We study the impact of a rigid sphere on a circular elastic plate whose thickness is not small with respect to its diameter, so that Kirchhoff's theory cannot be applied. For plate-like bodies of this kind it is convenient to apply a theory proposed by Levinson [J. Elasticity 7 (1985) 283], which is a compromise between Kirchhoff's solution and that obtained by the integration of Lamé equation of three-dimensional elasticity. The pressure distribution and the extent of the (circular) area of contact of the sphere on the plate-like body is mathematically described by Hertz's theory. By combining these two theories in a dynamical framework, we derive a non-linear ordinary differential equation able to describe the normal slow impact of a rigid sphere against an elastic plate-like body.

An exact solution for the impact law in thick elastic plates

SBURLATI, ROBERTA
2004

Abstract

We study the impact of a rigid sphere on a circular elastic plate whose thickness is not small with respect to its diameter, so that Kirchhoff's theory cannot be applied. For plate-like bodies of this kind it is convenient to apply a theory proposed by Levinson [J. Elasticity 7 (1985) 283], which is a compromise between Kirchhoff's solution and that obtained by the integration of Lamé equation of three-dimensional elasticity. The pressure distribution and the extent of the (circular) area of contact of the sphere on the plate-like body is mathematically described by Hertz's theory. By combining these two theories in a dynamical framework, we derive a non-linear ordinary differential equation able to describe the normal slow impact of a rigid sphere against an elastic plate-like body.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/210143
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact