Some problems of stability of propagation of non-linear waves in shells and plates

In the present paper equations of modulations taking into account the second order derivatives of amplitude and stability conditions are obtained. The general results are applied to the stability problems of propagation of quasimonochromatic waves in plates, shells, plates in contact with fluid, shells containing fluid, plate in magnetic field, tree-layered plate and viscoelastic plate.     

Some results of variational inclusion problems and fixed point problems with applications

This paper introduces a general iterative algorithm to approximate a common element in the solution set of quasi-variational inclusion problems and the common fixed point set of an infinite family of nonexpansive mappings. It is proven that the iterative sequences generated in the proposed iterative algorithm converge strongly to some common element in the framework of the real Hilbert spaces.     

顺层岩质边坡爆破的振动控制及损伤特性

为了更好地了解顺层岩质边坡爆破开挖时振动速度的传播规律以及坡体的损伤程度,以云南省普宣高速公路顺层边坡爆破开挖为工程背景,利用声波测试结合监测点振动速度的方法,获取坡体不同深度的声速变化及不同位置的振动速度,分析不同药量下单次和多次爆破的坡体损伤范围以及振动速度的衰减规律。研究表明,爆破区任意点的振动速度与损伤深度存在对应关系:对单次爆破,振动速度与损伤深度呈线性关系,而对多次爆破,振动速度与损伤深度呈非线性关系;以声速降低率10%作为损伤界限,并作为爆破控制时,单次爆破对应的临界振动速度为11.54 cm/s,损伤半径为5.57 m;,基于首次爆破的多次爆破临界振动速度为24.20 cm/s,最大损伤半径为7.56 m,并由萨道夫基公式得到2种方式的最大起爆药量。     

Some problems in plane thermopiezoelectric materials with holes

Piezoelectric materials have recently attracted considerable attention due to their potential use in intelligent structural systems. In this paper, we treat the plane problem of thermopiezoelasticity with various holes and subject to coupled mechanical, electric and thermal loads. An analytical solution is obtained by applying the technique of conformal mapping and some identities in the Stroh formalism. The solution has a simple unified form for various holes such as ellipse, circle, triangle and square. By way of the solution, the expressions for the energy release rate and stress intensity factors of cracks are presented. Numerical results for concentration coefficients of stress and electric displacement along the hole boundary are given to assess the acceptability of the proposed method.     

Some theoretical problems on variational data assimilation

Theoretical aspects of variational data assimilation (VDA) for a simple model with both global and local observational data are discussed. For the VDA problems with global observational data, the initial conditions and parameters for the model are revisited and the model itself is modified. The estimates of both error and convergence rate are theoretically made and the validity of the method is proved. For VDA problem with local observation data, the conventional VDA method are out of use due to the ill-posedness of the problem. In order to overcome the difficulties caused by the ill-posedness, the initial conditions and parameters of the model are modified by using the improved VDA method, and the estimates of both error and convergence rate are also made. Finally, the validity of the improved VDA method is proved through theoretical analysis and illustrated with an example, and a theoretical criterion of the regularization parameters is proposed.     

Automatic control of a modified tractor to work on steep side slopes

The main purpose of this paper is to investigate the control and stability of a tractor moving over obstacles on steep side slopes. To this end, a modified slope tractor is considered and the lateral stability of the vehicle is studied. The modified tractor is able to roll against the side slope and change the position of its mass centre. The tractor behaviour in a sloped field on a straight path is simulated in ADAMS software environment. A two-layer controller consisting of a Fuzzy upper layer and a PI lower layer is designed for the control of tractor stability. The dynamics of hydraulic actuators adjusting the body roll angle is also included. The stability of controlled and uncontrolled tractors is investigated by several simulations. It is shown that in comparison with the two types of ordinary and uncontrolled slope tractors, the controller is capable of maintaining the stability of modified tractor and preventing it from rollover and instability on various side slopes and obstacles.     

Some static problems for elastic bodies with a crust

Summary This paper studies the diffusion of stresses in a linear isotropic elastic body coated with a thin elastic shell called the ?crust?. Two static problems are considered. The first is that of the semi-infinite half-space covered by a thin plate subject to a point load at the origin. In the second problem a solid elastic sphere enveloped by a thin spherical elastic shell with two opposite point loads at the poles is investigated. Solutions for the displacement within the thin crust are obtained in the two problems by means of the Hankel transform and the Legendre polynomial respectively.

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Sommario Questo lavoro studia la diffusione degli sforzi in un corpo elastico, lineare, isotropo rivestito da un guscio elastico sottile denominato la ?crosta?. Sono considerati due problemi elastostatici. Il primo è quello di un semispazio coperto da una piastra sottile soggetta and un carico concentrato nell'origine. Nel secondo problema si studia una sfera solida elastica avvolta da un guscio sottile elastico con due carichi concentrati opposti nei poli. Nei due problemi le soluzioni in termini di spostamenti entro la crosta si ottengono rispettivamente mediante la trasformata di Hankel e i polinomi di Legendre.

     

Some remarks on the stability of shock waves

Summary Some questions arising in linear stability and reflection stability of a plane shock are discussed, both in classical and relativistic fluid dynamics. The stability properties of a van der Waals gas are discussed.

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Sommario Vengono trattate alcune questioni riguardanti la stabilità lineare e per riflessione di un'onda d'urto piana in gas dinamica classica e relativistica. Sono discusse le proprietà di stabilità di un gas di van der Waals.

     

Inverse boundary value problems with unknown boundaries: Optimal stability

In this paper we obtain essentially best possible stability estimates for a class of inverse problems associated to elliptic boundary value problems in which the role of the unknown is played by an inaccessible part of the boundary and the role of the data is played by overdetermined boundary data for the elliptic equation assigned on the remaining, accessible, part of the boundary. We treat the case of arbitrary space dimension n≥2 . Such problems arise in applied contexts of nondestructive testing of materials for either electric or thermal conductors, and are known to be ill-posed.     

Some problems and issues in geophysical turbulence

Velocity fluctuations in the large scales of the atmosphere's meso-scale have turbulent characteristics of random fluctuations and a scale-size distribution near k^−5/3 (Gage, 1979. J. Atmos. Sci. 36, 1950–1954; Lilly, 1983. J. Atmos. Sci. 40, 749–761; Lilly et al., 1998. Theoret. Comput. Fluid Dyn. 11, 139–153). Explanations of this motion field have ranged from inverse cascading quasi-geostrophic (i.e. quasi-two-dimensional) turbulence, to gravity waves (VanZandt, 1982. Geophys. Res. Lett. 9, 575–578). We describe efforts to relate observational spectra to various theories ranging from quasi-geostrophic turbulence to gravity waves. We note that at the larger scales quasi-geostrophic theory may suffice, but at smaller scales, a quasi-geostrophic explanation becomes untenable because the importance of rotation becomes progressively weaker as scales of the flow becomes smaller (the Rossby number approaches unity). We then discuss numerical simulations designed to discriminate between alternative explanations of the flow. Several simulations are reviewed, starting with those of Herring and Métais (1989. J. Fluid Mech. 202, 97–115), and finally those described by Lilly et al. (1998. Theoret. Comput. Fluid Dyn. 11, 139–153).     

Some basic problems in anisotropic bimaterials with a viscoelastic interface

This research is devoted to the study of anisotropic bimaterials with Kelvin-type viscoelastic interface under antiplane deformations. First we derive the Green’s function for a bimaterial with a Kelvin-type viscoelastic interface subjected to an antiplane force and a screw dislocation by means of the complex variable method. Explicit expressions are derived for the time-dependent stress field induced by the antiplane force and screw dislocation. Also presented is the time-dependent image force acting on the screw dislocation due to its interaction with the Kelvin-type viscoelastic interface. Second we investigate a rectangular inclusion with uniform antiplane eigenstrains embedded in one of the two bonded anisotropic half-planes by virtue of the derived Green’s function for a line force. The explicit expressions for the time-dependent stress field induced by the rectangular inclusion are obtained in terms of the simple logarithmic and exponential integral functions. It is observed that in general the stresses exhibit the logarithmic singularity at the four corners of the rectangular inclusion. Our results also show that when one side of the rectangular inclusion lies on the viscoelastic interface, the interfacial tractions are still regular at the two corners of the inclusion which are located on the interface. Last we address a finite Griffith crack normal to the viscoelastic interface by means of the obtained Green’s function for a screw dislocation. The crack problem is formulated in terms of a resulting singular integral equation which is solved numerically. The time-dependent stress intensity factors at the two crack tips are obtained and some interesting features are discussed.     

Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints

A parametric variational principle and the corresponding numerical algo- rithm are proposed to solve a linear-quadratic （LQ） optimal control problem with control inequality constraints. Based on the parametric variational principle, this control prob- lem is transformed into a set of Hamiltonian canonical equations coupled with the linear complementarity equations, which are solved by a linear complementarity solver in the discrete-time domain. The costate variable information is also evaluated by the proposed method. The parametric variational algorithm proposed in this paper is suitable for both time-invariant and time-varying systems. Two numerical examples are used to test the validity of the proposed method. The proposed algorithm is used to astrodynamics to solve a practical optimal control problem for rendezvousing spacecrafts with a finite low thrust. The numerical simulations show that the parametric variational algorithm is ef- fective for LQ optimal control problems with control inequality constraints.