Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach

Abstract

Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

A practical multiscale approach for optimization of structural damping

“…Other similar formulations have been suggested by Ling et al (2011);El-Sabbagh and Baz (2014) for damping treatments of plane plate structures, but where the final designs contain large regions with intermediate densities.…”

A novel viscoelastic damping treatment for honeycomb sandwich structures

“…Relative amplitude reduction to the undamped structure (%) Loss efficiency E Loss efficiency E Hajela [11] Hau [29] Marcelin [12] Figure 5b Loss efficiency E Loss efficiency E Loss efficiency E Simply supported plate DSLJ [5] Chen [15] Hou [20] Ling [21] Zheng [22] Figure 12…”

“…The location of the CLDs was determined with a restriction on the mass added. Ling et al [21] used the Method of the Moving Asymptotes to determine the optimal layout of CLD on a cantilever and simply supported plate in order to maximise the damping ratio while minimising the added mass. Finally, Zheng et al [22] had a similar approach considering the maximisation of the modal loss factor.…”

Microstructural topology optimization of viscoelastic materials for maximum modal loss factor of macrostructures

“…Chia (2009) and Li (2012) used cellular automata (CA) algorithm to obtain an optimal coverage of PCLD on structures. Ling et al (2011) recently used topology optimization approach to design the constrained layer damping treatment for maximizing the modal loss factor, which was found with a modal strain energy (MSE) approach . Kang et al (2012) studied the optimal distribution of damping material in vibrating structures subject to harmonic excitations by using a topology optimization method.…”