AN APPLICATION OF SCHAUDER’S FIXED POINT THEOREM TO THEEXISTENCE OF SOLUTlONS OF IMPULSIVELYDIFFERENTIAL EQUATIONS

In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results.     

Response of a hypersonic blunt cone boundary layer to slow acoustic waves with assessment of various routes of receptivity

The hypersonic boundary-layer receptivity to slow acoustic waves is investigated for the Mach 6 flow over a 5-degree half-angle blunt cone with the nose radius of 5.08 mm. The plane acoustic wave interacts with the bow shock, and generates all types of disturbances behind the shock, which may take various routes to generate the boundary-layer unstable mode. In this paper, two routes of receptivity are investigated in detail. One is through the disturbance in the entropy layer. The other is through the slow acoustic wave transmitted downstream the bow shock, which can excite the boundary-layer mode due to the synchronization mechanism. The results show that, for a low frequency slow acoustic wave, the latter route plays a leading role. The entropy-layer instability wave is able to excite the first mode near the neutral point, but its receptivity efficiency is much lower.     

AN APPLICATION OF UNGAR’S DIFFERENTIAL TRANSFORM TO ELASTODYNAMICS

In recent years,a lot of writers have used Cagniard-de,Hoop’s method to solvesome problems of elastic wave But it is a difficult and complicated lask to change the pathof integration when we use this method.A differential transform by A.Ungar canobviate this difficulty.In this paper,we use Ungar’s differential transform to solve a case ofLamb’s problem.     

EKELAND’S VARIATIONAL PRINCIPLE AND CARISTI’S COINCIDENCE THEOREM FOR SET-VALUED MAPPINGS IN PROBABILISTIC METRIC SPACES

By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ) —NOETHER’S THEOREM

The existing various couple stress theories have been carefully restudied.The purpose is to propose a coupled Noether’s theorem and to reestablish rather complete conservation laws and balance equations for couple stress elastodynamics. The new concrete forms of various conservation laws of couple stress elasticity are derived. The precise nature of these conservation laws which result from the given invariance requirements are established. Various special cases are reduced and the results of micropolar continua may be naturally transited from the results presented in this paper.     

THE COMPLEMENTARY PROPERTY OF LINDELF’S WORK AND CHAPLYGIN’S WORK

Lindelf’s equation is derived by using the Vakonomic model,which shows that Lindelf’s work coincides with Vakonomic model. Chaplygin’s equation is derived by using Chetaev’s model, which shows that Chaplygin’s work coincides with Chetaev’s model. On basis of these, by improving the expressions of Chaplygin’s equation and Lindelf’s equation, the reasonable transition from Chaplygin’s equation to Lindelf’s equation is realized, the reasonable transition from Lindelf’s equation to Chaplygin’s equation is realized too. Finally, a typical example is given. The work of this paper shows that, just as the Vakonomic model and Chetaev’s model are complementary to each other, Lindelf’s work and Chaplygin’s work are complementary to each other too.     

THE METHOD OF DERIVATION OF MAC－MILLAN＇S EQUATION FOR THE NON－LINEAR NON－HOLONOMIC SYSTEM

ＴＨＥＭＥＴＨＯＤＯＦＤＥＲＩＶＡＴＩＯＮＯＦＭＡＣ－ＭＩＬＬＡＮ＇ＳＥＱＵＡＴＩＯＮＦＯＲＴＨＥＮＯＮ－ＬＩＮＥＡＲＮＯＮ－ＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭ￥ＱｉｕＲｏｎｇ（邱荣）（ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ，ＦｕｚｈｏｕＵｎｉｖｅｒｓｉ...     

ROUTH’S EQUATIONS FOR GENERAL NONHOLONOMIC MECHANICAL SYSTEMS OF VARIABLE MASS

In this paper,Routh’s equations for the mechanical systems of the variable masswith nonlinear nonholonomic constraints of arbitrary orders in a noninertial referencesystem have been deduced not from any variational principles,but from the dynamicalequations of Newtonian mechanics.And then again the other forms of equations fornonholonomic systems of variable mass are obtained from Routh’s equations.     

KANE’S EQUATIONS FOR PERCUSSION MOTION OF VARIABLE MASS NONHOLONOMIC MECHANICAL SYSTEMS

ＫＡＮＥ’ＳＥＱＵＡＴＩＯＮＳＦＯＲＰＥＲＣＵＳＳＩＯＮＭＯＴＩＯＮＯＦＶＡＲＩＡＢＬＥＭＡＳＳＮＯＮＨＯＬＯＮＯＭＩＣＭＥＣＨＡＮＩＣＡＬＳＹＳＴＥＭＳＺｈａｎｇＹｕｅｌｉａｎｇ（张耀良）（ＨａｒｂｉｎＥｎｇｉｎｅｅｒｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｈ...     

KANE’S EQUATIONS FOR PERCUSSION MOTION OF VARIABLE MASS NONHOLONOMIC MECHANICAL SYSTEMS

In this paper,the Kane’s equations for the Routh’s form of variable massnonholonomic systems are established.and the Kane’s equations for percussion motionof variable mass holonomic and nonholonomic systems are deduced from them. Secondly,the equivalence to Lagrange’s equations for percussion motion and Kane’sequations is obtained,and the application of the new equation is illustrated by anexample.     

TO SOLVE THE SHALLOW SHELL EQUATIONS WITH THE HELP OF THE PLATE’S EQUATION SOLUTION(LOWERING THE ORDER OF PARTIAL DIFFERENTIAL EQUATION FROM 8 TO 2)

If a plate solution is known which has the same boundary and loading conditions with a shallow shell, the solution of that shell can be reduced to a non-homogeneous Helmholtz’s equation in complex domain. Two examples are given to illustrate our method.     

THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE’S TYPE IN EVENT SPACE

The conservation law of nonholonomic system of second-order non-Chataev’s type in event space is studied. The Jourdain’s principle in event space is presented. The invariant condition of the Jourdain’s principle under infinitesimal transformation is given by introducing Jourdain’s generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.     

ON THE LIAPUNOV’S STABILITY OF A CLAMPED ORTHOTROPIC ROUND PLATE UNDER RADIAL AXISYMMETRICAL IMPACTLOAD

ＯＮＴＨＥＬＩＡＰＵＮＯＶ＇ＳＳＴＡＢＩＬＩＴＹＯＦＡＣＬＡＭＰＥＤＯＲＴＨＯＴＲＯＰＩＣＲＯＵＮＤＰＬＡＴＥＵＮＤＥＲＲＡＤＩＡＬＡＸＩＳＹＭＭＥＴＲＩＣＡＬＩＭＰＡＣＴＬＯＡＤＪｉｅＭｉｎ（揭敏）（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃｓ．Ｈｕ...     

GREEN’S FUNCTION AND EFFECTIVE ELASTIC STIFFNESS TENSOR FOR ARBITRARY AGGREGATES OF CUBIC CRYSTALS

A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic c…