Dynamics of thermoelastic thin plates: A comparison of four theories

TL;DR

This paper compares four theories of thermoelastic thin plates, analyzing their accuracy and applicability in modeling flexural motion and damping, highlighting the Norris model's surprising accuracy despite its simplicity.

Contribution

It provides a detailed comparison of four thermoelastic plate theories, identifying the Norris model as a simple yet accurate alternative to more complex models.

Findings

Lagnese and Lions model captures essential damping features but has inaccuracies.

Simmonds' model is accurate only at low frequencies.

Norris model is as accurate as Chadwick's despite simplicity.

Abstract

Four distinct theories describing the flexural motion of thermoelastic thin plates are compared. The theories are due to Chadwick, Lagnese and Lions, Simmonds, and Norris. Chadwick's theory requires a 3D spatial equation for the temperature but is considered the most accurate as the others are derivable from it by different approximations. Attention is given to the damping of flexural waves. Analytical and quantitative comparisons indicate that the Lagnese and Lions model with a 2D temperature equation captures the essential features of the thermoelastic damping, but contains systematic inaccuracies. These are attributable to the approximation for the first moment of the temperature used in deriving the Lagnese and Lions equation. Simmonds' model with an explicit formula for temperature in terms of plate deflection is the simplest of all but is accurate only at low frequency, where the damping is linearly proportional to the frequency. It is shown that the Norris model, which is almost as simple as Simmond's, is as accurate as the more precise but involved theory of Chadwick.