Applied Mathematics and Mechanics (English Edition)

A NUMERICAL METHOD FOR FRACTIONAL INTEGRAL WITH APPLICATIONS

朱正佑;李根国;程昌钧

2003, 24(4): 373-384.

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A new numerical method for the fractional integral that only stores part history data is presented, and its discretization error is estimated. The method can be used to solve the integro-differential equation including fractional integral or fractional derivative in a long history. The difficulty of storing all history data is overcome and the error can be controlled. As application,motion equations governing the dynamical behavior of a viscoelastic Timoshenko beam with fractional derivative constitutive relation are given. The dynamical response of the beam subjected to a periodic excitation is studied by using the separation variables method. Then the new numerical method is used to solve a class of weakly singular Volterra integro-differential equations which are applied to describe the dynamical behavior of viscoelastic beams with fractional derivative constitutive relations. The analytical and unmerical results are compared. It is found that they are very close.

A THEORETICAL MODELLING OF THE CHAIN STRUCTURE FORMATION IN ELECTRORHEOLOGICAL FLUIDS

刘玉岚;王彪;王殿富

2003, 24(4): 385-395.

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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 accompanying the growth of the chain should equal to the dissipated energy related with friction resistance of the viscous 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 microstructural 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

杨凌;刘曾荣;茅坚民

2003, 24(4): 396-401.

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

POSTBUCKLING OF PRESSURE-LOADED SHEAR DEFORMABLE LAMINATED CYLINDRICAL PANELS

沈惠申

2003, 24(4): 402-413.

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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 deformations, 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 illustrations 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

袁鸿;刘人怀

2003, 24(4): 414-420.

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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 nondeformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the corrugated 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 corrugated 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

郭茂林;孟庆元;王彪

2003, 24(4): 421-426.

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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 results are also obtained for compact tension specimen, three point bend specimen and single edge cracked specimen. In comparison with theoretical results,the error can be limited within 1 per cent. This method can be extended to analyze the fracture of composite laminates with various delamination cracks.

THE EFFECT OF AN ELASTIC TRIANGULAR INCLUSION ON A CRACK

焦贵德;王银邦

2003, 24(4): 427-433.

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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 calculated 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

陈立群;刘延柱

2003, 24(4): 434-440.

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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 existence of a complicated nonwandering Cantor set. The dynamical behaviors were numerically investigated by means of time history, Poincar 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 torque of the magnetic forces.

ALMOST DISTURBANCE DECOUPLING FOR A CLASS OF MINIMUM-PHASE HIGHER-ORDER CASCADE NONLINEAR SYSTEMS

毕卫萍;慕小武;林澜

2003, 24(4): 441-448.

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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 integrator techniques, the ADD problems via a smooth static state feedback is solved.

PARAMETER IDENTIFICATION IN OFFSHORE PLATFORM USING ARMA MODEL AND TECHNOLOGY OF EXTRACTING FREE VIBRATION SIGNAL

欧进萍;何林;肖仪清

2003, 24(4): 449-457.

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A procedure for identifying the dynamic parameter of offshore platform is presented. The present procedure consists of two key features. First uses random decrement (RD) technology to extract free vibration signal in strong noise environment in which it may not white noise. Second technology which called autoregressive moving average (ARMA) was 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 eliminating multi-values of parameters identified, an updating moving average method is used. The dynamic parameters of structure under arbitrary input are identified. Example of the method as applied to a scale-model offshore platform was used to evaluate the technology of efficiency and the value of on-line.

MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

王向东;徐小增;梁(汲金)廷

2003, 24(4): 458-467.

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Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi-linear elliptic equations.

FORM INVARIANCE AND NOETHER SYMMETRICAL CONSERVED QUANTITY OF RELATIVISTIC BIRKHOFFIAN SYSTEMS

罗绍凯

2003, 24(4): 468-478.

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A form invariance of the relativistic Birkhoffian 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 constructed. 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 Birkhoffian system under certain conditions.

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

肖海滨

2003, 24(4): 479-490.

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The existence of monotone and non-monotone solutions of boundary value problem on the real line for Li閚ard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Li閚ard 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. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.

RANDOM VARIABLE WITH FUZZY PROBABILITY

吕恩琳;钟佑明

2003, 24(4): 491-498.

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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, the foundation of perfecting fuzzy probability operation method is laid.

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