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Unified Approach to the Solution of Problems of Unsteady Laminar Flow in Long Pipes
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amplitude analysis Applied Mechanics Division approximation ASME Applied Mechanics ASME Journal assumed axial behavior boundary conditions boundary layer buckling calculated circular coefficient components Composite Materials computed considered constant constitutive equations coordinate corresponding crack cross section curve cylinder defined deformation denotes derived determined differential equations discussed disk dislocation displacement dynamic effect eigenvalues elastic equilibrium fiber finite element flow fluid formulation Fracture Fracture Mechanics frequency friction function given Green's function INFO initial integral equation interface isotropic Journal of Applied linear loading Manuscript received matrix method mode modulus nondimensional nonlinear normal numerical obtained paper parameters particles perturbation plane plane strain plastic plate Poisson's ratio present pressure problem radial ratio received by ASME region response rotation shear stress shown in Fig simple shear solid solution stiffness strain stress intensity factor surface symmetric theory transverse variables vector velocity Vibration viscoelastic viscosity wave zero