The present paper is concerned with the linear thermoelastic plate model based on a Mindlin-type assumption on the displacements. The bending of a Mindlin-type thermoelastic rectangular (semi-in¯nite) plate is studied when the boundary end data are time-harmonic with angular frequency ɷ and the lateral sides are clamped and thermally insulated and su±cient time has elapsed for the system to have reached a steady-state. A line-integral cross-sectional measure is associated with the amplitude of the resulting harmonic oscillation and then a first-order differential inequality is established in terms of the measure, provided that the angular frequency ɷ is lower than of an explicit critical frequency ɷm. An integration leads to a spatial estimate describing the spatial exponential decay of the amplitude with the distance to the excited end.
A mathematical study of the spatial behaviour of the time-harmonic oscillations in a thermoelastic rectangular plate
D'APICE, Ciro
2005-01-01
Abstract
The present paper is concerned with the linear thermoelastic plate model based on a Mindlin-type assumption on the displacements. The bending of a Mindlin-type thermoelastic rectangular (semi-in¯nite) plate is studied when the boundary end data are time-harmonic with angular frequency ɷ and the lateral sides are clamped and thermally insulated and su±cient time has elapsed for the system to have reached a steady-state. A line-integral cross-sectional measure is associated with the amplitude of the resulting harmonic oscillation and then a first-order differential inequality is established in terms of the measure, provided that the angular frequency ɷ is lower than of an explicit critical frequency ɷm. An integration leads to a spatial estimate describing the spatial exponential decay of the amplitude with the distance to the excited end.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
