Vibrations Of Circular Cylindrical Shells Research Articles

Modal response of circular cylindrical shells with structural damping

Although a vast literature exists dealing with the free vibrations of circular cylindrical shells, relatively little can be found for the problem of dynamic response due to sinusoidally varying exciting forces, especially when damping exists. In the present work the response of a shell subjected to a sinusoidal radial pressure is studied, when the pressure has the same distribution as the normal mode shape. Structural (hysteresis) damping is considered. For a unit amplitude of exciting pressure, the lowest frequency modes are found to yield the largest resonant response. Because of a small amount of mode coupling, the peak amplitudes are found to be not quite inversely proportional to the strength of the damping, and there is a slight shift in the locations of the resonant peaks.

Vibrations of circular cylindrical shells with cutouts

An experimental and analytical study was carried out to examine the effect of circular cutouts on the resonant frequencies of thin cylindrical shells. The experimental results were obtained from tests performed on clamped-free aluminum cylinders and clamped ring-stiffened tri-acetyl cellulose shells with a lap-joint seam. The analytical solution was a simplified Rayleigh-Ritz type approximation. For the beam type mode, the circular cutouts had a significant influence on the frequency. For the mode with higher numbers of circumferential waves, however, the cutouts had a relatively small effect on the frequency spectra.

Free vibrations of circular cylindrical shells

The finite element method is used to predict the dynamic behaviour of circular cylindrical shells in free vibrations. A suitable shape function for the circumferential displacement distribution has been proposed. This reduces the three-dimensional character of the problem to a two-dimensional one. The simultaneous iteration method to determine the eigen-frequencies and eigenvectors is utilised for solving the eigenvalue problem. The accuracy of the method has been checked by verifying the results of known cases. Finally an experimental shell structure containing elastic rings welded at the ends has also been analysed and the experimental results compared with the theoretical ones.

Effects of rotation on vibrations of circular cylindrical shells

The effects of rotation due to centrifugal and Corliolis forces on the frequencies are analyzed on the basis of the Herrmann-Armenakas bending theory. Closed-form expressions for the frequency and the nodal rotational velocity of the flexural modes are discussed, and their accuracy is compared with previously published results.

A note on beam-type vibrations of circular cylindrical shells

The basic equations of vibration of a thin circular cylindrical shell are reduced to a single equation involving one potential function. It is shown that, if the shell is very long and the number of circumferential waves, n, equals unity, this equation reduces to the equation of transverse vibrations of a beam with rotatory inertia included.

Three-dimensional theory on the natural vibration of circular cylindrical shells

From the viewpoint of the three-dimensional theory of elasticity, a direct method of solution for the natural vibration of a circular cylindrical shell is formulated based on the principle of virtual work. In the present method of solution, all the assumptions, on which the majority of existing theories are based are abandoned, and the vibration characteristics of a circular cylindrical shell with arbitrary thickness to curvature ratio will be studied in the unified way. In a numerical analysis influences of the length-curvature as well as thickness-curvature ratios are extensively studied for various cases of geometrical boundary conditions.

Free vibration of circular cylindrical shells of finite length

= mean radius of the shell = arbitrary complex constants = modulus of elasticity = thickness of shell wall = length of shell = number of circumferential waves around shell = mode identification number; equal to the number of axial nodal circles, excluding the ends, plus 1 = time = displacements of a point in the middle surface of the shell (axial, tangential, and radial, respectively) = axial and circumferential coordinates respectively = ith root of the auxiliary equation = mass density of shell = circular frequency = frequency parameter, = paco(l — p)/E = poisson's ratio E h L m p

Vibrations of Circular Cylindrical Shells Due to Gyroscopically Induced Inertia Loads

An analytical study is described for both open and closed circular cylindrical shells subjected to gyroscopically induced inertia loads. The shells are considered to be spinning at a constant rate about their longitudinal axis of revolution, which is simultaneously precessing at a constant rate at a fixed angle of nutation. Based on shallow-shell theory and assuming a dominantly transverse deformation, the equations of motion are formulated for this type of loading. These equations are found to contain distributed harmonic inertia forces whose amplitude and frequency are dependent on the precessional and spin angular velocities, respectively. The solutions of these equations of motion show that the natural frequencies of the shell are reduced by both the spin and precessional angular velocities and that only certain modes of vibration will respond to the gyroscopically induced inertia loading. It is also shown that the reduction in natural frequencies can become important for very shallow shells.