Analysis Of Wave Equation Research Articles

Finite‐amplitude acoustic pulse propagation in dispersive thermo‐viscous fluids

We have investigated the propagation of initially square and exponentially decaying finite‐amplitude pulses in dispersive thermaviscous fluids via numerical analysis of the appropriate nonlinear acoustic wave equations for liquids containing gas bubbles and for mono‐relaxing fluids. In a computer generated film, we begin by exhibiting the degeneration of these simple pulses in a lossless fluid dynamic‐steady state solitons and their subsequent collisions during the course of propagation. Viscous absorption and spherical spreading losses are then introduced independently so that their effect in damping soliton structure as it forms, is clearly demonstrated. The example of “solitonlike” formulation in a leggy dispersive fluid which we have included in the film, was chosen to simulate an experiment in a gas liquid medium previously reported In the literature [S. S. Kutateladze, A. P. Burdukov, V. V. Kuznetsov et al., Sov. Phys.—Dokl. 17, 1051–1052 (1973)]. Following this presentation, the physical conditions required to induce “solitonlike” behavior via acoustic pulses in different types of dispersive thermoviscous fluids will then be briefly considered.

Application of the wave equation analysis to friction piles in sand

Based on the information gathered during a design pile testing program and the subsequent construction of a large pile foundation in Quebec City, the potential and limitation of the wave equation method for analysing pile driving behaviour are demonstrated.The application of the wave equation method to instrumented precast concrete piles driven under well controlled conditions leads to excellent predictions both in terms of driving stresses and of ultimate bearing capacities.The same high quality of prediction is obtained for a steel H-pile and a precast concrete pile driven incrementally to a depth of 53 ft (16.2 m) in a uniform sand deposit. However, proper simulation of the joints is required for the precast concrete pile.On the contrary, a very poor correlation between computed and observed ultimate capacities is obtained for the production piles. This is attributed to the poor reliability of the blow counts used as input data in the classical wave equation method of analysis.

Problems in Design and Installation of Offshore Piles

Offshore structures in water up to 385-ft deep require long pipe piles with ultimate compressive and tension capacities up to 3,500 and 2,000 tons, respectively. Static analysis is the most reliable and widely used method for predetermining pile penetrations and predicting pile capacity. Significant design uncertainties result, however, from dependence on empirical data derived from short, lightly loaded piles driven and tested on land. Pile loads have increased faster than the driving capability of available pile hammers, which include some with rated energy of 180,000 ft-lb. Larger hammers are needed to achieve a higher percentage of successful installations by driving alone. Wave-equation analysis may aid selection of optimum pile wall thickness to improve drivability. Pile installation aids, including jetting, drilling, and grouting, are useful but increase design uncertainty. Four case histories illustrate the problem of both design and installation of offshore piles.

Dynamical Formation of a Small-Scale Filament

We report a numerical analysis of the electromagnetic wave equation with a saturable, intensity-dependent, refractive index. The solutions show the dynamical self-focusing of an intense optical beam through the focus. The transverse intensity profile develops a complex ringed structure, the central maximum of which has many of the properties of the small-scale filaments observed experimentally.

Expressions for the Electromechanical Coupling Factor in Terms of Critical Frequencies

Many expressions for the coupling factor in terms of the fundamental resonant and antiresonant frequencies have been developed. The applicability of many of these is limited, either because they have been obtained from simplified equivalent circuits, or because they apply to particular electromechanical configurations. Approaching the problem by way of the wave equation and mechanical analysis raises difficulties that can only be resolved for relatively simple cases. An approach through a generalized equivalent circuit is used to determine more-general expressions for the coupling factor in terms of the resonant and antiresonant frequencies at the fundamental and overtone modes of vibration. Theoretical and practical applications of these expressions are presented.