Waves induced by a submerged moving dipole in a two-layer fluidof finite depth

The waves induced by a moving dipole in a two-fluid system are analytically and experimentally investigated. The velocity potential of a dipole moving horizontally in the lower layer of a two-layer fluid with finite depth is derived by superposing Greens functions of sources (or sinks). The far-field waves are studied by using the method of stationary phase. The effects of two resulting modes, i.e. the surface- and internal-wave modes, on both the surface divergence field and the interfacial elevation are analyzed. A laboratory study on the internal waves generated by a moving sphere in a two-layer fluid is conducted in a towing tank under the same conditions as in the theoretical approach. The qualitative consistency between the present theory and the laboratory study is examined and confirmed.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

Fission and Fusion of Localized Coherent Structures for a Higher-Order Broer-Kaup System

Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more generalexpression of solution that includes some variable separated functions for the higher-order Broer-Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.

CAVITY FORMATION AND ITS VIBRATION FOR A CLASS OF GENERALIZED INCOMPRESSIBLE HYPER-ELASTIC MATERIALS

The problem of radial symmetric motion for a solid sphere composed of a class of generalized incompressible neo-Hookean materials, subjected to a suddenly applied surface tensile dead load, is examined.The analytic solutions for this problem and the motion equation of cavity that describes cavity formation and growth with time are obtained. The e?ect of radial perturbation of the materials on cavity formation and its motion is discussed. The plane of the perturbation parameters of the materials is divided into four regions. The existential conditions and qualitative properties of solutions of the motion equation of the cavity are studied in di?erent parameters’ regions in detail. It is proved that the cavity motion with time is a nonlinear periodic vibration. The vibration center is then determined.

A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

QUALITATIVE ANALYSIS OF SPHERICAL CAVITY NUCLEATION AND GROWTH FOR INCOMPRESSIBLE GENERALIZED VALANIS-LANDEL HYPERELASTIC MATERIALS

A cavitated bifurcation problem is examined for a sphere composed of a class of generalized Valanis-Landel materials subjected to a uniform radial tensile dead-load. A cavitated bifurcation equation is obtained. An explicit formula for the critical value associated with the vari- ation of the imperfection parameters is presented. The distinguishing between the left-bifurcation and right-bifurcation of the nontrivial solution of the cavitated bifurcation equation at the critical point is made. It is proved that there exists a secondary turning bifurcation point on the nontrivial solution branch, which bifurcates locally to the left. It is shown that the dimensionless cavitated bifurcation equation is equivalent to normal forms with single-sided constraint conditions at the critical point by using the singularity theory. The stability and catastrophe of the solutions of the cavitated bifurcation equation are discussed.

GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline ma- terial with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given. Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.

Nonpropagating Solitons in （2＋1）-Dimensional Dispersive Long-Water Wave System

With the help of an extended mapping approach, a new type of variable separation excitation with three arbitrary functions of the (2+1)-dimensional dispersive long-water wave system (DLW) is derived. Based on the derived variable separation excitation, abundant non-propagating solitons such as dromion, ring, peakon, and compacton etc.are revealed by selecting appropriate functions in this paper.

A Modified Sensitive Driving Cellular Automaton Model

A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel-Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model,in which the randomization brake is arranged before the deterministic deceleration. A parameter related to the variable security gap is determined through simulation. Comparison of the simulation results indicates that the variable security gap has different influence on the two models. The fundamental diagram obtained by simulation with the modified sensitive driving NaSch model shows that the maximumflow are in good agreement with the observed data, indicating that the presented model is more reasonable and realistic.

A New Class of （2＋1）-Dimensional Localized Coherent Structures with CompletelyElastic and Non-elastic Interactive Properties

From the variable separation solution and by selecting appropriate functions, a new class of localized coherent structures consisting of solitons in various types are found in the (2+1)-dimensional long-wave-short-wave resonance interaction equation. The completely elastic and non-elastic interactive behavior between the dromion and compacton, dromion and peakon, as well as between peakon and compacton are investigated. The novel features exhibited by these new structures are revealed for the first time.

Lie Symmetries and Non-Noether Conserved Quantities of Nonholonomic Systems

A new conservation theorem of the nonholonomic systems is studied. The conserved quantity is onlyconstructed in terms of a general Lie group of transformation vector of the dynamical equations. Firstly, we establish thedynamical equations of the nonholonomic systems and the determining equations of Lie symmetry. Next, the theore mof non-Noether conserved quantity is deduced. Finally, we give an example to illustrate the application of the result.

GENERALIZED VARIATIONAL PRINCIPLES FOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

CONSTRAINT VIOLATION STABILIZATION OF EULER-LAGRANGE EQUATIONS WITH NON-HOLONOMIC CONSTRAINTS

Two constraint violation stabilization methods are presented to solve the Euler Lagrange equations of motion of a multibody system with nonholonomic constraints. Compared to the previous works, the newly devised methods can deal with more complicated problems such as those with nonholonomic constraints or redundant constraints, and save the computation time. Finally a numerical simulation of a multibody system is conducted by using the methods given in this paper.

Solitary Wave and Periodic Wave Solutions for the Relativistic Toda Lattices

In this work, an adaptation of the tanh/tan-method that is discussed usually in the nonlinear partial differential equations is presented to solve nonlinear polynomial differential-difference equations. As a concrete example,several solitary wave and periodic wave solutions for the chain which is related to the relativistic Toda lattice are derived.Some systems of the differential-difference equations that can be solved using our approach are listed and a discussion is given in conclusion.

Semifolded Localized Structures in Three-Dimensional Soliton Systems

By means ora Painlevé-Backlund transformation and a multi-linear variable separation approach, abundant localized coherent excitations of the three-dimensional Broer-Kaup-Kupershmidt system with variable coefficients are derived. There are possible phase shifts for the interactions of the three-dimensional novel localized structures discussed in this paper.

Dynamic Stability of Viscoelastic Plates with Finite Deformation and Shear Effects

Based on Reddy's theory of plates with higher order shear deformations and the Boltzmann superposition principles, the governing equations were established for dynamic stability of viscoelastic plates with finite deformations taking account of shear effects. The Galerkin method was applied to simplify the set of equations. The numerical methods in nonlinear dynamics were used to solve the simplified system. It could be seen that there are plenty of dynamic properties for this kind of viscoelastic plates under transverse harmonic loads. The influences of the transverse shear deformations and material parameter on the dynamic behavior of nonlinear viscoelastic plates were investigated.

Applications of Extended Mapping Deformation Method in Two （3＋1）-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.

DYNAMICAL FORMATION OF CAVITY IN TRANSVERSELY ISOTROPIC HYPER-ELASTIC SPHERES

The cavity formation in a radial transversely isotropic hyper-elastic sphere of an incompressible Ogden material, subjected to a suddenly applied uniform radial tensile boundary deadload, is studied following the theory of finite deformation dynamics. A cavity forms at the center of the sphere when the tensile load is greater than its critical value. It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillations.