Weakly nonlinear dynamics of a thin aerogel coating governed by Rajagopal’s continuum model

This paper addresses a dynamic problem for a thin aerogel layer with one face fixed and a time-harmonic vertical displacement prescribed on the opposite face. The constitutive relations rely on Rajagopal’s nonlinear implicit model. To validate the material parameters, we conduct uniaxial compression experiments on organic–inorganic hybrid silica aerogels, confirming the predictive capability of the proposed model. A weakly nonlinear asymptotic analysis is conducted and the associated two-term approximate solution is obtained, for both the one-dimensional problem for transverse displacement and the plane-strain problem. Comparisons with numerical solutions are performed, highlighting the importance of the nonlinear corrector. The integrated approach involving asymptotic analysis, numerical investigations, and experimental characterization advances the understanding of the dynamic behaviour of aerogels and paves the way for the design of aerogel-based insulation applications.