This paper studies the spatial behaviour of the transient and steady-state solutions in the problem of bending of a plane elastic plate. When the transient solutions are discussed a bounded or unbounded plane plate of an arbitrary regular form is considered. Then an appropriate time-weighted line-integral measure is introduced and, for each fixed t 2 ½0; T , it is shown that it vanishes at distances from the support of the given data on the time interval ½0; T greater than ct, where c is a characteristic material constant. Moreover, for distances to the support lower than ct, it is established a spatial decay estimate of Saint-Venant-type. For the harmonic vibrations the case of an elastic plate whose middle surface is like a (semi-infinite) strip is considered for which the lateral sides are clamped. Then a cross-sectional line-integral measure is associated with the amplitude of the vibration and the spatial estimate is established for describing the spatial behaviour of the amplitude, provided that the frequency of the harmonic vibration is lower than a critical frequency.

ON THE SPATIAL BEHAVIOUR OF THE TRANSIENT AND STEADY-STATE SOLUTIONS IN THIN PLATES WITH TRANSVERSE SHEAR DEFORMATION

CIARLETTA, Michele
2002

Abstract

This paper studies the spatial behaviour of the transient and steady-state solutions in the problem of bending of a plane elastic plate. When the transient solutions are discussed a bounded or unbounded plane plate of an arbitrary regular form is considered. Then an appropriate time-weighted line-integral measure is introduced and, for each fixed t 2 ½0; T , it is shown that it vanishes at distances from the support of the given data on the time interval ½0; T greater than ct, where c is a characteristic material constant. Moreover, for distances to the support lower than ct, it is established a spatial decay estimate of Saint-Venant-type. For the harmonic vibrations the case of an elastic plate whose middle surface is like a (semi-infinite) strip is considered for which the lateral sides are clamped. Then a cross-sectional line-integral measure is associated with the amplitude of the vibration and the spatial estimate is established for describing the spatial behaviour of the amplitude, provided that the frequency of the harmonic vibration is lower than a critical frequency.
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/11386/1062139
 Attenzione

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

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact