Damping optimization of viscoelastic cantilever beams and plates under free vibration. (August 2022)

• Record Type: Journal Article
• Authors: Joubert, A.; Allaire, G.; Amstutz, S.; Diani, J.
• Is Part Of: Computers & structures. Volume 268(2022)
• Publication Date: 2022-08
• Subjects: Free vibration -- Damping -- Linear viscoelasticity -- Eigenvalue optimization -- Optimal design; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2022.106811
• Languages: English
• ISSNs: 0045-7949

Abstract

Graphical abstract: Highlights: Damping optimization of viscoelastic structures under free vibration. Coupled shape and sizing optimization of polymer plates. Impact of the material properties on the optimal design. Abstract: The goal of this work is to significantly enhance the damping of linear viscoelastic structures under free vibration by relying on optimal design. Homogeneous cantilever slender beams and plates satisfying, respectively, the Euler-Bernoulli and Kirchhoff-Love assumptions are considered. A sizing optimization of the beam or plate thickness is proposed, as well as a coupled optimization of the thickness and geometry of the plate applying Hadamard's boundary variation method. The isotropic linear viscoelastic material is modeled by a classical generalized Maxwell model, well suited for polymers. Gradients of the objective functions are computed by an adjoint approach. Optimization is performed by a projected gradient algorithm and the mechanical models are evaluated by the finite element method. Numerical tests indicate that the optimal designs, as well as their damping properties, strongly depend on the material parameters.