Two-tier model reduction of viscoelastically damped finite element models. (15th July 2019) - Kuether, Robert J.
Highlights: Two-tier model reduction solves transient responses for linear viscoelastic models. Tier-one model reduced with real modes linearized about various frequencies. Tier-two model reduced with complex modes from nonlinear eigenvalue problem. Demonstrated on a cantilevered sandwich plate structure at various temperatures. Reduction scheme accurately and efficiently predicts transient response. Abstract: Transient simulations of linear viscoelastically damped structures require excessive computational resources to directly integrate the full-order finite element model with time-stepping algorithms. Traditional modal reduction techniques are not directly applicable to these systems since viscoelastic materials depend on time and frequency. A more appropriate reduction basis is obtained from the nonlinear, complex eigenvalue problem, whose eigenvectors capture the appropriate kinematics and enable frequency-based mode selection; unfortunately, the computational cost is prohibitive for computing these modes from large-scale engineering models. To address this shortcoming, this work proposes a novel two-tier reduction procedure to reduce the upfront cost of solving the complex, nonlinear eigenvalue problem. The first reduction step reduces the full-order model with real mode shapes linearized about various centering frequencies to capture the kinematics over a full range of viscoelastic material behavior (glassy, rubbery, and glass-transition zones). This tier-one reduction preserves time-temperature superposition and allows the equations to depend parametrically on operating temperature. The second-level reduction then solves the complex, nonlinear eigenmode solutions in the tier-one reduced space about a fixed temperature to further reduce the equations-of-motion. The method is demonstrated on a cantilevered sandwich plate to showcase its accuracy and efficiency in comparison to full-order model predictions.