Generic Low-Rank Parametric Model Order Reduction for Vibro-Acoustics Using Modal Projection
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Parametric Model Order Reduction (pMOR) methods are valuable performance enablers for the execution of design optimization and uncertainty quantification studies in computational vibro-acoustics, where multiple variations of a large base problem are sought given a bounding parameter space. In this work, the inverse matrix modification formula is explored to decompose the vibro-acoustic Frequency Response Function (FRF) of a parametric realization into two distinct contributions. The first consists of the nonparametric FRF of the base problem, which is further reduced using the traditional projection into modal coordinates. The second is the parameter dependent FRF update, constructed by means of a low rank affine parametrization. Furthermore, a generic approach is presented to translate different types of parametric spaces into the affine form of the framework. The accuracy of the methodology is validated against the direct method for the finite element model of a plate under harmonic vibration with variations in mass, stiffness, boundary condition and edge contour. Moreover, a pseudo-static correction formulation is introduced in order to enhance the accuracy of the results. Finally, the efficiency of the methodology is evaluated when computing the vibro-acoustic indicators of a large vibrating planar structure coupled to an acoustic cavity under different parametric update scenarios, demonstrating significant performance gains for localized variations in the model.
