The main goal of this work involves conducting numerical simulations to determine the vibrational behavior of composite shell structures. The introduction of doubly-curved laminated shells plays a pivotal role in diverse engineering applications, offering an expanded design space and the potential to enhance mechanical performance. However, the analysis of this kind of structures poses significant challenges due to the need to account for the curvature of the shell mid-surface. Moreover, the aspect ratio strongly influences the structural response in terms of free vibrations, also affecting the accuracy of the numerical solution. To address these complexities, this work employs the Carrera’s unified formulation, a well-established methodology for evaluating composites structural behavior which allows to set the expansion order of through-the-thickness polynomials as a free parameter of the simulation. In this context, the governing equations of the problem are derived through pure displacement and mixed formulations, within a finite element framework, ensuring a robust and adaptable analysis approach. This study extends the application of the unified formulation to complex shell geometries featuring non-uniform curvatures along the mid-surface principal directions. Free vibration analyses are performed to determine fundamental frequencies and mode shapes, with results benchmarked against 3D models from Abaqus and classical theoretical predictions. The comparison demonstrates the effectiveness of the proposed approach, establishing its efficacy for advanced structural investigation of fiber-reinforced shells with spatially varying curvatures, regardless of the considered slenderness ratio. • Carrera’s unified formulation is adopted for the modal analysis of curved shells. • Governing equations are derived using displacement-based and mixed theories. • Numerical results are validated against three-dimensional Abaqus reference models. • Lower-order models show accurate results for thin shells at reduced numerical cost. • Layer-wise mixed models achieve top accuracy.

In this paper, we compare two parametric model order reduction methods, the multi-moment matching method and the interpolation of projection subspaces method for the magneto-quasistatic (MQS) and electro-quasistatic (EQS) problems derived from Maxwell’s equations and discretized with the Finite Element (FE) method. The two problems considered are both governed by the differential–algebraic equations. The material characteristic parameters as well as the geometry parameters have been considered. The applications are two realistic test cases: an EQS model of a transformer bushing under insulation defect uncertainty and a MQS model of a planar inductor with geometric and material variations. The result shows that both methods approximate well global quantities, such as the current or the voltage, as well as the local quantities like field distributions. The multi-moment matching method remains always faster in the online stage, since the reduced basis is not parameter dependent, requiring no reduced basis calculation. The multi-moment matching method requires an affine decomposition of the FE model, which is not easy to obtain when considering geometry parameters. A hybrid method is proposed and tested leading to more accurate results than the interpolation of projection subspaces method but much easier to implement than the multi-moment matching method.