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Research Papers

Static and Dynamic Behavior of Circular Cylindrical Shell Made of Hyperelastic Arterial Material

[+] Author and Article Information
Ivan D. Breslavsky, Mathias Legrand

Department of Mechanical Engineering,
McGill University,
817 Sherbrooke Street West,
Montréal, QC H3A 0C3, Canada

Marco Amabili

Professor
Department of Mechanical Engineering,
McGill University,
Macdonald Engineering Building,
817 Sherbrooke Street West,
Montréal, QC H3A 0C3, Canada
e-mail: marco.amabili@mcgill.ca

Manuscript received September 4, 2015; final manuscript received January 19, 2016; published online February 19, 2016. Assoc. Editor: George Kardomateas.

J. Appl. Mech 83(5), 051002 (Feb 19, 2016) (9 pages) Paper No: JAM-15-1474; doi: 10.1115/1.4032549 History: Received September 04, 2015; Revised January 19, 2016

Static and dynamic responses of a circular cylindrical shell made of hyperelastic arterial material are studied. The material is modeled as a combination of Neo-Hookean and Fung materials. Two types of pressure loads are studied—distributed radial forces and deformation-dependent pressure. The static responses of the shell under these two loads differ essentially at moderate strains, while the behavior is similar for small loads. The principal difference is that the axial displacements are much larger for the shell under distributed radial forces, while for actual pressure the shell is stretched both in circumferential and axial directions. Free and forced vibrations around preloaded configurations are analyzed. In both cases, the nonlinearity of the single-mode (driven mode) response of the preloaded shell is quite weak, but a resonant regime with both driven and companion modes active has been found with more complicated nonlinear dynamics.

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Figures

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Fig. 1

The shell and coordinate system

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Fig. 2

Pressure–deflection curves for two types of load: gray dots—distributed radial force and black dots—actual pressure. A and B are the points, around which the dynamical analyses are performed.

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Fig. 3

Initial shape of the shell (filled) and deformed shape of the shell (contour lines). (a) Shell under the real pressure corresponding to point A in Fig. 2 and (b) shell under the radial force corresponding to point B in Fig. 2.

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Fig. 4

Frequency response (solid line) and backbone curves of free vibrations of the shell preloaded by radial distributed forces (load case B). Thick black line—regime with dominant mode w1,n,c; thick gray line—resonant regime with both w1,n,c and w1,n,c modes active; and thick light gray line—regime with dominant mode w1,n,s. (a) Generalized coordinate w1,n,c (driven mode) and (b) generalized coordinate w1,n,s (companion mode).

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Fig. 5

Frequency responses for the forced vibrations of the shell preloaded by radial force: (a) axial coordinate u1,n,c and (b) circumferential coordinate v1,n,c

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Fig. 6

Frequency response (solid line) and backbone curve (thick black line) of free vibrations of the shell preloaded by actual pressure (load case A); Pt= 0.375 N. (b) is the magnification of (a).

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Fig. 7

Frequency responses for the forced vibrations of the shell preloaded by pressure, Pt= 0.375 N: (a) axial coordinate u1,n,c and (b) circumferential coordinate v1,n,c

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Fig. 8

Frequency response of the shell preloaded by actual pressure (load case A), Pt= 0.76 N: (a) generalized coordinate w1,n,c (driven mode) and (b) generalized coordinate w1,n,s (companion mode)

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