Dynamic stability of flexible electronic structures under step loads

• The dynamic model of a stiff thin film on a compliant thick substrate is built.
• Dynamic response is solved analytically by using Jacobi elliptic functions.
• The critical step load in dynamic buckling is the same as that in static buckling.
• The maximum amplitude in dynamic buckling is larger than that in static buckling.
• Increasing the step load and initial amplitude will decrease the period.

The 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 under a uniaxial step load. Dynamic equilibrium equation is deduced according to the Euler–Lagrange equation. The dynamic response of the film is solved analytically by using Jacobi elliptic functions. It is a periodic vibration influenced by the step load. The critical load in dynamic buckling is determined by the characteristics of phase graphs and Budiansky–Roth criterion. It is the same as that in static buckling. In dynamic buckling, the amplitude of vibration is larger than that in static buckling. With the increment of the load and initial amplitude, the period of vibration decreases.

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