The coupled fluid-structure simulation was carried out using the commercial software ABAQUS. The shape of the buckled structure was obtained from a nonlinear postbuckling analysis. Then, a steady-state dynamic analysis enabled the calculation of the vibration mode and resonant frequency under PZT actuation. To account for the effect of the fluid on the vibration, the vibration velocity of each vibration mode was transferred to the computational fluid dynamics (CFD) analysis, which predicted the forces applied on the 3D structure by the surrounding fluids as a function of frequency. These forces were then fed back to the steady-state dynamic analysis to recalculate the resonant frequency. A Python script was developed to transfer quantities between the steady-state analysis and the CFD analysis.

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