A SIMPLIFIED METHOD FOR DYNAMIC STRESS ANALYSIS OF AXIALLY SYMMETRIC SOLID PROPELLANT GRAINS

The report investigates the response to transient axially symmetric end pressure of a finite length hollow circular cylinder with a fixed outer surface. Axially symmetric thickness shear motion is assumed predominant and a correspondingly simplified equation of motion is derived. It is found that, f...

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Bibliographic Details
Main Authors: Jones, John Paul, Whittier, James S
Format: Report
Language:English
Subjects:
BESSEL FUNCTIONS
CYLINDRICAL BODIES
DEFORMATION
DYNAMICS
EQUATIONS OF MOTION
GALERKIN'S METHOD
INTEGRAL EQUATIONS
Mechanics
MOTION
PRESSURE
PROPELLANT GRAINS
SHEAR STRESSES
STRESSES
THICKNESS
VIBRATION
VISCOELASTICITY
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Summary:The report investigates the response to transient axially symmetric end pressure of a finite length hollow circular cylinder with a fixed outer surface. Axially symmetric thickness shear motion is assumed predominant and a correspondingly simplified equation of motion is derived. It is found that, for forced motion problems, considerable simplification is obtained if, instead of solving the equations of motion exactly, one uses Galerkin's method. One- and two-term' Galerkin expansions are compared with exact solutions for free vibrations and for transient response to suddenly applied pressure. Agreement is good for the one-term expansion and excellent for the two-term expansion. The equations are derived for a standard linear solid as well as an elastic grain, calculations are performed for the elastic grain only. (Author)