INTERPOLATION METHODS FOR THE EVALUATION OF 2π-PERIODIC FINITE BAIRE MEASURE

We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.

PERIODIC WINDOWS OF NONLINEAR GEAR SYSTEM BASED ON SYMBOLIC DYNAMICS

The periodic window is researched by means of the symbolic dynamics and formal language. Firstly, the proper sampling period is taken and the orbital points of periodic motion are obtained through Poincar6 mapping. Secondly, according to the method of symbolic dynamics of one-dimensional discrete mapping, the symbolic sequence describing the periodic orbit is obtained. Finally, based on the symbolic sequence, the corresponding model of minimal finite automation is constructed and the entropy is obtained by calculating the maximal eigenvalue of Stefan matrix. The results show that the orbits in periodic windows can be strictly marked by using the method of symbolic dynamics, thus a foundation for control of switching between target orbits is provided.

Different optical properties in different periodic slot cavity geometrical morphologies

In this paper,optical properties of two-dimensional periodic annular slot cavity arrays in hexagonal close-packing on a silica substrate are theoretically characterized by finite difference time domain（FDTD） simulation method.By simulating reflectance spectra,electric field distribution,and charge distribution,we confirm that multiple cylindrical surface plasmon resonances can be excited in annular inclined slot cavities by linearly polarized light,in which the four reflectance dips are attributed to Fabry–Perot cavity resonances in the coaxial cavity.A coaxial waveguide mode TE11 will exist in these annular cavities,and the wavelengths of these reflectance dips are effectively tailored by changing the geometrical pattern of slot cavity and the dielectric materials filled in the cavities.These resonant wavelengths are localized in annular cavities with large electric field enhancement and dissipate gradually due to metal loss.The formation of an absorption peak can be explained from the aspect of phase matching conditions.We observed that the proposed structure can be tuned over the broad spectral range of 600–4000 nm by changing the outer and inner radii of the annular gaps,gap surface topography.Meanwhile,different lengths of the cavity may cause the shift of resonance dips.Also,we study the field enhancement at different vertical locations of the slit.In addition,dielectric materials filling in the annular gaps will result in a shift of the resonance wavelengths,which make the annular cavities good candidates for refractive index sensors.The refractive index sensitivity of annular cavities can also be tuned by the geometry size and the media around the cavity.Annular cavities with novel applications can be implied as surface enhanced Raman spectra substrates,refractive index sensors,nano-lasers,and optical trappers.

A variational principle analysis of surface acoustic waves propagating under periodic metal grating with finite thickness

A theoretical method is presented,which analyzes properties of surface acoustic waves propagating on metallic gratings with finite thickness by combining finite element method with variational principle on surface acoustic waves propagating on periodic metal gratings. Based on D.P.Chen and Haus theory,a finite element method is used to investigate the effects of metallic gratings upon the propagation of surface acoustic waves.The coupling-of-modes parameters contributed by mechanical loading are expressed by the matrix derived from the finite element method.Consequently D.P.Chen and Haus theory can also be applied to analyze the properties of surface acoustic waves propagating on metallic gratings with finite thickness and arbitrary shape.Finally,the characteristics of surface acoustic waves propagating under gold and aluminum or silver gratings on a few piezoelectric crystals are studied.Numerical results of the coupling-of-modes parameters of the surface acoustic waves are obtained.

Theoretical aspects of selecting repeated unit cell model in micromechanical analysis using displacement-based finite element method

Repeated Unit Cell（RUC）is a useful tool in micromechanical analysis of composites using Displacement-based Finite Element（DFE）method,and merely applying Periodic Displacement Boundary Conditions（PDBCs）to RUC is almost a standard practice to conduct such analysis.Two basic questions arising from this practice are whether Periodic Traction Boundary Conditions（PTBCs,also known as traction continuity conditions）are guaranteed and whether the solution is independent of selection of RUCs.This paper presents the theoretical aspects to tackle these questions,which unify the strong form,weak form and DFE method of the micromechanical problem together.Specifically,the solution’s independence of selection of RUCs is dealt with on the strong form side,PTBCs are derived from the weak form as natural boundary conditions,and the validity of merely applying PDBCs in micromechanical Finite Element（FE）analysis is proved by referring to its intrinsic connection to the strong form and weak form.Key points in the theoretical aspects are demonstrated by illustrative examples,and the merits of setting micromechanical FE analysis under the background of a clear theoretical framework are highlighted in the efficient selection of RUCs for Uni Directional（UD）fiber-reinforced composites.

Temperature stability of magnetic field for periodic permanent-magnet focusing system

In this study, finite element analysis based on an Ansoft Maxwell software was used to reveal the temperature stability of a magnet ring and the equivalent structural periodic permanent-magnet（PPM） focusing system. It is found that with the temperature increasing, the decrease rate of magnetic induction peak（Bz）maxof single magnet ring is greater than that of remanence Brof magnet in the range from room temperature to 200 °C, however,the PPM focusing system do have the same temperature characteristics of permanent-magnet materials. It indicates that the magnetic temperature properties of the PPM system can be effectively controlled by adjusting the temperature properties of the magnets. Moreover, the higher permeability of the magnets indicates the less Hcb, giving rise to lower magnetic induction peak （Bz）′max： Finally, it should be noted that the magnetic orientation deviation angle θ（／15°） of permanent magnets has little effect on the focusing magnetic field of the PPM system at different temperatures and the temperature stability. The obtained results are beneficial to the design and selection of permanent magnets for PPM focusing system.

Prediction of vibrations induced by trains on line 8 of Beijing metro

This paper mainly discusses the problem of ground-borne vibrations due to the planned line 8 of Beijing metro which passes under the National Measurement Laboratory.A lot of vibration sensitive equipments are placed in the laboratory.It is therefore necessary to study the impact of vibrations induced by metro trains on sensitive equipments and important to propound a feasible vibration mitigation measure.Based on the coupled periodic finite element-boundary element (FE-BE) method,a 3D dynamic track-tunnel-soil interaction model for metro line 8 has been used to predict vibrations in the free field induced by trains running at variable speeds between 30 km/h and 80 km/h.Four types of track structures commonly used on the Beijing metro network have been considered:(1) high resilience direct fixation fasteners,(2) Vanguard fasteners,(3) a floating slab track and (4) a floating ladder track.For each of these track types,the vibration isolation efficiency has been compared.The results of the numerical study can be used to predict vibrations in nearby buildings and to decide upon effective vibration countermeasures.

Multiaxial fatigue life prediction of composite materials

In order to analyze the stress and strain fields in the fibers and the matrix in composite materials,a fiber-scale unit cell model is established and the corresponding periodical boundary conditions are introduced.Assuming matrix cracking as the failure mode of composite materials,an energy-based fatigue damage parameter and a multiaxial fatigue life prediction method are established.This method only needs the material properties of the fibers and the matrix to be known.After the relationship between the fatigue damage parameter and the fatigue life under any arbitrary test condition is established,the multiaxial fatigue life under any other load condition can be predicted.The proposed method has been verified using two different kinds of load forms.One is unidirectional laminates subjected to cyclic off-axis loading,and the other is filament wound composites subjected to cyclic tension-torsion loading.The fatigue lives predicted using the proposed model are in good agreements with the experimental results for both kinds of load forms.