Abstract: The discretization size is limited by the sampling theorem,the limit is 1/2 of the wavelength of highest frequency of the problem. The 1/2 of the wavelength is an ideal value,in general,the discretization size which could ensure the accuracy of the simulation is much smaller than this value in the traditional finite element method. The possible reason of the phenomena was analyzed. An efficient method was given to improve the accuracy of the simulation.
Abstract: On the basis of the theory of Timoshenko beam,taking into account finite-deflection and axial inertia,the nonlinear partial differential equations governing flexural waves in a beam were derived.When employing the method of the traveling wave solution,the nonlinear partial differential equations can be transformed into an ordinary differential equation by using certain integral skills.The qualitative analysis indicates that the corresponding dynamic system has heteroclinic orbit under certain condition.The exact periodic solution of nonlinear wave equation was obtained by means of Jacobi elliptic function expansion.When the modulus of Jacobi elliptic function m → 1 in the degenerate case,the shock wave solution was given.Further,small perturbations arising from damping and external load to original Hamilton's system are introduced and the threshold condition of the existence of transverse heteroclinic point is obtained by Melnikov's method.It is proved from this that the perturbed system has chaotic property under Smale horseshoe transform.
Abstract: Vibration mode of constrained damping cantilever was built up according to elastic cantilever beam mode superposition.Then the control equation of constrained damping cantilever beam was derived by using Lagrange's equation.Dynamic response of the constrained damping cantilever beam was obtained according to the principle of virtual work,when the concentrated force was suddenly unloaded.Frequencies and transient response of a series of constrained damping cantilever beam were calculated and tested.The influence of parameters of the damping layer on the response time was analyzed.Resolution and experimental approach are considered.The results show that this method is reliable.
Abstract: The wave propagation problem in nonlinear periodic mass-spring structure chain was analyzed using the symplectic mathematical method. Firstly the energy method was applied to construct the dynamical equation and then the nonlinear dynamical equation was linearized using the small parameter perturbation method. The eigen-solutions of the symplectic matrix were applied to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain,arising from the nonlinear spring stiffness effect,has profound effects on the overall transmission of the chain. The wave propagation characteristics are not only altered due to the nonlinearity but also related with the incident wave intensity, which is a genuine nonlinear effect that is not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to a closing of the transmitting gaps. Comparison with the normal recursive approach demonstrates the effectiveness and superiority of the symplectic method in wave propagation problem for nonlinear periodic structures.
Abstract: The Painlev? integrability and exact solutions of a coupled nonlinear Schrödinger (CNLS) equation applied in atmospheric dynamics were discussed. Some parametric restrictions of the CNLS equation were given to pass the Painlevé test. 20 periodic cnoidal wave solutions were obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions of the CNLS equation are applied to explain the generation and propagation of atmospheric gravity waves.
Abstract: The theoretical investigation of a fundamental problem of flow of a biomagnetic fluid through a porous medium subjected to a magnetic field by using the principles of Biomagnetic Fluid Dynamics (BFD) was dealt with. The study pertains to a situation where magnetization of the fluid varies with temperature. The fluid was considered to be non-Newtonian,its flow being governed by the equation of a second-grade fluid,which takes into account the effect of fluid visco-elasticity. The walls of the channel were assumed to be stretchable,where the surface velocity was proportional to the longitudinal distance from the origin of coordinates. The problem was first reduced to that of solving a system of coupled nonlinear differential equations that involve seven parameters. Considering blood as a biomagnetic fluid and using the present analysis,an attempt had been made to compute some parameters of blood flow,by developing a suitable numerical method and by devising an appropriate finite difference scheme. The computational results were presented in graphical form and thereby some theoretical predictions were made in respect of the hemodynamical flow of blood in a hyperthermal state,under the action of a magnetic field. The results reported here clearly indicate that presence of a magnetic dipole bears the potential to affect the characteristics of blood flow in arteries to a significant extent during the therapeutic procedure of electromagnetic hyperthermia. The study should attract the attention of clinicians and the results should be useful to them in their treatment of cancer patients by the method of electromagnetic hyperthermia.
Abstract: The unsteady viscous flow over a continuously permeable shrinking surface was studied. Similarity equations were obtained through the application of similarity transformation techniques. Numerical techniques were used to solve the similarity equations for different values of the unsteadiness parameter, the mass suction parameter,the shrinking parameter and Prandtl number on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. Different from an unsteady stretching sheet,it is found that dual solutions exist for a certain range of mass suction and unsteadiness parameters.
Abstract: Based on domain decomposition,a parallel two-level finite element method for the stationary Navier-Stokes equations was proposed and analyzed. The basic idea of the method was to first solve the Navier-Stokes equations on a coarse grid,then to solve the resulted residual equations in parallel on a fine grid. This method has low communication complexity. It can be implemented easily. By local a priori error estimate for finite element discretizations,error bounds of the approximate solution were derived. Numerical results were also given to illustrate the high efficiency of the method.
Abstract: A new method of nonconforming local projection stabilization for the generalized Oseen equations was proposed by a nonconforming inf-sup stable element pair for approximating the velocity and pressure. The method has several attractive feature. It adds an local projection term only on the sub-scale (H ≥h). The stabilized term is simple compared with the residual-free bubble element method can handle the influence of strong convection. The numerical illustrations agree with the theoretical expectation very well.
Abstract: Regularity and finite dimensionality of global attractor for plate equation on unbounded domain Rn were studied. Existence of the attractor inphase space H2(Rn)×L2 (Rn) was established in the author's earlier paper. It is showed that the attractor is actually a bounded set of H4 (Rn)×H2(Rn) and has finite fractal dimensionality.
Abstract: A precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end was presented. Firstly,the interval was divided evenly,then a set of algebraic equations in the form of matrix by the precise integration relationship of each segment was given. Substituting the boundary conditions into the algebraic equations,the coefficient matrix could be transformed to the form of block tridiagonal matrix. Combining the special nature of the problem,an efficient reduction method for singular perturbation problems was given. Since the precise integration relationship gives no discrete error in the discrete process,the present method has very high precision. Numerical examples show the validity of the present method.