Derivation of a two-dimensional equation for shallow shells by means of the method of I. Vekua in the case of linear theory of elastic mixtures

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

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Asymptotic behavior of eigenfunctions and eigenfrequencies of oscillation boundary value problems of the linear theory of elastic mixtures

Georgian Mathematical Journal ◽

10.1007/bf02254739 ◽

1996 ◽

Vol 3 (2) ◽

pp. 177-200 ◽

Cited By ~ 3

Author(s):

M. Svanadze

Keyword(s):

Asymptotic Behavior ◽

Boundary Value Problems ◽

Linear Theory ◽

Boundary Value ◽

Theory Of Elastic Mixtures

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TSUNAMI GENERATION AND PROPAGATION

Coastal Engineering Proceedings ◽

10.9753/icce.v13.146 ◽

1972 ◽

Vol 1 (13) ◽

pp. 146

Author(s):

Joseph L. Hammack ◽

Frederic Raichlen

Keyword(s):

Linear Theory ◽

Source Region ◽

Three Dimensional ◽

Frequency Dispersion ◽

Nonlinear Effects ◽

Its Region ◽

Experimental Results ◽

Specific Class ◽

Two Dimensional ◽

Three Dimensional Models

A linear theory is presented for waves generated by an arbitrary bed deformation {in space and time) for a two-dimensional and a three -dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model. The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

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Two-dimensional generalizations of the Newcomb equation

Journal of Plasma Physics ◽

10.1017/s002237780001480x ◽

1990 ◽

Vol 43 (2) ◽

pp. 291-310 ◽

Cited By ~ 24

Author(s):

R. L. Dewar ◽

A. Pletzer

Keyword(s):

Rational Surface ◽

Cylindrical Symmetry ◽

Two Dimensional ◽

Transformation Theory ◽

Continuous Symmetry ◽

Scalar Form ◽

Complicated Form ◽

Dimensional Equation ◽

Zero Frequency ◽

The Ideal

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.

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