Axisymmetric Vibrations of Prolate Spheroidal Shells

Nemergut, P. J.; Brand, R. S.

doi:10.1121/1.1909651

Cited by 9 publications

(2 citation statements)

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“…Almost all of these analyzed circular cylindrical shells, conical shells, and spherical shells. Among them 18 references Silbiger, 1960, 1961;Sibliger and DiMaggio, 1961;Shiraishi and DiMaggio 1962;Gontkevich, 1964;Hayek and DiMaggio 1965;Hwang, 1965;Nemergut and Brand, 1965;Penzes andBurgin, 1965, 1966;Dimaggio and Rand, 1966;Ross andMatthews, 1966, 1967;Rand andDiMaggio, 1967, Yen andRand, 1968;Penzes 1969;Hayet, 1970) are related to spheroidal shells. Some additional investigations of dynamic and static characteristics of spheroidal shells have also been disclosed (Hwang, 1964;Bedrosian and DiMaggio, 1972;Berger, 1974;Cambou, 1975;Burroughs and Magrab, 1978;Ross and Johns, 1983;Popov and Chernyshev, 1985;Jones-Oliveria, 1990;Chen and Ginsberg, 1992;Ross, 1996;Al-Jumaily and Najim, 1997;Zhang et al, 1998;Chen, 2001;Ma et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Vibrations of deep and shallow hemi-spheroidal domes with non-uniform thickness having a top cut-out

Kang

2014

Journal of Vibration and Control

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A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hemi-spheroidal domes with non-uniform thickness having a top cut-out. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The edges of the shell may be free or may be subjected to any degree of constraint. Displacement components ur, uθ, and uz in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic simple polynomials in the r and z directions. Potential (strain) and kinetic energies of the hemi-spheroidal domes with non-uniform thickness having a top cut-out are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the algebraic polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Numerical results are presented for shallow and deep hemi-spheroidal domes with non-uniform thickness having a top cut-out of five values of aspect ratios, which are free at the inner edge and free or fixed at the bottom of the domes. The frequencies from the present 3-D Ritz method are compared with those from other 3-D analysis and a 2-D thin shell theory by previous researcher.

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Section: Introductionmentioning

confidence: 99%

Vibrations of deep and shallow hemi-spheroidal domes with non-uniform thickness having a top cut-out

Kang

2014

Journal of Vibration and Control

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“…Almost all of these dealt with shells of revolution (e.g., circular cylindrical, conical, spherical). Among them were 18 references Silbiger, 1960, 1961;Silbiger and DiMaggio, 1961;Shiraishi and DiMaggio, 1962;Gontkevich, 1964;Hwang, 1965;Penzes and Burgin, 1965;Nemergut and Brand, 1965;Hayek and DiMaggio, 1965;Matthews, 1966, 1967;DiMaggio and Rand, 1966;Penzes and Burgin, 1966;Rand and DiMaggio, 1967;Yen and DiMaggio, 1967;Rand, 1968;Penzes, 1969;Hayek, 1970) considering ellipsoidal shells. Some additional investigations of dynamic and static characteristics of ellipsoidal shells have also been uncovered (Hwang, 1964;Bedrosian and DiMaggio, 1972;Berger, 1974;Cambou, 1975;Burroughs and Magrab, 1978;Ross and Johns, 1983;Popov and Chernyshev, 1985;Jones-Oliveira, 1990;Chen and Ginsberg, 1992;Ross, 1996;Al-Jumaily and Najim, 1997;Zhang et al, 1998;Chen, 2001;Qatu, 2002).…”

Section: Introductionmentioning

confidence: 99%

Vibrations of hemi-ellipsoidal shells of revolution with eccentricity from a three-dimensional theory

Kang

2013

Journal of Vibration and Control

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A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hemi-ellipsoidal shells of revolution with eccentricity having uniform thickness. Unlike conventional shell theories, which are mathematically two-dimensional, the present method is based upon the 3-D dynamic equations of elasticity. Displacement components [Formula: see text], [Formula: see text], and [Formula: see text] in the radial, circumferential, and axial directions, respectively, are taken to be periodic in [Formula: see text] and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the hemi-ellipsoidal shells of revolution with eccentricity are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactitude is demonstrated for the first five frequencies of the shells of revolution. Numerical results are presented for a variety of hemi-ellipsoidal shells of revolution with eccentricity.

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The motion of the left ventricle: II

Vayo

1967

Bulletin of Mathematical Biophysics

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Axisymmetric Vibrations of Prolate Spheroidal Shells

Cited by 9 publications

References 0 publications

Vibrations of deep and shallow hemi-spheroidal domes with non-uniform thickness having a top cut-out

Vibrations of deep and shallow hemi-spheroidal domes with non-uniform thickness having a top cut-out

Vibrations of hemi-ellipsoidal shells of revolution with eccentricity from a three-dimensional theory

The motion of the left ventricle: II

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