Free and Forced Vibrations of an Infinitely Long Cylindrical Shell in an Infinite Acoustic Medium PDF Download
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Author: H. H. Bleich
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 52
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Book Description
A method is presented which permits the determination of the frequencies of vibrations of infinitely long thin cylindrical shells in an acoustic medium. Expressions are obtained for the displacements of the shell and for the pressures in the medium in the case of forced vibrations due to sinusoidally distributed radial forces. The results indicate that there is a low-frequency range, where no radiation takes place, and a high-frequency range where the external force provides energy which is radiated. Resonance occurs in the low-frequency range only; in the high-frequency range it is prevented by the damping due to radiation. Free and forced vibrations of steel shells submerged in water are discussed; with limitations, the theory may be applied approximately to stiffened shells. The method requires only a minor modification to account for the effect of static pressure in the surrounding medium. The treatment of transient problems is also considered. If high-frequency terms occur in the force, or shock effects are wanted within a short time after the application of the force, a treatment using solely modes of vibration of the submerged structure would be incomplete, as additional terms occur in the solution. As an alternative approach, the modes of free vibration of the structure may be used as generalized coordinates which fully describe the response of the structure but leave the medium to be treated, by means of the differential equations for the potential or in any other way desired.
Author: H. H. Bleich
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 52
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Book Description
A method is presented which permits the determination of the frequencies of vibrations of infinitely long thin cylindrical shells in an acoustic medium. Expressions are obtained for the displacements of the shell and for the pressures in the medium in the case of forced vibrations due to sinusoidally distributed radial forces. The results indicate that there is a low-frequency range, where no radiation takes place, and a high-frequency range where the external force provides energy which is radiated. Resonance occurs in the low-frequency range only; in the high-frequency range it is prevented by the damping due to radiation. Free and forced vibrations of steel shells submerged in water are discussed; with limitations, the theory may be applied approximately to stiffened shells. The method requires only a minor modification to account for the effect of static pressure in the surrounding medium. The treatment of transient problems is also considered. If high-frequency terms occur in the force, or shock effects are wanted within a short time after the application of the force, a treatment using solely modes of vibration of the submerged structure would be incomplete, as additional terms occur in the solution. As an alternative approach, the modes of free vibration of the structure may be used as generalized coordinates which fully describe the response of the structure but leave the medium to be treated, by means of the differential equations for the potential or in any other way desired.
Author: Donald J. Butler
Publisher:
ISBN:
Category :
Languages : en
Pages : 72
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Book Description
Author: Lord Rayleigh (Robert John Strutt)
Publisher:
ISBN:
Category :
Languages : en
Pages : 6
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Book Description
Author: Anthony E. Armenàkas
Publisher: Elsevier
ISBN: 1483158616
Category : Technology & Engineering
Languages : en
Pages : 225
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Book Description
Free Vibrations of Circular Cylindrical Shells deals with thin-walled structures that undergo dynamic loads application, thereby resulting in some vibrations. Part I discusses the treatment of problems associated with the propagation of plane harmonic waves in a hollow circular cylinder. In such search for solutions, the text employs the framework of the three-dimensional theory of elasticity. The text explains the use of tables of natural frequencies and graphs of representative mode shapes of harmonic elastic waves bounding in an infinitely long isotropic hollow cylinder. The tables are found to be useful as they can be used to check validity and provide estimates of the range of applicability of various shell theories. The purpose of the frequency equation and that of the numerical computations likewise are considered. The book includes a computer program written in the FORTRAN language to show how it is used in the computations, except in cases when H (the thickness of shell) and L (axial half of wavelength) result in extremely small values. Part II consists of related tables and graphs. Physicists, engineers, students, and researchers in advanced sciences will find this book of interest.
Author: Hans H. Bleich
Publisher:
ISBN:
Category : Cylinders
Languages : en
Pages : 143
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Book Description
Large amplitude forced vibrations of infinitely long, thin cylindrical shells are determined, using generalized coordinates which are the infinie sequence of normal modes of linear shell theory. The perturbation procedure employed gives solutions consisting only of a finite number of terms, so that arbitrary truncation of the infinite series in terms of the modes is avoided. As reported previously, unusual types of response are possible, in which the nodal lines of the applied sinusoidal pressure (in space) and of the radial displacement do not agree. Amplitude-frequency relations for regular and unusual responses are obtained. Numerical coefficients occurring in these relations are tabulated. It is demonstrated that the unusual responses exist only for sufficiently small values of a nondimensional parameter which increases with the ratio of critical damping. The unusual solutions become unstable, or do not exist, when the parameter exceeds cut-off values derived in the text. The situation is illustrated by a sequence of examples with varying values of damping. (Author).
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: Joshua E. Greenspon
Publisher:
ISBN:
Category : Acoustical engineering
Languages : en
Pages : 0
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Book Description
Author: Melvin L. Baron
Publisher:
ISBN:
Category : Shells (Engineering)
Languages : en
Pages : 31
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Book Description
Author: JOSHUA E. GREENSPON
Publisher:
ISBN:
Category :
Languages : en
Pages : 1
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Book Description
Author: Bruce S. Berger
Publisher:
ISBN:
Category :
Languages : en
Pages : 17
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Book Description
The solution of the vibration of an orthotropic layered cylindrical viscoelastic shell in an acoustic medium is derived through the application of the theorem of correspondence to the shell equations of motion. The acoustic fluid is modelled through a finite difference scheme. Numerical results for the normal displacements are in exact agreement with known elastic solutions. (Author).
