Applied Mathematics and Mechanics (English Edition)

Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

夏乐章朱克勤

2011, 32(11): 1357-1366. doi:10.1007/s10483-011-1506-x

摘要 ( 753 )

PDF (675KB) ( 540 )

相关文章 | 多维度评价

A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.

MHD effects on free convective flow over moving semi-infinite vertical cylinder with temperature oscillation

P.LOGANATHAN M.KANNAN P.GANESAN

2011, 32(11): 1367-1376. doi:10.1007/s10483-011-1507-6

摘要 ( 1103 )

PDF (451KB) ( 508 )

相关文章 | 多维度评价

Numerical solutions of magnetodynamics (MHD) effects on the free convective flow of an incompressible viscous fluid past a moving semi-infinite vertical cylinder with temperature oscillation are presented. The dimensionless, unsteady, non-linear, and coupled governing partial differential equations are solved by using an implicit finite difference method of the Crank-Nicolson type. The velocity, temperature, and concentration profiles are studied for various parameters. The local skin-friction, the average skinfriction, the Nusselt number, and the Sherwood number are also analyzed and presented graphically. The results are compared with available results in literature, and are found to be in good agreement.

Effect of residual interface stress on effective thermal expansion coefficient of particle-filled thermoelastic nanocomposite

黄汝超陈永强

2011, 32(11): 1377-1388. doi:10.1007/s10483-011-1508-9

摘要 ( 685 )

PDF (363KB) ( 520 )

相关文章 | 多维度评价

The surface/interface energy theory based on three configurations proposed by Huang et al. is used to study the effective properties of thermoelastic nanocomposites. The particular emphasis is placed on the discussion of the influence of the residual interface stress on the thermal expansion coefficient of a thermoelastic composite filled with nanoparticles. First, the thermo-elastic interface constitutive relations expressed in terms of the first Piola-Kirchhoff interface stress and the Lagrangian description of the generalized Young-Laplace equation are presented. Second, the Hashin’s composite sphere assemblage (CSA) is taken as the representative volume element (RVE), and the residual elastic field induced by the residual interface stress in this CSA at reference configuration is determined. Elastic deformations in the CSA from the reference configuration to the current configuration are calculated. From the above calculations, analytical expressions of the effective bulk modulus and the effective thermal expansion coefficient of thermoelastic composite are derived. It is shown that the residual interface stress has a significant effect on the thermal expansion properties of thermoelastic nanocomposites.

Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation

金肖玲黄志龙梁以德

2011, 32(11): 1389-1398. doi:10.1007/s10483-011-1509-7

摘要 ( 795 )

PDF (785KB) ( 403 )

相关文章 | 多维度评价

The nonstationary probability densities of system response of a single-degreeof-freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied. Using the stochastic averaging method based on the generalized harmonic functions, the averaged Fokker-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. According to the Galerkin method, the time-dependent coefficients can be solved from a set of first-order linear differential equations. Then, the semi-analytical formulae of the nonstationary probability density of the amplitude response as well as the nonstationary probability density of the state response and the statistic moments of the amplitude response can be obtained. A van der Pol-Duffing oscillator subject to modulated white noise is given as an example to illustrate the proposed procedures. The effects of the system parameters, such as the linear damping coefficient and the nonlinear stiffness coefficient, on the system response are discussed.

Exact solutions of two semi-infinite collinear cracks in piezoelectric strip

卢子兴刘萍郭俊宏

2011, 32(11): 1399-1406. doi:10.1007/s10483-011-1510-9

摘要 ( 865 )

PDF (252KB) ( 596 )

相关文章 | 多维度评价

Using the complex variable function method and the conformal mapping technique, the fracture problem of two semi-infinite collinear cracks in a piezoelectric strip is studied under the anti-plane shear stress and the in-plane electric load on the partial crack surface. Analytic solutions of the field intensity factors and the mechanical strain energy release rate are derived under the assumption that the surfaces of the crack are electrically impermeable. The results can be reduced to the well-known solutions for a purely elastic material in the absence of an electric load. Moreover, when the distance between the two crack tips tends to infinity, analytic solutions of a semi-infinite crack in a piezoelectric strip can be obtained. Numerical examples are given to show the influence of the loaded crack length, the height of the strip, the distance between the two crack tips, and the applied mechanical/electric loads on the mechanical strain energy release rate. It is shown that the material is easier to fail when the distance between two crack tips becomes shorter, and the mechanical/electric loads have greater influence on the propagation of the left crack than those of the right one.

Convergence and exact solutions of spline finite strip method using unitary transformation approach

J.KONG D.THUNG

2011, 32(11): 1407-1422. doi:10.1007/s10483-011-1511-9

摘要 ( 820 )

PDF (303KB) ( 611 )

相关文章 | 多维度评价

The spline finite strip method (FSM) is one of the most popular numerical methods for analyzing prismatic structures. Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems. To date, no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such, in this paper, the mathematical exact solutions of spline finite strips in the plate analysis are derived using a unitary transformation approach (abbreviated as the U-transformation method herein). These exact solutions are presented for the first time in open literature. Unlike the conventional spline FSM which involves assembly of the global matrix equation and its numerical solution, the U-transformation method decouples the global matrix equation into the one involving only two unknowns, thus rendering the exact solutions of the spline finite strip to be derived explicitly. By taking Taylor’s series expansion of the exact solution, error terms and convergence rates are also derived explicitly and compared directly with other numerical methods. In this regard, the spline FSM converges at the same rate as a non-conforming finite element, yet involving a smaller number of unknowns compared to the latter. The convergence rate is also found superior to the conventional finite difference method.

Propagation of harmonic waves through micro gap with consideration of frictional contact

陈小云于桂兰

2011, 32(11): 1423-1436. doi:10.1007/s10483-011-1512-7

摘要 ( 670 )

PDF (603KB) ( 463 )

相关文章 | 多维度评价

Transmission of elastic waves through a micro gap between two solids with consideration of frictional contact is investigated. By using the Fourier analysis technique and the corrective solution method, the nonlinear boundary problem is reduced to a set of algebraic equations. Numerical results exhibit the locations and extents of separation, slip, and stick zones, the interface tractions, and the energy partition. The effects of gap width, frictional coefficients, and the incident angle on the wave transmission are discussed in detail. The results show that higher harmonics are generated due to the local contact/slip at the interface.

Separation work analysis of cohesive law and consistently coupled cohesive law

何铭华辛克贵

2011, 32(11): 1437-1446. doi:10.1007/s10483-011-1513-x

摘要 ( 835 )

PDF (442KB) ( 645 )

相关文章 | 多维度评价

An appropriate coupled cohesive law for predicting the mixed mode failure is established by combining normal separation and tangential separation of surfaces in the cohesive zone model (CZM) and the cohesive element method. The Xu-Needleman exponential cohesive law with the fully shear failure mechanism is one of the most popular models. Based on the proposed consistently coupled rule/principle, the Xu-Needleman law with the fully shear failure mechanism is proved to be a non-consistently coupled cohesive law by analyzing the surface separation work. It is shown that the Xu-Needleman law is only valid in the mixed mode fracture when the normal separation work equals the tangential separation work. Based on the consistently coupled principle and the modification of the Xu-Needleman law, a consistently coupled cohesive (CCC) law is given. It is shown that the proposed CCC law has already overcome the non-consistency defect of the Xu-Needleman law with great promise in mixed mode analyses.

Self-similar solutions to Lin-Reissner-Tsien equation

J.HAUSSERMANN K.VAJRAVELU R.A.VAN GORDER

2011, 32(11): 1447-1456. doi:10.1007/s10483-011-1514-6

摘要 ( 771 )

PDF (214KB) ( 475 )

相关文章 | 多维度评价

The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

丁协平

2011, 32(11): 1457-1474. doi:10.1007/s10483-011-1515-x

摘要 ( 975 )

PDF (252KB) ( 551 )

相关文章 | 多维度评价

A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems (GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

罗志强陈志敏

2011, 32(11): 1475-1488. doi:10.1007/s10483-011-1516-6

摘要 ( 896 )

PDF (1512KB) ( 588 )

相关文章 | 多维度评价

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.

Retraction note: Similarity solutions for creeping flow and heat transfer in second grade fluid

AMM

2011, 32(11): 1489-1490. doi:10.1007/s10483-011-1517-x

摘要 ( 514 )

PDF (41KB) ( 395 )

相关文章 | 多维度评价

Retraction: Muhammet Y¨ur¨usoy. Similarity solutions for creeping flow and heat transfer in second grade fluid. Applied Mathematics and Mechanics (English Edition), 25(4), 467–474 (2004) DOI: 10.1007/BF02437531
This article is retracted because of duplicate publication.

当期目录