On the ratio of expectation crossings of random-excited dielectric elastomer balloon

- Stationary response of random-excited dielectric elastomer balloon is derived by combining a specific transformation and the stochastic averaging technique.
- Ratio of expectation crossings of dielectric elastomer balloon is derived from the joint probability density of stretch ratio and its ratio of change.

The ratio of expectation crossings of dielectric elastomer balloon excited by random pressure is analytically evaluated in this letter. The Mooney-Rivlin model is adopted to describe the constitutive relation while the random pressure is described by Gaussian white noise. Through a specific transformation, the stochastic differential equations for the total energy and phase are derived. With the application of the stochastic averaging, the system total energy is then approximated by a one-dimensional diffusion process. Solving the associated Fokker-Planck-Kolmogorov (FPK) equation yields the stationary probability density of the system total energy. The ratio of expectation crossings is then derived based on the joint stationary probability density of stretch ratio and its ratio of change. The efficacy and accuracy of the proposed procedure are verified by comparing with the results from Monte Carlo simulation (MCS).