A lower bound for the energy decay rate in piezoelectricity

TL;DR

This paper derives a mathematical lower bound for how quickly energy diminishes in piezoelectric cylinders, factoring in material and geometric properties, with specific calculations for circular cross-sections.

Contribution

It introduces a new lower bound for energy decay in piezoelectric cylinders that accounts for material and geometric constants, including Poincaré-Wirtinger and Korn constants.

Findings

Derived a lower bound for energy decay rate in piezoelectric cylinders.

Provided a precise numerical lower bound for circular cross-section cylinders.

Demonstrated the practical application of the theoretical bound.

Abstract

This paper establishes a lower bound for the energy decay rate in piezoelectric cylinders. The bound incorporates material properties and geometric factors, including the cross-section's Poincar\'e-Wirtinger and Korn constants. A detailed analysis of a circular cross-section cylinder yields a precise numerical lower bound, illustrating the practical application of this result.