In this study, a Monte Carlo simulation (MCs)-based isogeometric stochastic Finite Element Method (FEM) is proposed for uncertainty quantification in the vibration analysis of piezoelectric materials. In this method, deterministic solutions (natural frequencies) of the coupled eigenvalue problem are obtained via isogeometric analysis (IGA). Moreover, MCs is employed to solve various uncertainty parameters, including separate elastic and piezoelectric constants and their combined cases.

This study proposes a novel method for simulating sound scattering that accounts for the combined reflection effects of both the seabed and sea surface. The target geometry is modeled using isogeometric analysis to minimize geometric errors. The boundary element method incorporating a half-space fundamental solution is then employed to numerically simulate the external acoustic field in an infinite domain, incorporating the composite reflections from the sea surface and seabed. To enhance computational efficiency, the fast multipole method is implemented in the sound scattering model, significantly reducing computational time and memory requirements. The accuracy and effectiveness of the proposed algorithm are validated through numerical examples.

This study introduces an innovative model-order reduction (MOR) technique that integrates boundary element and finite element methodologies, streamlining the analysis of wideband vibro-acoustic interactions within aquatic and aerial environments. The external acoustic phenomena are efficiently simulated via the boundary element method (BEM), while the finite element method (FEM) adeptly captures the dynamics of vibrating thin-walled structures. Furthermore, the integration of isogeometric analysis within the finite element/boundary element framework ensures geometric integrity and maintains high-order continuity for Kirchhoff–Love shell models, all without the intermediary step of meshing. Foundational to our reduced-order model is the application of the second-order Arnoldi method coupled with Taylor expansions, effectively eliminating the frequency dependence of system matrices. The proposed technique significantly enhances the computational efficiency of wideband vibro-acoustic coupling analyses, as demonstrated through numerical simulations.