Methods of taking into account the nonlinearity of the deformation properties of the material in calculating thick-walled composite rings

The results of an investigation of the deformation properties of unidirectional composites are presented, and engineering models which take into account the effect of the nonlinearity of the properties in the radial direction on the state of stress of rings under pressure are proposed. The relations obtained are checked theoretically — by means of a refined calculation based on the nonlinear theory of elasticity — and experimentally — by loading rings with internal and external pressure by means of rubber cuffs in specially designed apparatus.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 73–84, January–February, 1976.     

Stability of token passing rings

A sufficient stability condition for the standard token passing ring has been known since the seminal paper by Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to the research community. In fact, Watson observed that in the performance evaluation of token passing rings, it is convenient to derive stability conditions ... (without proof). Our intention is to fill this gap, and to provide a formal proof of thesufficient and necessary stability condition for the token passing ring. In this paper, we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth a gatedl-limited (l ) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.This research was supported by NSF Grant CCR-8900305, and in part by AFOSR Grant 90-0107, and by Grant R01 LM05118 from the National Library of Medicine.     

Stability of pulse-modulated systems with a monotone equivalent nonlinearity in the modulator

A pulse-modulated system described by a functional differential equation is considered. Sufficient frequency conditions for global stability are obtained by using the averaging method and a frequency theorem.     

Nonlinear electro-dynamic analysis of micro-actuators: Effect of material nonlinearity

This paper presents a nonlinear dynamic analysis of a micro-actuator made of nonlinear elasticity materials. The theoretical formulations are based on Bernoulli–Euler beam theory and include the effects of mid-plane stretching due to large deformation and material nonlinearity. By employing Linstedt–Poincaré perturbation method, the nonlinear governing equation is transformed into a set of linear differential equations which are then solved using Galerkin’s method. Numerical results show that the linear constitutive relationship used in previous studies is valid for small deformation only whereas for large deformation, the nonlinear elasticity constitutive relationship must be used for accurate analysis. The effects of initial gap and beam length on the nonlinear electro-dynamic behavior of the micro-actuator are also discussed.     

Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity

This paper deals with the problem of absolute stability and robust stability of a class of neutral systems with sector-bounded nonlinearity and mixed time-varying delays. Some new delay-dependent stability criteria are presented based on Lyapunov stability theory and formulated in terms of strict linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is required in obtaining the stability conditions. Since both the neutral- and discrete-delays are taken into account, the obtained criterion is less conservative than the previous ones, which is illustrated by numerical examples.     

Stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity

This paper is concerned with the stability of non-monotone traveling waves for a discrete diffusion equation with monostable convolution type nonlinearity. By using the anti-weighted energy method and nonlin-ear Halanay’s inequality, we prove that all noncritical traveling waves (waves with speeds c > c_*, c_* is minimal speed) are time-exponentially stable, when the initial perturbations around the waves are small. As a corollary of our stability result, we immediately obtain the uniqueness of the traveling waves.     

Prime rings with PI rings of constants

It is shown that if the ring of constants of a restricted differential lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.     

Stability of an M|G|1 queue with thick tails and excess capacity

The behavior of queues with excess capacity whose service times have very thick tails is studied. Proceeding of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.     

Radicals of Jordan rings connected with alternative rings

Subject to a certain restriction on the additive group of an alternative ring A, we prove that R(A)=R(A⁽⁺⁾), where A⁽⁺⁾ is a Jordan ring and R is one of the following radicals: the Jacobson radical, the upper nil-radical, the locally nilpotent radical, or the lower nil-radical. For the proof of these relationships Herstein's well-known construction for associative rings is generalized to alternative rings.     

Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders,using a second-order point-collocation method

Nonlinear transient thermal stress and elastic wave propagation analyses are developed for hollow thick temperature-dependent FGM cylinders subjected to dynamic thermomechanical loads. Stress wave propagation, wave shape distortion, and speed variation under impulsive mechanical loads in thermal environments are also investigated. In contrast to researches accomplished so far, a second-order formulation rather than a first-order one is employed to improve the accuracy. The FDM method (as a point-collocation FEM method) is used. It is known that other FEM methods cannot show the actual trend jumps due to distributing the abrupt changes in the quantities as the numerical errors and the residuals of the governing equations among the nodal results. Furthermore, the required computational time and allocated computer memory are much reduced by the present solution algorithm. The cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic or impulsive loads are determined by solving the resulted highly nonlinear governing equations using an iterative updating solution scheme. A sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the thermoelastic stresses and present some interesting characteristics of the thermoelastic and wave propagation behaviors.     

Stability of fixed points of polynomial mappings on some compact rings

Theorems on the Lyapunov stability of fixed points for polynomial maps on the ring of m-adic integers are proved and applied to cognitive models of the reasoning process. A relationship between these problems and those arising in microcosm theory is discussed.     

Semigroup rings and group rings with large center

A ring R is called a ring with a large center or an IIC-ring if any nonzero ideal of R has a nonzero intersection with the center of R. We consider conditions which guarantee that a semigroup ring over an IIC-ring is an IIC-ring.     

Optical solitons with log-law nonlinearity

This paper obtains the 1-soliton solution of the nonlinear Schrödinger’s equation with log-law nonlinearity. The solitary wave ansatz method is used to carry out the integration of this equation. The three conserved quantities are derived for this equation. The adiabatic parameter dynamics is obtained in presence of perturbation terms. Finally, the study is extended to 1 + 2 dimensions where a closed form 1-soliton solution is also obtained.     

Physical nonlinearity with microstructural transitions

A physical model of a deformable body with a network structure composed of individual elements linked by valence bonds is considered. The effect of dissociated valence bonds on the irreversible deformation is investigated using Fermi-Dirac statistics. The physical stress-strain relation obtained is a generalization of certain known constitutive equations.Bulgarian Academy of Sciences, Sofia. Translated from Mekhanika Polimerov, No. 1, pp. 36–44, January–February, 1973.