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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

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Abstract

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.

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Abbreviations

c p :

plate velocity=(E p /ρ)1/2

c s :

shear velocity=k (G/ρ)1/2

E :

Young’s modulus of elasticity

E p :

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

G :

shear modulus of elasticity=E/2 (1+ν)

h :

thickness of shell

k 2 :

shear-correction factor=0.87

M s :

shell moment

N s ,Q s :

shell forces

r :

radial coordinate

r o :

radius of midsurface of cone at the small truncated end

R :

radius of midsurface of the shell

s, θ, ξ:

shell coordinates; meridional, circumferential and normal, respectively

u s ,u ξ :

meridional and normal displacements, respectively

u, w :

meridional and normal displacements of the centroidal surface, respectively

V :

velocity imparted to shell by ring

x :

axial distance

ɛ s :

meridional strain

ɛ θ :

circumferential strain

ϕ:

1/2 apex angle of cone

τ o :

pulse duration

ν:

Poisson’s ratio

η:

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

Ψ:

rotation about the centroidal surface

λ:

pulse length

References

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Authors and Affiliations

  1. Drexel University, 19104, Philadelphia, PA

    J. L. Rose (Assistant Professor of Mechanical Engineering) & R. W. Mortimer (Associate Professor of Mechanical Engineering)

  2. Catalytic Inc., 19102, Philadelphia, PA

    A. Blum (Engineer)

Authors
  1. J. L. Rose
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  2. R. W. Mortimer
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  3. A. Blum
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Rose, J.L., Mortimer, R.W. & Blum, A. Elastic-wave propagation in a joined cylindrical-conical-cylindrical shell. Experimental Mechanics 13, 150–156 (1973). https://doi.org/10.1007/BF02322668

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  • DOI: https://doi.org/10.1007/BF02322668

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