Oscillatory Pressure Distribution Research Articles

Estimation of Minimum Sonic Fatigue Life of Steel Beam and Plate Structures

Abstract Structures such as those of engine test cells or wind tunnels may be exposed to intense sound for extended periods and should be designed to ensure they are not prone to premature fatigue failure. This paper presents an approach to determining a lower bound to the fatigue life of structural components exposed to complex sound fields, enabling relatively simple evaluation of candidate structural designs. The presented approach is based on established characterizations of the fatigue behaviors of typical steels and relies on classical analytical results that relate the greatest stresses induced in simple structural elements to oscillatory pressure distributions acting on these elements. Practical application of this approach is discussed, as well as the limitations of the approach.

High-fidelity aerodynamic shape optimization using efficient orthogonal modal design variables with a constrained global optimizer

Abstract Aerodynamic shape optimization of aerofoils using efficient orthogonal design variables is considered using a global search algorithm. A novel approach is presented for deriving shape design variables, using a proper orthogonal decomposition of a set of training aerofoils to obtain an optimally efficient set of aerofoil deformation modes that represent typical design parameters such as thickness and camber. A major advantage of this extraction method is the production of orthogonal design variables, and this is particularly important in aerodynamic shape optimization. These design parameters have previously been tested on geometric shape recovery problems and been shown to be efficient at covering a large portion of the design space, hence the work is extended here to consider their use in aerodynamic shape optimization. A global search algorithm with an efficient constraint handling method has been developed and used here to optimize a suite of inviscid and viscous compressible aerofoil test cases using varying numbers of modal parameters. Often, an artefact of inviscid optimizations is an oscillatory pressure distribution, so to alleviate this drag minimization with a modulus of curvature penalty is also considered for the inviscid optimizations, where the penalty is used to force smoother pressure distributions; this is not necessary in the viscous optimizations. Results indicate that often fewer than 10 design parameters are required to obtain shock free solutions even from highly-loaded aerofoils with significant shocks.

Coupled phase transformations and plastic flows under torsion at high pressure in rotational diamond anvil cell: Effect of contact sliding

A three-dimensional large-sliding contact model coupled with strain-induced phase transformations (PTs) and plastic flow in a disk-like sample under torsion at high pressure in rotational diamond anvil cell (RDAC) is formulated and studied. Coulomb and plastic friction are combined and take into account variable parameters due to PT. Results are obtained for weaker, equal-strength, and stronger high pressure phases, and for three values of the kinetic coefficient in a strain-controlled kinetic equation and friction coefficient. All drawbacks typical of problem with cohesion are overcome, including eliminating mesh-dependent shear band and artificial plastic zones. Contact sliding intensifies radial plastic flow, which leads to larger reduction in sample thickness. Larger plastic strain and increased pressure in the central region lead to intensification of PT. However, the effect of the reduction in the friction coefficient on PT kinetics is nonmonotonous. Sliding increases away from the center and with growing rotation and is weakly dependent on the kinetic coefficient. Also, cyclic back and forth torsion is studied and compared to unidirectional torsion. Multiple experimental phenomena, e.g., pressure self-multiplication effect, steps (plateaus) at pressure distribution, flow to the center of a sample, and oscillatory pressure distribution for weaker high-pressure phase, are reproduced and interpreted. Reverse PT in high pressure phase that flowed to the low pressure region is revealed. Possible misinterpretation of experimental PT pressure is found. Obtained results represent essential progress toward understanding of strain-induced PTs under compression and shear in RDAC and may be used for designing experiments for synthesis of new high pressure phases and reduction in PT pressure for known phases, as well as for determination of PT kinetics from experiments.

Generation of Magneto-Hydrodynamic Waves by Moving Pressure Distribution.

Two-dimensional magneto-hydrodynamic surface waves generated by a moving oscillatory pressure distribution in an inviscid, incompressible and electrically conducting fluid of finite uniform depth are investigated. In the ultimate steady state, there exist six progressive waves, four original gravity waves and two other magnetic waves, all of which are mainly due to magnetic force. The effect of this force on the waves produced is studied in detail. It is found that, due to this force, disturbance in the wake is increased.

Some Nonlinear Evolution Equations in Water Waves

This paper deals with the two- and three-dimensional nonlinear water waves generated by a steady or oscillating pressure distribution acting at the free surface of a running stream on water of finite depth h. The solutions of the corresponding linearized problems become singular depending on the relative values of the water depth, frequency, and the speed of the applied pressure leading to a resonant phenomenon. When the applied oscillatory pressure distribution moves at a resonant speed, the finite amplitude response is governed by the forced nonlinear Schrödinger (fNLS) equation. Under certain circumstances, the generated wave disturbance may not reach a steady state; in particular, for deep water, a steady state is never attained. For the case of a two-dimensional wave generated by a localized steady pressure moving at a resonant speed, the generated waves are actually of bounded amplitude and are governed by a forced Korteweg–de Vries (fKdV) equation subject to appropriate asymptotic initial conditions. A computational study of the forced KdV equation reveals that a series of solitons is generated in front of the pressure distribution. On the other hand, for the case of the three-dimensional waves induced by a localized steady pressure traveling at a resonant speed, the nonlinear response is governed by a forced Kadomtsev–Petviashvili (fKP) equation. In order to extend the range of applicability of the Boussinesq-type equations in the theory of water waves, the modified Boussinesq equations are derived in terms of the velocity potential on an arbitrary elevation and the free surface displacement.

The effect of surface tension on the reflection of gravity waves from a vertical cliff

The two dimensional capillary-gravity waves generated by a moving oscillatory pressure distribution in a fluid bounded on one side by a vertical cliff is investigated. The ultimate steady state asymptotic waves at a large distance from the source are determined in all cases. It is found that while in noncapillary case one gravity wave is reflected from the cliff for all values of the parameters; this reflection does not always occur when the surface tension is taken into account. It imposes certain condition on the parameters for reflection and this condition is explicitly determined.

Weakly nonlinear resonant waves generated by an oscillatory pressure distribution in a channel

This paper analyzes the problem of wave generation in a deep, long channel by an oscillating pressure patch. Special attention is paid to the free-surface response in the neighborhood of the resonance where the frequency of the forced oscillation is equal to one of the natural frequencies of the channel. The linearized solution for an antisymmetric wave generation, which yields an infinite response at the cut-off frequency, is here modified to include contributions from the most-singular third-order terms. The resulting generalized solution is uniform and renders a finite response at critical conditions. The modified dispersion relationship, which incorporates a phase shift in the wave frequency, yields a finite value for the group velocity, hence providing the means for carrying energy away from the disturbance. The case of symmetric wave generation, resulting in a progressive wave moving down the channel, and the related subharmonic resonance are also briefly discussed. A comparison between theory and some laboratory experiments is presented.

On the excitation of nonlinear water waves by a moving pressure distribution oscillating at resonant frequency

A theoretical study is made of the free-surface flow induced by a traveling oscillatory pressure distribution acting at the surface of water of finite depth. Depending on the relative values of the water depth and the frequency and speed of the applied pressure, the solution of the linearized water-wave problem may be singular, owing to a resonance phenomenon. Through an asymptotic analysis, it is shown that, close to resonant conditions, the finite-amplitude response is bounded, and it is governed by a forced nonlinear Schrödinger equation. It is deduced that, under certain circumstances, the generated wave disturbance may not reach a steady state; in particular, for deep water, a steady state is never attained.

Forced Oscillations in a Two-Layer Fluid of Finite Depth

An initial value investigation is made of the development of surface and internal wave motions generated by an oscillatory pressure distribution on the surface of a fluid that is composed of two layers of limited depths and of different densities. The displacement functions both on the free surface and on the interface are obtained with the help of generalized Fourier transformation. The method for the asymptotic evolution of the wave integrals is based on Bleistein’s method. The behavior of the solutions is examined for large values of time and distance. It is found that there are two classes of waves—the first corresponds to the usual surface waves with a changed amplitude and the second arises entirely due to stratification. Some interesting features of the wave system have also been studied.

Capillary-gravity waves produced by a moving pressure distribution

The initial-value problem of surface waves generated by a moving oscillatory pressure distribution is considered and the effect of surface tension on such waves is studied in detail. It is found that the surface tension modifies the critical case in a remarkable way. And also it introduces two extra waves that exist in the upstream side of the pressure distribution.

Transient waves generated by a moving oscillatory pressure on a sloping beach

A uniform asymptotic analysis of the unsteady wave motion generated by a moving oscillatory pressure distribution on a sloping beach of slope angle π/4 is given. Our method of investigation gives important information regarding the nature, number and distribution of the resulting wave pattern. The effect of the sloping beach on the waves is exhibited.

An Improved Mach-Box Approach for Supersonic Oscillatory Pressures

An analytical refinement of the Mach-box approach has been developed which provides greatly improved supersonic oscillatory pressure distributions with almost no increase in computer time over that required by the original formulation. The refinement consists, in part, of applying physically justifiable weighting factors to the terms of the aerodynamic influence coefficient matrix. Unlike approaches that employ curve smoothing to eliminate the erratic undulations in computed pressures obtained by the basic method, the present analysis produces well-behaved pressure distributions while retaining essential flow discontinuities. Furthermore, the present method is more cost-effective than approaches relying on refinements in the aerodynamic grid to obtain comparable improvements in the calculated pressures.

The disturbance produced by an oscillatory pressure distribution in uniform translation on the surface of a liquid

Expressions are derived for the two-dimensional surface elevation resulting from an oscillatory translating surface pressure distribution. The surface elevation is given as the sum of four terms, each of which is associated with an improper integral having a simple pole singularity. Results are presented for the delta function and the uniform spatial pressure distribution.

Generation of dispersive surface waves in magnetohydrodynamics

A theory of the generation and propagation of two and three dimensional magnetohydrodynamic surface waves due to an arbitrary as well as special oscillatory pressure distribution acting on the free surface of an inviscid electrically conducting fluid is presented. The unsteady solutions for two as well as three dimensional free surface elevation are obtained explicitly. The asymptotic behaviour of these solutions for large time and distance are determined to describe the qualitative and quantitative nature of the wave motions. The solutions consist of both the steady-state and the transient components. The latter is found to decay asymptotically for large time, and the steady-state is reached. Magnetohydrodynamic surface waves in deep and shallow fluid are dispersive in nature.

On a Rectangular Pressure Distribution of Oscillating Strength Moving Over a Free Surface

Through the application of linearized water-wave theory, a solution of the free surface due to the disturbance of a moving, oscillatory pressure distribution of rectangular form is obtained. Such a solution provides the basis for formulating the wave resistance of the moving pressure distribution just cited, as well as the hydrodynamic coefficients of a captured-air bubble of rectangular footprint in heave motion. Numerical methods are developed to compute the aforementioned resistance and hydrodynamic coefficients, the numerical examples of which are also presented. Of special interest is the occurrence of negative effectivemass at low frequencies for the two forward speeds considered in the present work. Another interesting feature is the hydrodynamic instability and the negative damping that occurs in the low-frequency range when the Froude number is very high.

Waves Due to a Moving Oscillatory Surface Pressure in a Stratified Fluid

The initial value problem of waves generated by an oscillatory pressure distribution moving uniformly on the free surface of a two-layer fluid is solved. The integral representations of the waves both on the free surface and on the surface of separation are obtained. By a passage to the limit t → ∞, the steady-state solution of the problem is derived through an asymptotic evaluation of these integrals at large distances. It is noticed that stratification sharply changes the number and the character of the progressive waves and also introduces two critical speeds instead of one as found in homogeneous fluid. At these speeds the solution becomes singular.