Generalized shape optimization of transient vibroacoustic problems using cut elements

Abstract

AbstractThis article propose a generalized shape optimization method for transient coupled acoustic–mechanical interaction problems. The transient problem formulation allows to optimize for a broadband frequency content and the possibility to investigate transient phenomena such as pulse shaping. Throughout the work, the geometry is defined with the help of a nodal‐based design field, for which its zero‐level contour describes the interface between acoustic and structural domains. The approach utilizes a fixed background mesh to represent the geometry and a cut element immersed boundary method for the physical modeling. This modeling approach provides accurate solutions to the strongly coupled governing equations based on a special integration scheme. The optimization problem is solved using a gradient‐based optimizer and employs a fully discrete adjoint approach for calculating the sensitivity information. A numerical examination on the accuracy of the sensitivity analysis compares the fully discrete gradients to the commonly used semidiscrete adjoint approach for transient optimization revealing the importance of consistent sensitivities. The transient design formulation is validated on a 2D benchmark problem concerning the design of a time‐harmonic acoustic partitioner. The developed framework is then applied for the design of vibroacoustic pulse shaping devices to demonstrate control of a transient phenomena.