应用数学和力学

2003 Vol. 24, No. 4

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A Numerical Method for Fractional Integral With Applications

ZHU Zheng-you, LI Gen-guo, CHENG Chang-jun

2003, 24(4): 331-341.

Abstract(2801) PDF(895)

Abstract:
A new numerical method for the liactional integral that only stores part history data is preseated, and its discretization error is estimated.The method can be used to solve the integno-diffemntial equation including fiactional integral or fractional derivative in a long history.The difficulty of storing all history data is overcoane and the error can be controlled. As application, motion equations goverring the dynandcal behavior of a viscoelastic Timoshenko beam with fractional derivative constitutiverelation are gniven.The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables metiwd. Then the new numerical method is used to solve a class of wealdy singular Voltena integro-differential equations which are applied to descaibe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmeiical results are compared.It is foiurd that they are very close.

A Theoretical Modelling of the Chain Structure Formation in Electrorheological Fluids

LIU Yu-lan, WANG Biao, WANG Dian-fu

2003, 24(4): 342-350.

Abstract(2368) PDF(592)

Abstract:
A model was developed to understand the aggregation process of the particles in electrorheological(ER) fluids under the action of an applied electric field. By establishing a generalized virtual work principle based on the consideration that the released electromagnetic energy accompatlying the growth of the chain should equal to the dissipated energy related with friction resistance of the coos fluid in the chain formation, the governing differential equation of the chain growth was established.Based on this energy model,the velocity of the chain forming,and the response time of ER fluid can be predicted. The present model can also predict the effect of the temperature and some microshvctural parameters, such as the dielectric constants and concentration of the particles, etc.,on the response of an ER system.

Controlling Hyperchaos in Planar Systems by Adjusting Parameters

YANG ling, LIU Zeng-rong, MAO Jian-min

2003, 24(4): 351-356.

Abstract(2246) PDF(490)

Abstract:
For the two-parameter family of planar mapping, a method to stabilize an unstable fixed point without stable manifold embedding in hypetvhaos is introduced. It works by acjjusting the two parameters in each iteration of the map. The explicit expressions for the parameter a}ustments are derived,and strict proof of convergence for method is given.

Postbuckling of Pressure-Loaded Shear Deformable Laminated Cylindrical Panels

SHEN Hui-shen

2003, 24(4): 357-366.

Abstract(2573) PDF(611)

Abstract:
A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity.The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling,which includes the effects of nonlinear prebuckling deformstions, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure.A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illusttations concern the postbuckling response of perfect and imperfect, moderately thick, cross-ply laminated cylindrical panels. The effects played by transverse shear deformation,panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.

Nonlinear Bending of Corrugated Diaphragm With Large Boundary Corrugation Under Compound Load

YUAN Hong, LIU Ren-huai

2003, 24(4): 367-372.

Abstract(2353) PDF(658)

Abstract:
By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a non-deformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the comigated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so-called interpolated parameter important to prevent divergence is introduced into the iterative format. Computation shows that when loads are small, any, value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate; when loads are large,interpolated parameter cannot be taken too large in order to assure convergence. The characteristic curves of the comugated diaphragm for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.

Research for the Strain Energy Release Rate of Complex Cracks by Using Point-by-Point Closed Extrapolation Approach

GUO Mao-lin, MENG Qing-yuan, WANG Biao

2003, 24(4): 373-377.

Abstract(2563) PDF(506)

Abstract:
A new extrapolation approach was proposed to calculate the strain energy release rates of complex cracks. The point-by-point closed method was used to calculate the closed energy, thus the disadvantage of self-inconsistency in some published papers can be avoided.The disadvantage is that the closed energy is repeatedly calculated: when closed nodal number along radial direction is more than two,the displacement of nodes behind the crack tip that is multiplied by nodal forces,the closed energy has been calculated and the crack surfaces have been closed, and that closed energy of middle point is calculated repeatedly.A DCB(double cantilever beam) specimen was calculated and compared with other theoretical results,it is shown that a better coincidence is obtained.In addition the same resalts are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen.ln comparison with theoretical results,the error can be limited within 1 per cent.This method can be extended to analyze the fiacture of composite laminates with various delamination cracks.

The Effect of an Elastic Triangular Inclusion on a Crack

JIAO Gui-de, WANG Yin-bang

2003, 24(4): 378-384.

Abstract(2230) PDF(532)

Abstract:
The interaction between an elastic triangular inclusion and a crack is investigated. The problem is formulated using the boundary integral equations for traction boundary value problems derived by Chau and Wang as basic equations. By using the continuity condition of traction and displacement on interface as supplement equations, a set of equations for solving the interaction problem between an inclusion and a crack are obtained, which are solved by using a new boundary element method.The results in terms of stress intensity factors(SIFs) are caiculated for a variety of crack-inclusion arrangements and the elastic constants of the matrix and the inclusion. The results are valuable for studying new composite materials.

Chaotic Attitude Motion of a Magnetic Rigid Spacecraft

CHEN Li-qun, LIU Yan-zhu

2003, 24(4): 385-390.

Abstract(2841) PDF(533)

Abstract:
Chaotic attitude motion of a magnetic rigid spacecraft in a circular orbit of the earth is treated.The dynamical model of the problem was derived from the law of moment of momentum.The Melnikov analysis was carried out to prove the e}dstence of a complicated nonwandering Cantor set.The dynamical behaviors were numerically investigated by means of time history, Poincare map, power spectrum and Liapunov exponents.Numerical simulations indicate that the onset of chaos is characterized by break of torus as the increase of the tongue of the magnetic forces.

Almost Disturbance Decoupling for a Class of Minimum-Phase Higher-Order Cascade Nonlinear Systems

BI Wei-ping, MU Xiao-wu, IIN Lan

2003, 24(4): 391-397.

Abstract(2120) PDF(468)

Abstract:
The problem of almost disturbance decoupling (ADD) with internal stability is discussed,for a class of high-order cascade nonlinear systems having zero dynamics.Using adding power integeator techniques, the ADD problems via a static state feedback is solved.

Parameters Identification in Offshore Platform Using ARMA Model and Technology of Extracting Free Vibration Signal

OU Jin-ping, HE Lin, XIAO Yi-qing

2003, 24(4): 398-404.

Abstract(2386) PDF(729)

Abstract:
A procedure for identifying the dynamic parameter of offshore platform is presented. The present procedure consists of two key features.Fist uses random decrement (RD) technology to extract free vlbration signal in strong noise environment in which it may not white noise. Second technology which called autoregressive moving average (ARMA) is used to model the data treated by the random decrement method.In order to get rid of the color noise in the output signal response from the offshore platform an imaginary system is added in RD system and make the course of extracting performed under the state of color input by choosing the breakover condition and lead time. For elintinating multi-values of parameters identified, an updating moving average method is used. The dynamic parameters of structure under arbitrary input are identigied.Example of the method as applied to a scale-model offshore platform is used to evaluate the technology of efffciency and the value of on-line.

Maximum Principles for Greneralized Solutions of Quasi-Linear Elliptic Equations

WANG Xiang-dong, XU Xiao-zeng, HANG Xi-ting

2003, 24(4): 405-413.

Abstract(2430) PDF(504)

Abstract:
Under the assumption that the growth order of the free team to natural growth condition with respect to gradient of the generalized solutions the maximum principle is proved for the bounded generalized solutiom of quasi-linear elliptic equations.

Form Invariance and Noether Symmetrical Conserved Quantity of Relativistic Birkhoffian Systems

LUO Shao-kai

2003, 24(4): 414-422.

Abstract(2775) PDF(679)

Abstract:
A form invariance of the relativistic Birlchoffian system is studied,and the conserved quantities of the system are obtained. Under the infinitesimal transformation of groups, the definition and criteria of the form invariance of the system were given. In view of the invariance of relativistic Pfaff-Birkhoff-D'Alembert principle under the infinitesimal transformation of groups, the theory of Noether symmetries of the relativistic Birkhoffian system were consttvcted. The relation between the form invariance and the Noether symmetry is studied, and the results show that the form invariance can also lead to the Noether symmetrical conserved quantity of the relativistic Birlchoffian system under certain conditions.

Existence of Bounded Solutions on the Real line for Lienard System

XIAO Hai-bin

2003, 24(4): 423-433.

Abstract(2228) PDF(452)

Abstract:
The existence of monotone and non-monotone solutions of boundary value problem on the real line for Liénard equation is studied.Applying the theory of planar,dymamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained.Espeaaly,when the source function is bi-stable,tiie existence of infinitely many monotone solusion is obteained.

Random Variable With Fuzzy Probability

LÜ En-lin, ZHONG You-ming

2003, 24(4): 434-440.

Abstract(2394) PDF(588)

Abstract:
Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem,the feasible condition about a probability fuzzy number set was given,go a step further the definition and characters of random variable with fuzzy probability(RVFP) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward.The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability,as a result,山e foundation of perfecting fuzzy probability operation method is laid.