Stochastic response of a stiff film-substrate structure under an axial strain and Gaussian white noise

Purpose The flexible film-substrate-based electronics experience various service loadings. To prevent structural failure of the stiff film-substrate structure, this work investigates the stochastic response of a stiff film-substrate structure under harmonic axial strain and Gaussian white noise. It analyzes the stiff film-substrate structure’s dynamic behaviors and reliability under combined deterministic and random excitation. Design/methodology/approach A finite deformation model is established by using the energy method and the dynamic equation is derived via the Lagrange equation. The stationary probability density is obtained by applying the stochastic averaging method and the effects of damping coefficient, noise intensity and pre-strain on stationary probability density are analyzed. Numerical examples are given to discuss the influence of the applied harmonic strain and noise intensity on the dynamic peak strain. Findings Increased damping coefficient elevates the peak height of the stationary probability density without altering its position, whereas increased noise intensity reduces the stationary probability density peak while preserving peak location. Too large an amplitude of the applied strain or too small a period of the applied strain will lead to fracture of the film-substrate structure. Originality/value This study establishes a theoretical framework for predicting stochastic responses of film-substrate structures, with direct implications for design optimization in flexible electronics and micro-electro-mechanical systems applications.