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Showing papers in "Zeitschrift für Angewandte Mathematik und Physik in 1974"


Journal ArticleDOI
Arthur W. Leissa1
TL;DR: In this article, the Ritz-Galerkin method is applied to the classical eigenvalue problem of the free vibration of a rectangular membrane, and it is shown that the behavior of curves which approach each other and suddenly veer away may be the result of approximation in the representation of physical reality.
Abstract: In numerous places in the literature of eigenvalue problems of mathematical physics one finds curves which approach each other and suddenly veer away. The author postulates that this ugly behavior may be the result of approximation in the representation of physical reality. In the present paper such behavior is demonstrated to arise from the application of the well-known Ritz-Galerkin method to the classical eigenvalue problem of the free vibration of a rectangular membrane.

221 citations


Journal ArticleDOI
Nikolaus Rott1
TL;DR: In this article, the influence of heat conduction on acoustic streaming is considered including the effect of variable tube wall temperature in the limiting case when the boundary layer is thin compared to the tube radius.
Abstract: The influence of heat conduction on acoustic streaming is considered including the effect of variable tube wall temperature. The calculations are carried out in the limiting case when the boundary layer is thin compared to the tube radius.

81 citations


Journal ArticleDOI
TL;DR: In this paper, the three-dimensional incompressible laminar boundary layer past a flat plate is investigated, when suction with a slightly sinusoidal transverse suction velocity distribution at the wall is applied.
Abstract: The three-dimensional incompressible laminar boundary layer past a flat plate is investigated, when suction with a slightly sinusoidal transverse suction velocity distribution at the wall is applied. For the asymptotic flow conditions far downstream the components of the wall shear stress and the heat transfer including its dependence on Prandtl number are determined.

64 citations


Journal ArticleDOI
Nikolaus Rott1
TL;DR: In this article, the second-order effect of the steady "thermo-acoustic streaming" is calculated in boundary-layer approximation, and the results are applied to the calculation of the heat flow distribution out of a resonance tube, in the case when weak shocks occur.
Abstract: The second-order effect of the steady ‘thermo-acoustic streaming’ is calculated in boundary-layer approximation. The results are applied to the calculation of the heat flow distribution out of a resonance tube, in the case when weak shocks occur. Problems of the combined effect of shock heating and boundary layer heating, which can be treated only in an approximate way thus far, are discussed.

35 citations


Journal ArticleDOI
TL;DR: In this paper, a finite oscillatory shearing motion is shown to be possible in the absence of body force, in every homogeneous isotropic compressible or incompressible elastic solid.
Abstract: A finite oscillatory shearing motion is shown to be possible, in the absence of body force, in every homogeneous isotropic compressible or incompressible elastic solid. The spatial geometry is the same for all materials and the nature of the time-dependence, for a particular material, is determined by the generalized shear modulus. A motion of this type and a spatially uniform, time-dependent temperature can be supported in thermoelastic solids, without application of body force or volume supply of heat.

32 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the impact of a right circular fluid cylinder with a flat rigid surface with the aid of a two-dimensional axisymmetric finite difference code and showed that the maximum pressure sustained is precisely the one-dimensional maximum, i.e., the shock Hugoniot.
Abstract: The phenomena associated with the impact of a right circular fluid cylinder with a flat rigid surface are studied with the aid of a two-dimensional axisymmetric finite difference code. Both sub-and supersonic initial conditions are investigated. It is shown that, contrary to earlier reports, the maximum pressure sustained is precisely the one-dimensional maximum, i.e., the shock Hugoniot. The relaxation time corresponds to the time for the edge rarefaction, initiating at the impact corner, to traverse the jet radius. The maximum lateral speed, at the impact corner, was found to be nearly twice that of impact, slightly higher for very low Mach number and slightly lower for supersonic impact.

24 citations


Journal ArticleDOI
TL;DR: In this article, the Eigenschwingungen eines zylindrischen homogenen Plasmas konnen analytisch untersucht and in drei Klassen eingeteilt werden.
Abstract: Die Eigenschwingungen eines zylindrischen homogenen Plasmas konnen analytisch untersucht und in drei Klassen eingeteilt werden. Die Eigenwerte der ersten Klasse sind gut getrennt, jene der zweiten haben einen Haufungspunkt, und der Eigenwert der dritten Klasse ist unendlich entartet. Es wird untersucht, wie und unter welchen Bedingungen die Eigenwerte und-funktionen des mit finiten Elementen diskretisierten Problems gegen die wahre Losung streben.

22 citations


Journal ArticleDOI
TL;DR: In this article, the steady, two-dimensional incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow was calculated using the method of series truncation.
Abstract: The steady, two-dimensional incompressible MHD flow past a circular cylinder with an applied magnetic field parallel to the main flow is calculated using the method of series truncation. The differential equations are solved analytically and the Oseen approximation is made. The magnetic Reynolds number is assumed to be small. The results show that with an applied magnetic field the flow stays attached to the cylinder longer and in some cases does not separate until the rear stagnation point.

21 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that an isotropic, incompressible, elastic half-space with a rigidity modulus which increases linearly with depth from zero at the surface, responds to vertical surface loading exactly like a uniform array of springs (Winkler's medium).
Abstract: It is known that an isotropic, incompressible, elastic half-space with a rigidity modulus which increases linearly with depth from zero at the surface, responds to vertical surface loading exactly like a uniform array of springs (Winkler's medium). The validity of this result is examined here for a cross-anisotropic medium.

21 citations


Journal ArticleDOI
TL;DR: In this article, a study is made of finite Grashof number effects upon the flow in an unbounded domain, in the buoyant plume which forms over a horizontal line source of heat.
Abstract: In this paper a study is made of finite Grashof number effects upon the flow, in an unbounded domain, in the buoyant plume which forms over a horizontal line source of heat. The consequences of introducing a plane boundary into the domain are also assessed for two particular configurations.

17 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow and showed that the instability Reynolds number of 11,000 has a marked effect on the properties.
Abstract: Measurements of the growth of artificially generated turbulent spots and intermittency distribution in the transition region on a circular cylinder in axial flow show that the instability Reynolds number of 11,000 has a marked effect on the properties. In particular, it is found that the spot production in the initial region when a single turbulent spot has not yet wrapped around the cylinder and the propagation is essentially two-dimensional, is significantly altered. But the transition in the downstream or latter region, where most of the turbulent spots propagate onedimensionally (like the turbulent plugs in a pipe), is not affected. When the radius Reynolds number is more than 11,000, the intermittency law in the initial region is essentially the same as in twodimensional flow on a flat plate and in the latter region it is the one-dimensional flow in a pipe, the demarcation between the two regions being quite sharp.

Journal ArticleDOI
TL;DR: In this article, the canonical equations of motion of a dynamical system with nonlinear nonholonomic constraints of Cetaev's type are derived and a generalisation of the Hamilton-Jacobi theorem is presented.
Abstract: In this paper we consider a dynamical system whose position is defined by a certain number of the Poincare-Cetaev variables and which moves with nonlinear nonholonomic constraints of Cetaev's type. The canonical equations of motion of the system are derived and, for integrating them, a generalisation of the Hamilton-Jacobi theorem is presented.

Journal ArticleDOI
TL;DR: In this article, a broad theoretical investigation of plasticity in crystalline solids at finite deformation is presented, with primary attention focused upon single crystals and aggregates at large pressure.
Abstract: A broad theoretical investigation of plasticity in crystalline solids at finite deformation is presented, with primary attention focused upon single crystals and aggregates at large pressure. Nonlinear elastic and nonlinear plastic constitutive relations for cubic crystals undergoing quasistatic deformation processes are studied. An aggregate model is introduced which enables transition to macroscopic behavior, including a prediction of pressure-dependence of yield surfaces in macro-stress space.

Journal ArticleDOI
HK Hendrik Kuiken1
TL;DR: In this paper, the free convection boundary layer flow along a vertical isothermal semi-infinite cylinder is solved for the case that the boundary layer is thick in comparison with the radius of the cylinder.
Abstract: The free convection boundary-layer flow along a vertical isothermal semi-infinite cylinder is solved for the case that the boundary-layer is thick in comparison with the radius of the cylinder. Contrary to assertions in the literature that is has been solved, this problem is still awaiting solution. It is shown that a rather unorthodox boundary-layer transformation should be applied to obtain the solution. some numerical calculations are carried out and these are displayed in graphical form.

Journal ArticleDOI
TL;DR: In this paper, a half-space composed of two joined elastic quarter spaces of different material properties is subjected to anti-plane surface tractions parallel to the interface and a zone of rupture, or delamination, subsequently propagates at a relatively large velocity as a stress-free crack along the interface.
Abstract: A half-space composed of two joined elastic quarter spaces of different material properties is subjected to anti-plane surface tractions parallel to the interface. We investigate the case that the application of the surface tractions instantaneously gives rise to rupture at the surface trace of the interface. A zone of rupture, or delamination, subsequently propagates at a relatively large velocity as a stress-free crack along the interface. Wave motions in the two quarter spaces are analyzed, and the elastodynamic stress intensity factor of the interface stress is computed. An expression is derived for the rate of energy flux into the propagating crack tip.

Journal ArticleDOI
TL;DR: In this paper, the Second Law of Thermodynamics has been applied to the relaxation functions of heat conduction with finite wave speeds, and it has been shown that the initial values of the energy relaxation function and the heat flux relaxation function are non-negative.
Abstract: In this paper we establish the restrictions imposed by the Second law of Thermodynamics on the relaxation functions which arise in the theory of heat conduction with finite wave speeds. We show that (i) the initial values of the energy relaxation function and the heat flux relaxation function are non-negative, (ii) the initial slope of the heat flux relaxation function is non-positive, and (iii) the equilibrium conductivity is non-negative. These results have important implications with regard to the behavior of waves and the uniqueness of solutions.

Journal ArticleDOI
TL;DR: In this paper, a method by which the slowly convergent radial integrals over Coulomb functions, occurring in the theory of subcoulomb transfer reactions into the continuum, can be expressed analytically by means of generalized hypergeometric functions is discussed.
Abstract: We discuss a method by which the slowly convergent radial integrals over Coulomb functions, occurring in the theory of subcoulomb transfer reactions into the continuum, can be expressed analytically by means of generalized hypergeometric functions. Different analytic continuations of these functions for special cases of the parameters are given and the convergence of the corresponding series is discussed. The numerical calculation of the matrix elements can be very much simplified if recursion relations are used. Therefore, a complete set of recursion relations is given by which all the integrals necessary for the description of a transfer process can be obtained from four simple integrals as starting elements. A detailed discussion of this numerical procedure is given, showing that this method uses much less computing time than a numerical integration procedure of the matrix elements.

Journal ArticleDOI
TL;DR: In this paper, the asymptotic theory for the total change in the action of a simple oscillator is extended to modulation with a frequency minimum small compared with the general frequency level.
Abstract: The asymptotic theory for the total change in the action of a simple oscillator is extended to modulation with a frequency minimum small compared with the general frequency level. The action change then fails to be ‘exponentially small’, but remains transcendental, in fact, is found exponential in a new parameter. Moreover, almost the whole transition of the action may then occur during but a few oscillator periods! The resulting change of emphasis produces striking insights into the character of adiabatic invariance and suggests a marked enlargement of the class of modulations accessible to the theory.

Journal ArticleDOI
TL;DR: In this paper, an analysis is presented for the development of the thermal boundary layer on a heated flat plate with an unheated starting length, and solutions are determined which describe the initial growth of this boundary layer and also its decay to the ultimate temperature profile.
Abstract: In this paper an analysis is presented for the development of the thermal boundary layer on a heated flat plate with an unheated starting length. In particular, solutions are determined which describe the initial growth of this boundary layer and also its decay to the ultimate temperature profile.

Journal ArticleDOI
TL;DR: Using Noether's theorem and the generalized Killing equations, new integrals of the differential equation of motion for a class of non-conservative mechanical systems with one degree of freedom, a special case of which is a simple pendulum of variable length, are obtained as discussed by the authors.
Abstract: Using Noether's theorem and the generalized Killing equations [1], new first integrals of the differential equation of motion for a class of non-conservative mechanical systems with one degree of freedom, a special case of which is a simple pendulum of variable length, are obtained. These integrals are identified as Lyapunov's functions for non-autonomous systems. The stability conditions are established.

Journal ArticleDOI
TL;DR: In this paper, Verfasser zeigen, dass bei irreversiblen Prozessen, die durch gewisse Geschwindigkeiten und die zugehorigen dissipativen Krafte charakterisiert sind, die starke Konvexitat und and other wesentliche Eigenschaften der Dissipationsflachen aus der Orthogonalitatsbedingung and der Eineindeutigekeit des Zuzammenhangs zwischen Ges
Abstract: Die Verfasser zeigen, dass bei irreversiblen Prozessen, die durch gewisse Geschwindigkeiten und die zugehorigen dissipativen Krafte charakterisiert sind, die starke Konvexitat und andere wesentliche Eigenschaften der Dissipationsflachen aus der Orthogonalitatsbedingung und der Eineindeutigkeit des Zuzammenhangs zwischen Geschwindigkeiten und Kraften folgen.

Journal ArticleDOI
Niklaus Sigrist1
TL;DR: In this paper, the authors consider stabilization procedures, i.e. modifications of the original differential equations such that the solutions of the modified are Liapunov stable and thus the new system is better suited for numerical integration.
Abstract: For the solutions of a system of ordinary differential equations restricted Liapunov stability and the notion of Liapunov stable sets are discussed, in particular for separable and almost separable Hamiltonian systems. We consider stabilization procedures, i.e. modifications of the original differential equations such that the solutions of the modified are Liapunov stable and thus the new system is better suited for numerical integration. In this paper some theoretical aspects rather than numerical methods are pointed out.

Journal ArticleDOI
TL;DR: In this article, the authors give theoretical and experimental consideration to the problem of the flow of Newtonian and non-Newtonian liquids under a pressure gradient in a pipe which is rotating with constant angular velocity about an axis perpendicular to its length.
Abstract: We give theoretical and experimental consideration to the problem of the flow of Newtonian and non-Newtonian liquids under a pressure gradient in a pipe which is rotating with constant angular velocity about an axis perpendicular to its length. The theoretical predictions are limited by ‘computer-time’ problems, but they indicate the possibility ofenhanced flow rate for non-Newtonian fluids, in contrast to the reduction in flow rate predicted and observed in the Newtonian case.

Journal ArticleDOI
TL;DR: In this article, the authors studied spherical waves in a linear viscoastic solid, and showed that at large time the velocity wave is diffuse, propagating with the equilibrium speed of sound and dominated by a diffusing N wave with a magnitude proportional tor−2 and a base which grows liker 1/2.
Abstract: We study spherical waves in a linear viscoalastic solid,r 0

Journal ArticleDOI
TL;DR: In this paper, it was shown that the classical solution by Greenhill for the ideal, small displacement motion of a liquid in a tank with an included angle of 120° is not valid for alternate symmetric modes.
Abstract: It is shown that the classical solution by Greenhill for the ideal, small displacement motion of a liquid in a tank with an included angle of 120° is not valid for alternate symmetric modes. A valid solution for these modes is presented in this note. Numerical values of oscillation frequencies for all modes are also included.

Journal ArticleDOI
TL;DR: In this paper, the generalized Lie series is used to solve time-dependent cross-sections of monoenergetic equations with time dependent cross-section, where the variables are separated in the solution obtained.
Abstract: Monoenergetic, time-dependentP n equations with time-dependent cross-sections are solved using the method of the generalized Lie series. The variables are separated in the solution obtained. This solution is given in a closed form for the case of time-dependent cross-sections. a few numerical results are given for the case ofP 3 approximation and compared with those obtained by the time-dependentS 4 code.

Journal ArticleDOI
TL;DR: In this paper, ZAMP 25, 677 (1974) Reference CRPP-CONF-1974-002 Record created on 2008-05-13, modified on 2017-05 -12
Abstract: Note: ZAMP 25, 677 (1974) Reference CRPP-CONF-1974-002 Record created on 2008-05-13, modified on 2017-05-12

Journal ArticleDOI
TL;DR: In this article, the slow flow past a cylinder consists of a potential flow, with thin viscous boundary layers on the cylinder (Stewartson layers), and the modified form of such layers is found, when the cylinder has regions of high curvature.
Abstract: In a rapidly rotating frame, the slow flow past a cylinder consists of a potential flow, with thin viscous boundary layers on the cylinder (Stewartson layers). The modified form of such layers is found, when the cylinder has regions of high curvature. The flow past an elliptic cylinder is taken as a typical example and the solution determined for all aspect ratios and all angles of incidence. The range of Rossby numbers for which the linear theory holds is determined.

Journal ArticleDOI
TL;DR: In this paper, the problem of a steady liquid jet impacting on a cavity of arbitrary shape is attacked by employing the Belotserkovskii integral method, and the equations of motion written in suitably defined coordinates are integrated across the jet sheet formed over the cavity to give a set of ordinary differential equations.
Abstract: The problem of a steady liquid jet impacting on a cavity of arbitrary shape is attacked by employing the Belotserkovskii integral method. Hence, the equations of motion written in suitably defined coordinates are integrated across the jet sheet formed over the cavity to give a set of ordinary differential equations. This set of equations with proper boundary and initial conditions defines completely the shape of the jet sheet, the pressure distribution on the cavity wall, etc. In the numerical integration of the equations the shooting-splitting method is used successfully. The calculated results for a flat surface are in excellent agreement with experiments and theoretical calculations reported elsewhere.

Journal ArticleDOI
TL;DR: In this article, the slow flow past a flat plate is examined by a Wiener-Hopf method and it is shown that the infinite velocity in the potential flow at the edges of the plate can be made finite by the action of viscosity in the Stewartson layer.
Abstract: In a rapidly rotating frame, the slow flow past a flat plate is examined by a Wiener-Hopf method and it is shown that the infinite velocity in the potential flow at the edges of the plate can be made finite by the action of viscosity in the Stewartson layer. It is shown that, for small angles of incidence, there are small eddies at the two edges of the plate, but that as the angle is decreased, they disappear, and the dividing streamline meets the plate at the two edges only.