Experimental Mechanics

, Volume 13, Issue 4, pp 150–156 | Cite as

Elastic-wave propagation in a joined cylindrical-conical-cylindrical shell

Study results in an understanding of wave propagation across a joint-transition region in joined cylindrical-conical-cylindrical sections of a structure
  • J. L. Rose
  • R. W. Mortimer
  • A. Blum


The problem of longitudinal impact of a thin finite-joined shell, consisting of a cylinder-truncated cone-cylinder, is analyzed both experimentally and analytically. the model analyzed is a 1/100-scale replica of a portion of the Apollo/Saturn V vehicle. Experimental results were obtained from a drop-test system. Longitudinal and circumferential strain pulses were monitored on each section of the joined shell. The velocity of the impacter ring prior to impact was measured and used as a boundary condition in the solution of the governing partial-differential equations. A “bending” theory, including transverse-shear, radial-inertia and rotary-inertia effects, was used to analyze the finite-joined shell. Appropriate transformation relations were developed at each of the joints between the cylinders and truncated cone. The results were then obtained by solving the governing equations numerically by the method of characteristics. Good agreement between analytical and experimental strain profiles was obtained.


Boundary Condition Mechanical Engineer Fluid Dynamics Governing Equation Circumferential Strain 
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plate velocity=(E p /ρ)1/2


shear velocity=k (G/ρ)1/2


Young’s modulus of elasticity


\(E/(1 - v^2 )\)


shear modulus of elasticity=E/2 (1+ν)


thickness of shell


shear-correction factor=0.87


shell moment


shell forces


radial coordinate


radius of midsurface of cone at the small truncated end


radius of midsurface of the shell

s, θ, ξ

shell coordinates; meridional, circumferential and normal, respectively


meridional and normal displacements, respectively

u, w

meridional and normal displacements of the centroidal surface, respectively


velocity imparted to shell by ring


axial distance


meridional strain


circumferential strain


1/2 apex angle of cone


pulse duration


Poisson’s ratio


centroidal distance=\(\frac{{h^2 \cos \phi }}{{12(r_0 + ssin\phi )}}\)


rotation about the centroidal surface


pulse length


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Copyright information

© Society for Experimental Mechanics, Inc. 1973

Authors and Affiliations

  • J. L. Rose
    • 1
  • R. W. Mortimer
    • 1
  • A. Blum
    • 2
  1. 1.Drexel UniversityPhiladelphia
  2. 2.Catalytic Inc.Philadelphia

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