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The practical applications of gas-filled encapsulated microbubbles involveinherent nonspherical oscillations under acoustic fields. The gas-encapsulationand encapsulation-liquid interfaces significantly affect the mechanics of thebubbles, especially of smaller radii, and their consideration is vital formimicking the experimental setting. In this paper, we apply the interfaceenergy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022)] toexamine the nonspherical oscillations of an encapsulated microbubble with aradius of $2$$\mu$m and $5$$\mu$m under an acoustic field. Using the Lagrangianenergy formulation, the coupled dynamical governing equations for spherical andnonspherical modes are derived, incorporating the effects of interface energyat the interfaces, shell elasticity, and viscosity. Through a perturbationanalysis based on the Krylov-Bogoliubov method of averaging, a set offirst-order differential (slow-time) equations is obtained to conductsteady-state and conditional-stability analysis. The stability analysis helpedin determining the excitation pressure and frequency of the acoustic fieldrequired for smaller radii bubbles to exhibit finite amplitude shapeoscillations. Direct numerical simulations of the governing equations revealedthat the parametrically forced even mode ($n=2$) excites even modes, while theodd modes ($n=3$) excite both even and odd modes. For smaller radii bubbles, weobserve shape mode oscillations of finite non-zero amplitudes only in thepresence of interface parameters. The initial size-dependent interfaceparameter and shell viscoelastic parameters are identified as the keyparameters that play a critical role in exhibiting finite shape modeoscillations of the bubble.

Nonspherical oscillations of an encapsulated microbubble with interface energy under the acoustic field