Nonlinear vibrations of a homogeneous, isotropic, and shallow spherical caps under a harmonic pressure field are studied. The problem is addressed using a semi-analytical method based on Novozhilov's nonlinear shell theory. The partial differential equations (PDEs) are reduced to a set of ordinary differential equations (ODEs) through the Rayleigh-Ritz approach and Lagrange's equations. The resulting set of equations is numerically solved using both continuation techniques and direct integration. The results highlighted the activation of non-symmetric vibrational states, with the presence of multiple bifurcations and chaotic oscillations.

This study introduces a probabilistic approach to assess the stability of aeroelastic limit cycle oscillations. Utilising the Hill/Koopman method, data-driven models are trained to capture eigenvalue behaviour. The stability likelihood of the limit cycle oscillations is evaluated by analysing the percentage of stable responses in Monte Carlo experiments. The effectiveness of the method is demonstrated using a nonlinear aerofoil test case, revealing that it provides accurate stability information compared to experimental data. Ongoing efforts will focus on conducting a more thorough analysis of the method, considering both accuracy and computational efficiency.

The paper investigates the use of a multistable shallow von Mises truss as a piezoelectric energy harvester. The authors obtain the exact Lagrangian and apply Hamilton's principle to derive a nonlinear equation of motion that takes into account the piezoelectric coupling. The shallow von Mises truss exhibits highly nonlinear snap-through behavior, resulting in significant cross-well motions. This behavior improves the efficiency of the energy harvester by converting mechanical pressure into electricity more effectively. A parametric analysis demonstrates that increasing the number of units and the occurrence of snap-through can enhance the output voltage and power of the harvester.