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2015年 第36卷 第5期    刊出日期：2015-05-01

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Band structure calculations of in-plane waves in two-dimensional phononic crystals based on generalized multipole technique

Zhijie SHI, Yuesheng WANG, Chuanzeng ZHANG

2015, 36(5):  557-580.  doi:10.1007/s10483-015-1938-7

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A numerical method, the so-called multiple monopole (MMoP) method, based on the generalized multipole technique (GMT) is proposed to calculate the band structures of in-plane waves in two-dimensional phononic crystals, which are composed of arbitrarily shaped cylinders embedded in a solid host medium. To find the eigenvalues (eigenfrequencies) of the problem, besides the sources used to expand the wave fields, an extra monopole source is introduced which acts as the external excitation. By varying the excitation frequency, the eigenvalues can be localized as the extreme points of an appropriately chosen function. By sweeping the frequency range of interest and the boundary of the irreducible first Brillouin zone (FBZ), the band structures can be obtained. Some typical numerical examples with different acoustic impedance ratios and with inclusions of various shapes are presented to validate the proposed method.



论文

Statics of FGM circular plate with magneto-electro-elastic coupling: axisymmetric solutions and their relations with those for corresponding rectangular beam

Yanzheng WANG, Weiqiu CHEN, Xiangyu LI

2015, 36(5):  581-598.  doi:10.1007/s10483-015-1934-7

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This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic (MEE) materials under tension and bending. The analysis is directly based on the three-dimensional governing equations for magnetoelectro- elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately (in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material (FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic (FGMEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation

Zailin YANG, Baoping HEI, Yao WANG

2015, 36(5):  599-608.  doi:10.1007/s10483-015-1937-7

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Based on the theory of complex function and the principle of homogenization, harmonic dynamics stress of a radially infinite inhomogeneous medium with a circular cavity is investigated. Due to the symmetry, wave velocity is assumed to have power-law variation in the radial direction only, and the shear modulus is constant. The Helmholtz equation with a variable coefficient is equivalently transformed into a standard Helmholtz equation with a general conformal transformation method (GCTM). The displacements and stress fields are proposed. Numerical results show that the wave number and the inhomogeneity parameter of the medium have significant effects on the dynamic stress concentration around the circular cavity. The dynamic stress concentration factor (DSCF) becomes singular when the inhomogeneity parameter of medium is close to zero.

Pseudospectral method for optimal propellantless rendezvous using geomagnetic Lorentz force

Xu HUANG, Ye YAN, Yang ZHOU, Hua ZHANG

2015, 36(5):  609-618.  doi:10.1007/s10483-015-1936-7

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A charged spacecraft is subject to the Lorentz force when it orbits a central body with a magnetic field. The induced Lorentz force provides a new mean of propellantless electromagnetic propulsion for orbital control. Modeling the Earth magnetic field as a tilted dipole that co-rotates with the Earth, this paper develops a nonlinear dynamical model that describes the relative motion of the Lorentz spacecraft about an arbitrary reference orbit. Based on the proposed dynamical model, feasibility of Lorentz-propelled rendezvous with no restrictions on the initial states is investigated. The rendezvous problem is then formulated as an optimal control problem, and solved with the Gauss pseudospectral method (GPM). Numerical simulations substantiate the validity of proposed model and method, and results show that the propellantless rendezvous is achieved at both fixed and free final time.

On thermoelastic diffusion thin plate theory

M. AOUADI

2015, 36(5):  619-632.  doi:10.1007/s10483-015-1930-7

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The effect of diffusion on thermoelastic thin plates is investigated. The governing equations for thin thermoelastic diffusion plates under three different laws of heat and diffusion transmission are derived. By the C₀-semigroup theory, the well-posedness of the proposed equations is shown.

Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system

Jie CHEN, Hai WANG, Guanghui QING

2015, 36(5):  633-654.  doi:10.1007/s10483-015-1933-7

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Free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method (LRPIM) into a Hamilton system. The governing equation is derived with a transfer matrix technique and a spring layer model based on a local weak-form equivalent to the modified Hellinger-Reissner variational principle. Main superiority of the present model is that the scale of the governing equation involves only the so-called state variables at the top and bottom surfaces, and is insensitive to the thickness and the layer number of the composite laminates. Several numerical examples for analyzing the vibration frequencies and mode shapes of delaminated composite beams and plates are given to validate the model. The results are in good agreement with the pre-existing results.

Effects of thermophoresis and thermal radiation in mixed convection three-dimensional flow of Jeffrey fluid

S. A. SHEHZAD, T. HAYAT, A. ALSAEDI, B. AHMAD

2015, 36(5):  655-668.  doi:10.1007/s10483-015-1935-7

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Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

Ziwu GUAN, Yongliang YU

2015, 36(5):  669-680.  doi:10.1007/s10483-015-1931-7

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Large active wing deformation is a significant way to generate high aerodynamic forces required in bat's flapping flight. Besides the twisting, elementary morphing models of a bat wing are proposed, including wing-bending in the spanwise direction, wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing, and a three-dimensional unsteady panel method is used to predict the aerodynamic forces. It is found that the cambering model has great positive influence on the lift, followed by the area-changing model and then the bending model. Further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces. The mechanisms of aerodynamic force enhancement are asymmetry of the cambered wing and amplification effects of wing area-changing and wing bending. Lift and thrust are generated mainly during downstroke, and they are almost negligible during upstroke by the integrated morphing model-wing.

Fluid flow and fluid shear stress in canaliculi induced by external mechanical loading and blood pressure oscillation

Shulun LIU, Fan WANG, Renhuai LIU

2015, 36(5):  681-692.  doi:10.1007/s10483-015-1932-7

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The paper studies the problem of fluid flow and fluid shear stress in canaliculi when the osteon is subject to external mechanical loading and blood pressure oscillation. The single osteon is modeled as a saturated poroelastic cylinder. Solid skeleton is regarded as a poroelastic transversely isotropic material. To get near-realistic results, both the interstitial fluid and the solid matrix are regarded as compressible. Blood pressure oscillation in the Haverian canal is considered. Using the poroelasticity theory, an analytical solution of the pore fluid pressure is obtained. Assuming the fluid in canaliculi is incompressible, analytical solutions of fluid flow velocity and fluid shear stress with the Navier-Stokes equations of incompressible fluid are obtained. The effect of various parameters on the fluid flow velocity and fluid shear stress is studied.