Mode Coupling of Gun Tubes Caused by Space Curvature and Initial Twist

摘要

The report formulates equations of motion for a gun tube with arbitrary space curvature and cross section geometry and presents results showing the effects of curvature, torsion, and cross section shape on natural frequencies and mode shapes. Expressions for the kinetic and potential energy functions of a curved and twisted tube are formulated in terms of centerline displacements and cross section rotations. These expressions are first used to derive the equation of motion and natural boundary conditions using Hamilton's Principle. The equations of motion are then specialized for various variations of centerline curvature, torsion and cross section shape along the tube axis. Next, the kinetic and potential energy functions are used to formulate a Rayleigh-Ritz solution for the mode shapes and natural frequencies of helical tubes with fixed-fixed ends. The effects of space curvature and torsion and of cross section out-of-roundness on frequencies and mode shapes are examined. The natural frequencies and mode shapes of tubes are found to be significantly affected by even a slight change in values of the curvature and torsion parameters. The fundamental frequencies and the degree of coupling among displacement variables in natural modes always increased when either curvature parameter was increased. Out-of-roundness also introduces further complexity into the mode shapes. Keywords: Curved gun tube; Vibration of Gun tubes; Accuracy; Jump; Dispersion. (edc)