应用数学和力学

2007 Vol. 28, No. 10

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Stable Response of the Low-Gravity Liquid Non-Linear Sloshing in a Circle Cylindrical Tank

HE Yuan-jun, MA Xing-rui, WANG Ben-li

2007, 28(10): 1135-1145.

Abstract(2816) PDF(913)

Abstract:
Under pitch excitation,the sloshing of liquid in circular cylindrical tank includes planar motion,rotary motion and rotary motion inside planar motion.The boundaries between stable motion and unstable motion depend on the radius of the tank,the liquid height,the gravitational intension,the surface tensor and the sloshing damping.The differential equations of nonlinear sloshing are built first.And by variational principle,the Lagrange function of liquid pressure is constructed in volume intergration form.Then the velocity potential function is expanded in series by wave height function at the free surface.The nonlinear equations with kinematics and dynamics free surface boundary conditions through variation are derived.At last,these equations are solved by multiple-scales method.The influence of Bond number on the global stable response of nonlinear liquid sloshing in circular cylinder tank is analyzed in detail.Variations of amplitude frequency response characteristics of the system with Bond,jump,lag and other nonlinear phenomena of liquid sloshing are investigated.

On the Strong Convergence Theorems for Nonexpansive Semi-Groups in Banach Spaces

ZHANG Shi-sheng, YANG Li, LIU Jing-ai

2007, 28(10): 1146-1156.

Abstract(2703) PDF(931)

Abstract:
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established.The results not only extend and improve the corresponding results of Shioji-Takahashi,Suzuki,Xu and Aleyner-Reich,but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.

Dynamic Equations of Curved Submerged Floating Tunnel

DONG Man-sheng, GE Fei, ZHANG Shuang-yin, HONG You-shi

2007, 28(10): 1157-1165.

Abstract(3008) PDF(804)

Abstract:
In virtue of reference Cartesian coordinates,geometrical relations of spatial curved structure were presented in orthogonal curvilinear coordinates.Dynamic equations for helical girder were derived by Hamilton principle.These equations indicate that four generalized displacements are coupled with each other.When spatial structure degenerates into planar curvilinear structure,two generalized displacements in two perpendicular planes are coupled with each other.Dynamic equations for arbitrary curvilinear structure may be obtained by the method used.

Reflection for Three-Dimensional Plane Waves in Triclinic Crystalline Medium

A. Chattopadhyay

2007, 28(10): 1166-1174.

Abstract(2699) PDF(754)

Abstract:
The propagation of three-dimensional plane waves at a traction free boundary of a halfspace composed of triclinic crystalline material is discussed.A method has been developed t o find the analytical expressions of all the three phase velocities of quasi P(qP),quasi SV(qSV) and quasi SH (qSH) in three-dimensions.Closed form expressions in three-dimensions for the amplitude ratios of reflection coefficients of qP,qSV and qSH waves in a triclinic medium were obtained.These expressions are used for studying numerically the variation of the reflection coefficients with the angle of incidence.The graphs were drawn for different polar angle and azimuth.Numerical results presented indicate that the anisotropy affect the reflection coefficients significantly in three-dimensional case compared to two-dimensional case.

Dynamic Stability of Viscoelastic Circular Cylindrical Shells Taking Into Account Shear Deformation and Rotatory Inertia

B. Kh. Eshmatov

2007, 28(10): 1175-1184.

Abstract(3110) PDF(695)

Abstract:
The problem of dynamic stability of a viscoelastic circular cylindrical shell was discussed accor ding to Timoshenko revised theory,with a ccount of shear de formation and rotatory inertia in the geometrically nonlinear statement.Proceeding by Bubnov-Galerkin method in combination with numerical method based on the quadrature formula the problem was reduced to a solution of a system of nonlinear integro-differential equations with singular kernel of relaxation.For wide range of variation of physical-mechanical and geometrical parameters,dynamic behavior of the shell was studied.The influence of visco elastic properties of the material on the dynamical stability of the circularcy lindrical shell is shown.Results obtained using different theories are compared.

Diffusion Approximations for Multiclass Queueing Networks Under Preemptive Priority Service Discipline

DAI Wan-yang

2007, 28(10): 1185-1196.

Abstract(2485) PDF(860)

Abstract:
A heavy traffic limit theorem is proved to justify diffusion approximations for multiclass queueing networks under preemptive priority service discipline and provide effective stochastic dynamical models for the systems.Such queueing networks typically appear in high-speed integrated services packet networks in telecommunication system.In the network,there are a number of packet traffic types.Each type needs a number of job classes (stages) of processing and each type of jobs is assigned the same priority rank at every station where it possibly receives service.Moreover,there is no inter-routing among different traffic types throughout the entire network.

Singularly Perturbed Soluton for Weakly Nonlinear Equations With Two Parameters

CHEN Li-hua, MO Jia-qi

2007, 28(10): 1197-1202.

Abstract(2780) PDF(1033)

Abstract:
A class of singularly perturbed boundary value problem of weakly nonlinear equation for fourth order on the finite interval with two parameters is considered.Under suitable conditions,firstly,using the expansion method of power series,the reduced solution and formal outer solution are constructed.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near the left endpoint is constructed which possesses exponential attenuation behavior.And then,using the stronger transformation of stretched variable,the second boundary layer corrective term near the left endpoint is constructed too,which also possesses exponential attenuation behavior.The thickness of second boundary layer smaller than first boundary layer and forms the cover layer near the left endpoint.Finally,using the theory of differential inequalities the existence,uniform validity in the whole interval and asymptotic behavior of solution for the original boundary value problem are proved.The satisfying results are obtained.

Dynamic Analysis of a Rotating Rigid-Flexible Coupled Smart Structure With Large Deformations

HUANG Yong-an, DENG Zi-chen, YAO Lin-xiao

2007, 28(10): 1203-1212.

Abstract(2938) PDF(896)

Abstract:
Based on Hamilton.s principle,a new kind of fully coupled nonlinear dynamic model for a rotating rigid-flexible smart structure with a tip mass is proposed.The geometrically nonlinear effects of the axial,transverse displacement and rotation angle are considered by means of the first-order approximation coupling (FOAC) model theory,in which the large deformations and the centrifugal stiffening effects are considered.Three kinds of systems are established respectively,which are a structure without piezoelectric layer,with piezoelectric layer in open circuit and closed circuit.Several simulations based on simplified models are presented to show the differences in characteristics between structures with and without the tip mass,between smart beams in closed and open circuit,and between the centrifugal effects in high speed rotating state or not.The last simulation calculates the dynamic response of the structure subjected to external electrical loading.

L-leaping:Accelerating the Stochastic Simulation of Chemically Reacting Systems

PENG Xin-jun, WANG Yi-fei

2007, 28(10): 1213-1222.

Abstract(2302) PDF(792)

Abstract:
Presented here is an L-leap method for accelerating stochastic simulation of well stirred chemically reacting systems,in which the number of reactions occurring of a reaction channel with the largest propensity function is calculated from the leap condition and the numbers of reactions occurring of the other reaction channels are generated by using binomial random variables during a leap.The L-leap method can better satisfy the leap condition.Numerical simulation results indicate that the L-Leap method can obtain better perfor mance than established methods.

Infinitely Many Solutions of p-Laplacian Equations With Limit Sub-Critical Growth

GENG Di

2007, 28(10): 1223-1231.

Abstract(2662) PDF(1205)

Abstract:
A class of p-Laplacian boundary problem on a bounded smooth domain was discussed.The nonlinearity is odd symmetric and limit sub-critical gro wth at infinite.A sequence of critical values of the variational functional was constructed after the generalized Palais-Smale condition was verified.It is obtained that the problem possesses infinitely many solutions and corresponding energy levels of the functional pass to positive infinite.The result is a generalization of the similar problem in case of subcritical.

Non-Axisymmetrical Vibration of Elastic Circular Plate on Layered Transversely Isotropic Saturated Ground

WANG Xiao-gang

2007, 28(10): 1232-1244.

Abstract(2479) PDF(766)

Abstract:
The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground is studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soil were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth,and the state equation was established by Hankel integral transform method,furthermore the transfer matrixes within layered media were derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions,drainage conditions on the surface of ground as well as the contact conditions.Thirdly,the problem was led to a pair of dual integral equations describing the mixed boundary-value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end,a numerical result concerning vertical and radical displacements of both the surface of saturated ground and plate was evaluated.

A New Matrix Method for Response Analysis of Circumferentially Stiffened Non-Circular Cylindrical Shells Under Harmonic Pressure

ZHOU Shi-zhi, HUANG Yu-ying, HE Zeng, XIANG Yu

2007, 28(10): 1245-1252.

Abstract(2800) PDF(853)

Abstract:
Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order,a new matrix method is presented for steady state vibration analysis of a non-circular cylindrical shell simply supported at two ends and circumferentially stiffened by rings under harmonic pressure.Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration approach rather than the Runge-Kutta-Gill integration method.The transfer matrix can easily be determined by a high precision integration scheme.In addition,besides the normal interacting forces,which were commonly adopted by researchers before,the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function.The effects of the exciting frequencies on displacements and stresses responses have been investigated.Numerical results show that the proposed method is more efficient than the above mentioned method.

A New Smoothing Technique for Mathematical Programs With Equilibrium Constraints

ZHU Zhi-bin, LUO Zhi-jun, ZENG Ji-wen

2007, 28(10): 1253-1260.

Abstract(2616) PDF(917)

Abstract:
A kind of mathematical programs with equilibrium constraints(MPEC) is studied.By using the idea of successive approximation,a smoothing nonlinear programming,which is equivalent to the MPEC problem,was proposed.Thereby,it is ensured that some classical optimization methods can be applied for the MPEC problem.In the end,two algorithm models were proposed with the detailed analysis of the global convergence.