Infinite Circular Cylindrical Shell Research Articles

The structural and acoustic response of a submerged infinite cylindrical shell in the presence of hydrostatic pressure fields

The dynamic response of an infinite circular cylindrical shell submerged in an acoustic medium was formulated using Flugge's thin shell theory. The effects of a uniform hydrostatic pressure field were modeled by including constant initial stress terms in the shell equations of motion. The driving point impedance of the shell was examined and characterized in terms of the in‐vacuo shell impedance and the additional fluid impedance. The effects of the hydrostatic pressure on both were determined and examined as a function of frequency. The surface acoustic intensity field resulting from a localized harmonic driving force was formulated and integrated numerically over the surface of the shell in order to determine the radiated acoustic power. The relative effects of the fluid loading and the hydrostatic pressure field on the acoustic response were subsequently examined as a function of the frequency of the excitation.

Acoustic high‐frequency scattering by elastic cylindrical shells

Acoustical scattering resulting from a high‐frequency plane‐wave incident upon an infinite aluminum circular cylindrical shell immersed in and filled with water is determined by applying the Sommerfeld–Watson transformation to the classical Rayleigh normal‐mode series solution. The resulting contour integrals are computed by both the saddle point method and by summing residues over poles which correspond to the zeros of a 6 ×6 determinant resulting from satisfying the necessary boundary conditions. The Bessel functions and their derivatives which appear in the 6 × 6 determinant are evaluated using asymptotic representations of both the Airy and Debye type depending upon the region of the complex plane. Emphasis is placed on the transitions in the scattering characteristics as the shell goes from a solid cylinder to a thin‐walled shell. This dual behavior will be discussed in terms of the number and trajectories of allowed modes of the scatterer, the dispersion curves of various modes, and the contributions of the various modes to the scattered pressure field.

The input mobility of an infinite circular cylindrical elastic shell filled with fluid

The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h a = 0·05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.

Effect of a nonstationary acoustic wave on a cylindrical orthotropic shell

Study of the nonstationary deformation of thin-walled structure elements subjected to waves in an acoustic medium (an ideal compressible fluid or gas) has advanced significantly in recent years. The fundamental results obtained in this area are shown in the monographs [6, 8, 15, 16] and in the survey [5]. The overwhelming majority of these investigations concern isotropic plates and shells. At the same time, in connection with the much broader utilization of glass--plastic materials and thin-walled structure elements using them in the most diverse branches of engineering and machine construction, investigation of shocks on such objects has become urgent. Some of the most important objects from the practical viewpoint are multilayered cylindrical shells. In this area, we should note [7-10]. The effect of a plane step wave on an infinite elastic cylindrical shell reinforced by a number of periodically arranged ribs is examined in [9]. Approximate relations to describe the interaction between the obstacle and the medium are used in analyzing the transients in the papers mentioned. The present paper is devoted to an investigation of the nonstationary deformation of an orthotropic cylindrical shell subjected to a plane step wave whose front is parallel to the shell generatriz. A method consisting of the application of the Laplace integral transform and its subsequent inversion by using a Volterra integral equation for each of the vibrations modes is used to solve the problem. This method had been used earlier to solve nonstationary hydroelasticity problems for cylindrical and spherical bodies [2, 12, 13, 14]. 1. An infinite circular cylindrical shell submerged in an acoustic medium is considered. It is assumed that the shell material is cylindrically srthstropic, i.e., its elastic properties in the generatrix and directrix directions are distinct. We use the equations, presented in [1], but supplemented by inertial terms, to describe the elastic deformation of the shell. We hence limit ourselves at once to the case of plane deformation. We will have

Asymptotic analysis of the state of stress of am infinite circular cylindrical shell: PMM vol. 40, n≗1, 1976, pp. 96–103

The transverse sections of a shell are deformed identically under the effect of external forces which do not vary along the generator. In this case it is admissible to limit oneself to a study of the state of stress of an elastic concentric ring. A large quantity of papers is devoted to this classical problem. Primarily the case of nonthin shells is treated. The exception is in the papers of Ustinov [1, 2], where the state of stress of a very thin ring subjected to normal forces is considered. The stress field in a thin ring, seemingly subjected to both normal and tangential external forces, is also analyzed in this paper by another method.

Dynamic Stresses of an Infinite Circular Cylindrical Shell Subjected to Concentrated Impulsive Loads

Dynamic Stresses of an Infinite Circular Cylindrical Shell Subjected to Concentrated Impulsive Loads

Dynamic Stresses of an Infinite Circular Cylindrical Shell Subjected to Concentrated Impulsive Loads

The dynamic response of an infinite circular cylindrical shell, which is suddenly imposed with equal and opposite radial loads, is treated within the framework of Flugge's and Donnell's shell theories. Donnell's theory is not recommended as compared with Flugge's theory for predicting the deformations but is satisfactorily accurate for predicting the stresses. In the case of the concentrated loads, the bending moments beneath the load are equal to infinity but the stress distributions agree approximately with the stress distributions under the loads applied constantly over a small area until the radius of the area equals to roughly ten percent of the radius of the cylindrical shell.

Wave propagation in a piezoelectric crystal shell

In this study, we first present a two-dimensional theory of high-frequency vibrations of piezoelectric crystal surfaces, coated with thin electrodes. The theory is systematically and consistently extracted using a method of direct integration [cf. M. C. Dökmeci, J. Acoust. Soc. Am. 54, 292 (1973) and L. Al, Nuovo Cimento 7, 449–454 (1973)] appropriate to the linear expansions of the mechanical and electric displacement fields, from the three-dimensional field equations. The interactions between crystal plate and electrodes are taken into account through the usual continuity conditions. Next, we use logarithmic convexity arguments to enumerate a set of sufficient conditions for uniqueness in the theory [cf. M. C. Dökmeci, “On the Higher-order Theories of Piezoelectric Crystal Surfaces,” to appear in J. Math. Phys. 15, (1974)]. Further, we exhibit some applications of the theory, and, in particular, study wave propagations in an infinite circular cylindrical anisotropic thin shell of uniform thickness, with its inner and outer faces being both traction free and completely coated with electrodes. The transcendental equations of resonant frequencies are obtained and the dispersion curves are calculated for a rotated Y-cut quartz shell. The results are compared with those of unplated shell, and considerable deviations in the dispersion spectrum are found. [Work supported by the Turkish Office of Naval Research.]

Green's Functions in the Non‐Stationary Theory of Elastic Shells

AbstractThe method of Green's function is extended to the thermoelastic Kirchhoff‐Love theory of thin shells. A reciprocity theorem and heat conduction equations appropriate to the Kirchhoff‐Love theory are used to derive integral solution formulas for middle surface displacements involving six Green's functions. The equations determining the Green's functions are deduced and compared to those for shallow shells. Both sets of equations are solved by conventional techniques for an infinite circular cylindrical shell. One of the Green's functions is evaluated numerically at the source point for both theories, and a comparison between them is made for various ratios of shell thickness to radius.

Further comparison of elasticity and shell theory solutions.

Abstract : The problem of an infinite circular cylindrical shell subjected to periodically spaced axisymmetric band loads is investigated using a Reissner-Naghdi higher-order shell theory. The generalized equilibrium equations, which include the effects of transverse normal stress and transverse shear deformation, were applied to the specific problem at hand. These equilibrium equations were successfully uncoupled, and an expression describing the transverse displacement of the median surface was obtained. The solution of this expression was then used to calculate the stress resultants, stresses, and displacements. A comparison of the resulting stresses and displacements with the exact elasticity solution and some lower-order shell theory solutions of the same problem was carried out for ratios of inner to outer shell radius equal to 0.7, 0.8, 0.87, 0.9, 0.93, and for a ratio of distance between band loads to outer shell diameter equal to 0.2. The ratio of band width to distance between band loads was also equal to 0.2. The Poisson's ratio used is equal to 0.3. (Author)