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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.

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In many engineering challenges, the whole interaction between the structural domain and the acoustic domain must be taken into account, particularly for the acoustic analysis of thin structures submerged in water. The fast multipole boundary element approach is used in this work to simulate the external acoustic domain and the finite element method is used to describe the structural components. To improve coupling analysis accuracy, discontinuous higher-order boundary components are created for the acoustic domain. The isogeometric boundary element method (IGABEM) discretizes unknown physical fields by using CAD spline functions as basis functions. IGABEM is inherently compatible with CAD and can perform numerical analysis on CAD models without having to go through the time-consuming meshing process required by traditional FEM/BEM and volume parameterization in isogeometric finite element methods. IGABEM’s power in tackling infinite domain issues and combining CAD and numerical analysis is fully used when it is applied to structural form optimization of three-dimensional external acoustic problems. The structural-acoustic design and optimization procedures benefit from the use of structural-acoustic design sensitivity analysis because it may provide information on how design factors affect radiated acoustic performance. This paper provides adjoint operator-based equations for sound power sensitivity on structural surfaces and direct differentiation-based equations for sound power sensitivity on arbitrary closed surfaces surrounding the radiator. Numerical illustrations are provided to show the precision and viability of the suggested approach.