Corrigendum: Direct determination of stresses from the stress equations of motion and wave propagation for a new class of elastic bodies

2017 ◽  
Vol 25 (3) ◽  
pp. 866-868 ◽  
Author(s):  
Roger Bustamante

In this note it is shown there is an error in the analysis used to obtain an exact solution for the wave propagation problem, for the case of a one-dimensional body considering a new type of constitutive equation.

Author(s):  
I. Goudas ◽  
I. Stavrakis ◽  
S. Natsiavas

In the present study, dynamic response of single-cylinder reciprocating engines is investigated. The models examined take into account the flexibility of the engine mechanism associated with either its connecting rod or its supporting bearings. In addition, both the driving and the resisting moments are expressed as functions of the crankshaft motion. This leads to dynamic models with equations of motion appearing in a strongly nonlinear form. These equations are then solved numerically, by employing methodologies of both the time and the frequency domain. In particular, these methodologies include determination of transient response by direct integration or direct determination of complete branches of steady state response. The first set of numerical results refers to engine mechanisms with a flexible connecting rod. After dealing briefly with the special case of constant crank angular velocity, which can be investigated more easily and provides valuable insight into some aspects of the system dynamics, the emphasis is shifted to the general case of non-ideal forcing. Next, numerical results are presented for engine models with flexible bearings. Initially, mechanisms with rigid members supported by bearings involving linear anisotropic or isotropic properties are considered. Finally, similar results are also presented for hydrodynamic bearings, whose behavior is governed by the classical finite-length impedance theory. In all cases, the attention is focused on investigating the influence of the system parameters on its dynamics.


Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.


2006 ◽  
Vol 128 (20) ◽  
pp. 6676-6682 ◽  
Author(s):  
Yusuke Wakabayashi ◽  
Atsushi Kobayashi ◽  
Hiroshi Sawa ◽  
Hiroyuki Ohsumi ◽  
Naoshi Ikeda ◽  
...  

1981 ◽  
Vol 48 (4) ◽  
pp. 743-748 ◽  
Author(s):  
T. C. T. Ting

Characteristic forms of differential equations for wave propagation in nonlinear media are derived directly from equations of motion and equations which combine the constitutive equations and the equations of continuity. Both Lagrangian coordinates and Eulerian coordinates are considered. The constitutive equations considered here apply to a large class of nonlinear materials. The characteristic forms derived here clearly show which components of the stress and velocity are involved in the differentiation along the bicharacteristics. Moreover, the reduction to one-dimensional cases from three-dimensional problems is obvious for the characteristic forms obtained here. Examples are given and compared with the known solution in the literature for wave propagation in linear isotropic elastic solids and isentropic compressible fluids.


2000 ◽  
Vol 39 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Luca A. Pardi ◽  
Alia K. Hassan ◽  
Frans B. Hulsbergen ◽  
Jan Reedijk ◽  
Anthony L. Spek ◽  
...  

1971 ◽  
Vol 38 (4) ◽  
pp. 888-894 ◽  
Author(s):  
P. A. Tuschak ◽  
A. B. Schultz

For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave-propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod.


Author(s):  
R. B. Neder ◽  
A. Halbhuber ◽  
F. Frey

AbstractA procedure for the direct determination of defect structures is presented. The procedure uses the average structure to calculate starting phases. An iterative cycle of inverse Fourier transforms and interpretations of the scattering density is applied. Within each cycle the scattering density is interpreted to yield a structure deviating from the average structure by missing, replaced or shifted atoms. The procedure usually converges after a few cycles and allows a direct determination of substitutional and displacement disorder. By analyzing the correlations between different atoms, extended defects can be recognized. The current results are preliminary and have been limited to an idealized one dimensional situation, under the assumption of a negligible experimental resolution function.


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