Showing papers in "Advances in Applied Mechanics in 1966"

Fundamental Problems in Viscoplasticity

Abstract: Publisher Summary The fundamental assumption of all theories of plasticity—that of time independence of the equations of state—makes simultaneous description of the plastic and rheologic properties of a material impossible. I t is well-known that in many practical problems, the actual behaviour of a material is governed by plastic as well as by rheologic effects. It can even be said that for many important structural materials, rheologic effects are more pronounced after the plastic state has been reached. Every material shows more or less pronounced viscous properties. In some problems, the influence of viscous properties of the material may be negligible, while in others, it may be essential. Both sciences—plasticity and rheology—are concerned with the description of important mechanical properties of structural materials. Each of them has created its own methods of investigation and has developed within the framework of certain assumptions which, unfortunately, cannot always be satisfied in reality. The results of rheology are confined to cases where plastic strain is of no decisive importance.

On Nonlinear Vibrations of Systems with Many Degrees of Freedom

Abstract: Publisher Summary The study of the vibrations of nonlinear systems with many degrees of freedom is concerned with the search for some or all periodic solutions of systems of nonlinear differential equations and to deduce as many properties of these solutions as the state of the applicable mathematical knowledge permits. Unfortunately, this body of knowledge is limited and not unified; in consequence, many and vaned disciplines within mathematics are commonly used to deduce partial results. In a general way, these results fall into two broad categories: those which apply to systems that are “weakly nonlinear,” and those which apply when the systems are “strongly nonlinear.” The results in the first category contain a good deal of detailed information, and they resemble in many ways those familiar from linear theory. Those in the latter category usually contain fewer details, being more concerned with general questions of existence, uniqueness, boundedness, and stability of solutions.

Hydrodynamic Stability of Parallel Flow of Inviscid Fluid

Abstract: Publisher Summary In the beginning, analyzing the fundamental theory of inertial instability of plane parallel flow of inviscid fluid, the chapter discusses certain integral issues such as eigenvalue problem for inertial modes, general stability characteristics of plane parallel flow, the initial-value problem and the stability of nonparallel flow, and stability characteristics of various basic flows. In the next phase, it discusses the waves and stability of plane parallel flow of inviscid fluid under the actions of various force fields. The heuristic theory of instability is described in detail in the chapter, along with its dimensional analysis and physical arguments. The general stability characteristics and stability characteristics of various basic flows related to the instability of an incompressible fluid of variable density are also analyzed in the chapter.

Magneto-elasticity and magneto-thermo-elasticity

Abstract: Publisher Summary The theories of magneto-elasticity and magneto-thermo-elasticity are concerned with the interacting effects of an externally applied magnetic field on the elastic and thermo-elastic deformations of a solid body. These theories are being developed readily in recent years because of the possibilities of their extensive practical applications in diverse fields, such as geophysics, optics, acoustics, and damping of acoustic waves in the magnetic field. However, while the theory of interaction between fluid-flow and an electro-magnetic phenomenon in electrically conducting fluids (magneto-fluid-dynamics) has been much developed since the discovery of Alfven waves, the theory of magneto-thermo-elasticity is still in its infancy.

The Calculation of Free Oscillations of a Liquid in a Motionless Container

Abstract: Publisher Summary The chapter discusses the basic ideas of the theory of oscillations of a liquid and the liquid-containing body. It gives an account of the numerical methods and results of the calculation of free oscillations of a liquid in a motionless container. This is the simplest problem that appears in the investigation of the general dynamics of a body containing liquid masses with a free surface. Despite the simplicity of the mathematical formulation, it is not a t all easy to obtain accurate numerical results in this problem of free oscillations of a heavy liquid. Only in the simplest cases, one can manage to solve it analytically by the Fourier method. In this respect, the chapter describes the importance of the Ritz method and its application to the calculation of natural oscillations of a liquid in containers of various shapes. The chapter discusses free oscillations in an inclined circular cylinder, a conical container, a spherical container, and in a container formed by two horizontal coaxial cylinders.

Wave Propagation in Real Gases

Abstract: Publisher Summary This chapter presents an elementary account, which retains the essential features of the wave motion. A basic understanding of the general and distinctive features of waves propagating in real gases is necessary in aerodynamics, astrophysics, and related areas. In recent years, extensive studies of real gas effects on wave propagation have been made, including various dissipative processes with and without nonlinear effects due to convection. The analyses of these problems and the results can be quite complex. Although the physical mechanisms by which the dissipation is produced may be different, their effects on the flow field may be similar in certain respects. To more easily understand the general characteristics of waves propagating in real gases, one typical, and simple, wave propagation problem is treated in detail in this chapter, using methods of analysis, which are fairly general. By this procedure, general principles and methods can be illustrated, which may be useful in other similar but more complicated problems.