Vibration-Wave Coupling of Wrinkled Film-Substrate Structures Under Dynamic Navier–Winkler Foundation

Abstract The post-buckling dynamics of wrinkled film-substrate structures has attracted sustained attention due to its potential for tunable functional devices and critical role in the reliability of flexible electronics. To accurately predict the dynamic performance of wrinkle-based devices, establishing a comprehensive post-buckling dynamic model is essential, though dynamic substrate characterization presents challenges owing to its inherently complex deformation and interfacial coupling with film morphology. In this study, a vibration-wave coupled parameter excitation dynamic model for wrinkled film-substrate structures is developed. To characterize dynamic film-substrate interactions, a dynamic Navier–Winkler foundation model is proposed that incorporates the inertial effect and elastic wave propagation within the substrate. The results reveal an evanescent-to-traveling wave transition in the substrate under periodic surface-distributed loads, leading to threshold-activated damping above a critical frequency. A complex effective dynamic stiffness is derived, which comprehensively characterizes the transition of substrate behavior from elastic to damping and finally to inertial with increasing excitation frequencies. By using linear perturbation analysis, the steady-state vibration responses of wrinkled films under periodic axial excitations are derived. The results demonstrate characteristic amplitude–frequency responses indicative of both substrate and film-dominated resonances, and substantially lower resonant frequencies and amplitudes than previously reported values attributed to substrate inertia and wave-induced dissipation. This model advances the fundamental understanding of wrinkle dynamics in film-substrate structures and establishes a theoretical framework for designing tunable wrinkle-based functional devices with optimized dynamic performance.