The Structural Response of Cylindrical Shells to Internal Shock Loading

Abstract

The internal shock loading of cylindrical shells can be represented as a step load advancing at constant speed. Several analytical models are available to calculate the structural response of shells to this type of loading. These models show that the speed of the shock wave is an important parameter. In fact, for a linear model of a shell of infinite length, the amplitude of the radial deflection becomes unbounded when the speed of the shock wave is equal to a critical velocity. It is evident that simple (static) design formulas are no longer accurate in this case. The present paper deals with a numerical and experimental study on the structural response of a thin aluminum cylindrical shell to shock loading. Transient finite element calculations were carried out for a range of shock speeds. The results were compared to experimental results obtained with the GALCIT 6-in. shock tube facility. Both the experimental and the numerical results show an increase in amplitude near the critical velocity, as predicted by simple steady-state models for shells of infinite length. However, the finite length of the shell results in some transient phenomena. These phenomena are related to the reflection of structural waves and the development of the deflection profile when the shock wave enters the shell.

On the Adequacy of Shell Models for Predicting Stresses and Strains in Thick-Walled Tubes Subjected to Detonation Loading

“…5. The predominance of these two frequencies has also been verified experimentally by Beltman et al [3]. Within the low-frequency vibrations behind the load, the peak hoop and axial strains from the finite element and shell models differ only by 2-3%, which is expected since the wavelength of these is vibrations fairly large compared to the wall thickness.…”

“…For practical cases involving detonations or shock waves in metal tubes, the velocities are small enough that the first branch plays the most important role in the response. The dispersion curves can be used to estimate the most prominent wavelengths in the response: these are the intersection points between the load speed and the dispersion curve, which correspond to steady-state solutions to the shell equations [3,11]. As discussed by Tang, these steadystate solutions exhibit a resonance at the critical velocity υ co corresponding to the minimum of the first branch of the dispersion curve [11].…”

“…For instance, Beltman et al used a steady-state shell model to analyze peak strains in thin (a/h = 16) tubes subjected to internal shock waves and found reasonably good agreement with finite element models and experimental measurements except in the vicinity of the first critical velocity, where effects of material damping are important and the steady-state approximation is inadequate [3,4]. Likewise Simkins measured hoop strains in a much thicker tube (a/h = 5.2) and found good agreement with the predictions of shell theory [5].…”

Dynamic Stability of Cylindrical Shells under Moving Loads by Applying Advanced Controlling Techniques Part I—Using Periodic Stiffeners

“…These challenging counteractions lead many 2 Advances in Acoustics and Vibration investigators to propose theoretical and experimental solutions. The dynamic behavior of cylindrical shells was studied experimentally by Finlayson [2], Simkins [3,4], Beltman et al [5], Thomas [6], and Baz et al [7], the results indicated that increasing bullet velocity by expanding pressure step causing the axisymmetric radial vibration to be several times higher than that produced by the static application of the same load. So, the traveling velocity of the moving load affects the amplitude of the radial response and critical velocity, above which the shell response becomes unstable.…”

A Simple Model for Axial Displacement in a Cylindrical Pipe With Internal Shock Loading

“…[1] and [2]. These observations consist primarily of point measurements of strain, which have been extremely useful for quantitative characterization of structural loading as well as point validation of simulations.…”