A PARAMETRIC STUDY ON THE AXISYMMETRIC MODES OF VIBRATION OF MULTI-LAYERED SPHERICAL SHELLS WITH LIQUID CORES OF RELEVANCE TO HEAD IMPACT MODELLING
✍ Scribed by P.G. YOUNG
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 307 KB
- Volume
- 256
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The free vibration of spheres composed of inviscid compressible liquid cores surrounded by spherical layers of linear elastic, homogeneous and isotropic materials are studied using three-dimensional elasticity equations. The exact three-dimensional equations are "rst derived for an N-layered sphere with a liquid core and an extensive parametric study is then presented for the "rst few natural frequencies of the spheroidal modes of vibration. Non-dimensional frequency parameters are compared with values obtained using lower order membrane and shell theories. It is shown that for a remarkably wide range of geometric and material parameters, which encompasses values typical for the human head, the "rst ovalling mode of a #uid-"lled shell behaves like a membrane "lled with incompressible #uid and a simple closed-form expression is derived which closely approximates the natural frequencies obtained using the exact three-dimensional equations.