Dynamic Stability of a Thin Film Bonded to a Compliant Substrate Subjected to a Step Load with Damping

Abstract

AbstractThe flexible electronic structure is based on the buckling of a thin film on a compliant substrate. This paper studies the dynamic stability of this structure subjected to a uniaxial step load with damping. The equation of motion is derived by Hamilton’s principle and Euler-Lagrange equation. Through the qualitative analysis of the phase portraits of the dynamic equation, as well as the quantitative analysis of the responses according to Budiansky-Roth criterion, the critical dynamic load is determined. It is the same as that in static buckling. Affected by damping, at the stage of pre-buckling, the amplitude of the film vibrates and attenuates, where the maximum response is the initial amplitude. The structural damping can be derived by the logarithm of the ratio between two adjacent peaks of the vibration. At the stage of post-buckling, the amplitude of the film vibrates and tends to a stable response, which is the amplitude in static buckling. The upper and lower bounds of the post-buckling response are asymmetric and solved by modified Krylov-Bogoliubov method.