipes becomes a major concern.Considering that the elastic modulus,density,and coefficient of viscoelastic damping of the pipe material vary along the axial direction,the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory.The generalized integral transform technique(GITT)is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time.The time domain diagram,phase portraits,Poincarémap and power spectra diagram at different dimensionless pulsation frequencies,are discussed in detail,showing the characteristics of chaotic,periodic,and quasi-periodic motion.The results show that the distributions of the elastic modulus,density,and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes.With the increase of the material property coefficient k,the transition between chaotic,periodic,and quasi-periodic motion occurs,especially in the high-frequency region of the flow pulsation.

Detection of a Quasiperiodic Phenomenon of a Binary Star System Using Convolutional Neural Network

Pattern recognition algorithms are commonly utilized to discover certain patterns,particularly in image-based data.Our study focuses on quasiperiodic oscillations(QPO)in celestial objects referred to as cataclysmic variables(CV).We are dealing with interestingly indistinct QPO signals,which we analyze using a power density spectrum(PDS).The confidence in detecting the latter using certain statistical approaches may come out with less significance than the truth.We work with real and simulated QPO data of a CV called MV Lyrae.Our primary statistical tool for determining confidence levels is sigma intervals.The aforementioned CV has scientifically proven QPO existence,but as indicated by our analysis,the QPO ended up falling below 1-σ,and such QPOs are not noteworthy based on the former approach.We intend to propose and ultimately train a convolutional neural network(CNN)using two types of QPO data with varying amounts of training dataset lengths.We aim to demonstrate the accuracy and viability of the classification using a CNN in comparison to sigma intervals.The resulting detection rate of our algorithm is very plausible,thus proving the effectiveness of CNNs in this scientific area.

Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators

In this paper,we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrodinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green’s function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Holder continuity of the integrated density of states(IDS)for such QP Schrodinger operators.This gives an affirmative answer to Bourgain’s problem in Bourgain(2000).

Effect of temporal disorder on wave packet dynamics in one-dimensional kicked lattices

Inspired by the recent experimental progress in noisy kicked rotor systems,we investigate the effect of temporal disorder or quasi-periodicity in one-dimensional kicked lattices with pulsed on-site potential.We found that,unlike the spatial disorder or quasi-periodicity which usually leads to localization,the effect of the temporal one is more complex and depends on the spatial configuration.If the kicked on-site potential is periodic in real space,then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity.On the other hand,if the kicked on-site potential is spatially quasi-periodic,then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range.The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization.

Distribution of empirical recurrence intervals for segment-rupturing earthquakes onactive faults of the Chinese mainland

For the two main recurrence behaviors of segment-rupturing earthquakes on active faults of the Chinese mainland,this paper establishes corresponding empirical distributions forearthquake recurrence interval. The results show that, for the time-predictable recurrence, the normalized recurrence interval, T/Tt, obeys very well the lognormal distributions: LN (μ1=0.00, σ21 =0. 152), where, T is an observed recurrence interval, and Tt is the average recurrence interval that is correlative with the size of the preceding event. For the quasi-periodic recurrence, the normalized recurrence interval, T/T, follows the lognormal distribution : LN(μq=0.00, σ2q=0.242), where, T is the median of recurrence intervals for various cycles. A statistical test suggests that, there is no significant difference between the latter distribution, built by this paper, and the recurrence interval distribution for the characteristic earthquakes of the Circum-Pacific Plate boundaries (NB model). Accordingly, this paper combines these two distributions into one and obtains a more stable lognormal distribution :LN (μ = 0.00, σ2 = 0.222), for the quasi-periodic recurrence interval.

Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.

Dynamical response of hyper-elastic cylindrical shells under periodic load

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.