Abstract
A thick-walled solid cylinder, with a gas filling the circular cylindrical cavity, is encased in a thin elastic shell. The material of the solid cylinder is incompressible, and the behavior in shear is dependent on frequency. In this paper, the transcendental frequency equation for free nonaxially symmetrical motion in plane strain of the gas-solid-case system is derived, and is solved numerically. For various values of the relative thickness of the shell and for a large number of modes, the frequencies are shown vs the ratio of inner and outer radius of the cylinder. The dynamic interaction between gas and solid is discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 964-968 |
| Number of pages | 5 |
| Journal | Journal of Spacecraft and Rockets |
| Volume | 5 |
| Issue number | 8 |
| DOIs | |
| State | Published - Jul 1968 |
| Externally published | Yes |
Funding
ical model for investigation of the vibrations of solid-propellant rocket motors. The structural dynamics of solid-propellant rockets require investigation, not only for the obvious reason that the structural integrity of the grain-casing system may be affected by intense vibrations or high-rate wave propagation phenomena, but also because information on natural frequencies and mode shapes of the rocket motor is of importance in studies of the dynamics of the complete launching vehicle or missile. We mention here the relevance of information on the vibratory characteristics of the rocket motor to the design of the guidance system, to staging studies, and to transportation and handling studies. The natural frequencies of the structural system consisting of case, propellant, and gas are also of particular importance in studies of acoustic instability of the combustion process.1 Free radial and circumferential oscillations of gas-filled cylinders were studied by Deters2 and Bird et al.3 In these studies, the propellant was either rigidly supported at the outer surface, or the contact with a rigid case was smooth, or the rigid case and the propellant cylinder were separated by a layer of gas. Since solid-propellant grains are encased in metal or fiberglass-reinforced cases, the boundary conditions at the outer radius of the propellant cylinder, considered in Refs. 2 and 3, do not represent in a satisfactory manner the actual boundary conditions. The present paper is, therefore, concerned with the more realistic situation in which the gas-filled cylinder is encased in a shell of high relative rigidity. In related work, Sann and Shaffer4 have considered the free transverse vibrations of a solid cylinder bonded to a thin casing. The radial and torsional motions of an encased hollow cylinder were considered by one of the present authors.5""7 In this paper it is assumed that the assembly is very long, so that, except near the end sections, it is permissible to assume a state of plane strain. The only nonvanishing components of the displacement are then the radial displacement ur(r,6,t) and the circumferential displacement ue(r,8,t). It is assumed that the excess pressure and the particle velocity in the gas satisfy linearized equations. The material of the cylinder is homogeneous, isotropic, and incompressible. The Received November 6, 1967; revision received May 3, 1968. The work reported in this paper was supported by the Office of Naval Research under Contract ONR Nonr 1228(34) with Northwestern University. * Associate Professor, Department of Civil Engineering. Member AIAA. t Graduate Student, Department of Civil Engineering.
ASJC Scopus subject areas
- Aerospace Engineering
- Space and Planetary Science