Download Free Vibrations Of Infinitely Long Cylindrical Shells Under Initial Stress Book in PDF and EPUB Free Download. You can read online Vibrations Of Infinitely Long Cylindrical Shells Under Initial Stress and write the review.

The bending theory of shells under the influence of initial stress is applied in this investigation to study the effect of initial uniform circumferential stress, uniform bending moment and uniform radial shear on the dynamic response of an infinitely long (motion is independent of the axial coordinate) elastic circular cylindrical shell. (Author).
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.
The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.
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.
The primary aim of this book is to give the reader an insight into the mechanics of vibrations of cylindrical shells, rather than to present him with a method for straightforward eigendata calculations. The contents are laid out phenomenologically. The first chapter conveys an elementary idea on the elastic strain in a thin shell, arising from the so-called membrane theory, the limitations of this theory are assessed with a clear physical interpretation of its drawbacks. The main emphasis of the book lies in the second chapter, where the reader will find a rigorous interpretation of the fundamental aspects of the so-called bending theory of shells. The major part of this chapter is devoted to thin-shell deformation theories. The solution of the exact equations of dynamic equilibrium that can be derived by the underlying linear theory of mathematical elasticity is discussed in the third chapter. The fourth chapter is an extension of the original Slovak version of this book. New research data in the field of vibrations of shell-like structures are presented mainly for layered shells. A simple mathematical approach is used throughout the book.
There are numerous engineering applications for high-speed rotating structures which rotate about their symmetric axes. For example, free-flight sub-munition projectiles rotate at high speeds in order to achieve an aerodynamically-stable flight. This is the first book of its kind to provide a comprehensive and systematic description of rotating shell dynamics. It not only provides the basic derivation of the dynamic governing equations for rotating shells, but documents benchmark results for free vibration, critical speed and parametric resonance. It is written in a simple and clear manner making it accessible both the expert and graduate student. The first monograph to provide a detailed description of rotating shell dynamics Dynamic problems such as free vibration and dynamic stability are examined in detail, for basic shells of revolutions
This monograph will be valuable for English-speaking scientists wanting to know more about the state-of-the-art in Russian research on non-linear shell theory. It will also be of value to all materials scientists concerned with the use and behaviour of composite materials in structural applications.