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advanced in papers analysis angle angular angular velocity Applied Mechanics Division approximate ASME Applied Mechanics assumed authors axial axis beam bending blade boundary conditions buckling calculated circular co-ordinates coefficients components computed constant corresponding cosh creep cross section curve cylinder damping deflection deformation derived determined differential equation dimensionless Discussion displacement edge effect elastic Equa Equation 15 experimental flow force given inertia initial integral isotropic Journal of Applied linear load Manuscript received maximum Mechanical Engineers method mode motion natural frequencies normal obtained parameter photoelastic plane plane strain plastic plastic deformation plate Poisson's ratio present pressure problem radius ratio received by ASME rotation shear shear stress shell shown in Fig simply supported sinh solution strain surface symmetric tangential temperature theoretical theory Theory of Elasticity thermal thickness tion torque torsion tractions Trans understood as individual values velocity vibration West Coast Conference yield zero