Showing papers in "Advances in Applied Mechanics in 1976"
TL;DR: In this article, the authors discuss the varied physical circumstances in which interactions among water waves and currents occur and different mathematical approaches, relevant observations, and experiments that are applicable to all or some of these physical circumstances are described.
Abstract: Publisher Summary This chapter discusses the varied physical circumstances in which interactions among water waves and currents occur. Different mathematical approaches, relevant observations, and experiments that are applicable to all or some of these physical circumstances are described. The emphasis is on waves and their interaction with preexisting currents rather than on wave-generated currents. Common simplifying assumption is that the waves are of sufficiently small amplitude for the free-surface boundary conditions to be linearized and evaluated at, or close to, the mean free surface. Most progress can be made in this subject with such a constraint, but wherever possible, finite-amplitude effects are discussed. Unlike some other common forms of wave motion, water waves involve water motion varying with direction perpendicular to the space in which they propagate. The chapter concludes on the interaction of waves generated by a ship with the flow around it.
564 citations
TL;DR: In this article, the same moment fields minimize the volume of continuously variable reinforcement in fiber-reinforced plates of constant thickness for truss-like continua in which the cross-sectional areas are proportional to the absolute value of the member forces.
Abstract: Publisher Summary This chapter outlines optimality conditions for truss-like continua in which the cross-sectional areas are proportional to the absolute value of the member forces. It has been found that the optimal moment field is the same for any one of the following three criteria: rigid-plastic grillages: prescribed ultimate load; linearly or nonlinearly elastic grillages: prescribed maximum stress; and linearly elastic grillages: prescribed value of the work of the specified loads on the actual elastic deflections. The same moment fields minimize the volume of continuously variable reinforcement in fiber-reinforced plates of constant thickness. The problem is also referred to as the “minimum moment-volume problem” because it gives a minimum value for the integral of the sum of the absolute values of principal moments, considering the set of all statically admissible moment fields for given boundary conditions and loading. The theory discussed has several useful applications, such as beam systems in floors and roofs, and reinforced concrete slabs. Another aspect of grillage design is that the quantitative implications of optimization appear to be more significant than for most other types of structures.
31 citations
TL;DR: The Earth's magnetic field can only be explained in terms of electromagnetic induction, whereby the electric currents that provide the field are generated by the motion of the fluid in the core across the selfsame field, which permeates the core region as well as the nonconducting exterior.
Abstract: Publisher Summary This chapter highlights that the existence of the magnetic field of the Earth, and its variation with time, presents a profound challenge to geophysics. This field, though influenced slightly by electric currents in the ionosphere, is predominantly of internal origin and is associated with a large-scale azimuthal current distribution in the liquid core of the Earth. It is now generally agreed that this persistence of the Earth's field can only be explained in terms of electromagnetic induction, whereby the electric currents that provide the field are generated by the motion of the fluid in the core across the self-same field, which permeates the core region as well as the nonconducting exterior. The characteristic feature of such dynamo action is that the field is maintained exclusively by the action of the fluid velocity and without the help of any external source of field. This type of behavior is most simply explained in terms of the simple disk dynamo. The Earth is not the only celestial body that exhibits a significant large-scale magnetic field. Among the planets, Jupiter, Mars, and Mercury are now known to have this property; the radii, rotation rates, and dipole moments of these planets are compared with that of the Earth.
22 citations
TL;DR: In this paper, the instability of surface waves propagating in water of uniform depth, finite or infinite, by a variational method by considering two side-band wave numbers and frequencies in addition to the wave number and frequency of the primary wave train was investigated.
Abstract: Publisher Summary This chapter investigates the instability of surface waves propagating in water of uniform depth, finite or infinite, by a variational method by considering two side-band wave numbers and frequencies in addition to the wave number and frequency of the primary wave train. It discusses that the instability of stationary waves because of a flow over a wavy boundary is treated first and then the theory is applied to progressive waves propagating in water (stratified or not) of constant depth. Whether the waves are stationary or progressive, instability is found whenever Hasselmann's conditions are met. Yet the results presented are outside the pale of Hasselmann's theorem, because a flow over a wavy boundary is considered, whereas Hasselmann treated free waves; or for freely propagating waves, the variation with amplitude of the wave velocity is considered, whereas Hasselmann did not. When the present theory is applied to progressive surface or internal waves, instability is found only if the wave velocity increases with the amplitude of the basic wave train.
10 citations
TL;DR: There is much to be said for the view that experimenters ought to have a better understanding of the underlying theory of their subjects, but there is at least as much in the complaint that applied mathematicians should become aware of the existence of a real world and be prepared to leave the field of elegant speculation to pure mathematicians, who are paid to study it.
Abstract: Publisher Summary This chapter describes and discusses a number of experimental techniques in the field of solid mechanics, and outlines the way they have enabled theoretical advances to be made and physical assumptions to be either validated or shown to be erroneous. This chapter attempts to assess the role of experimental work in the development of the subject of solid mechanics. The development of the experimental aspects of the subject has, to a large extent, been concerned with the measurement of the stress-strain response of real solids under various conditions of loading, or in the fashionable jargon, the determination of the constitutive relation of the solid. A large part of the contribution of experimental work to the interpretation of the problems of solid mechanics is concerned with measurements of the stress-strain behavior of specimens of various solids, which are carried out with the object of assessing the nature of the deviations from ideal behavior, both with respect to nonlinearity and with respect to time dependence. These are sometimes carried out over a range of ambient temperatures. To conclude, there is much to be said for the view that experimenters ought to have a better understanding of the underlying theory of their subjects, but there is at least as much in the complaint that applied mathematicians should become aware of the existence of a real world and be prepared to leave the field of elegant speculation to pure mathematicians, who are paid to study it.
5 citations