Multimodal vibration damping of a thin circularring
coupled to an analogous piezoelectric network

At LMSSC, Paris, January 11th 2023, 1.30 p.m.

Alan Luo
Doctorate, Smart Structures & Dynamical Systems Laboratory (SSDSL),
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, USA

Keywords: broadband damping, vibration, piezoelectricity, electrical networks

Vibrations in structures can be attenuated by coupling to a piezoelectric electrical network that exhibits analogous modal properties of the structure. Previously, this method of vibration damping has been successfully shown for rods, beams, and plates.

This study considers the multimodal vibration damping of thin circular rings using this method. The electrical network is derived by applying a finite difference model to the constitutive equations of motion for a segment of a thin curved beam and applying an electromechanical analogy to the physical constants as well as the internal forces and moments. The resulting discrete network unit cell for a curved beam segment can be assembled into a complete network for a circular ring. The electrical network for a circular ring displays modal properties similar to its mechanical analogue in both the spatial and frequency domain.

Depending on the number of discrete unit cells in the network, it is theoretically possible to replicate the entire frequency spectrum of the ring in the electrical domain. The ring and the electrical network are coupled using piezoelectric patches, which act as capacitive elements in the network. Numerical simulations of a ring coupled to the analogous network using realistic dissipative components demonstrate the validity and effectiveness of the theory.

From the frequency response function of a ring coupled to a 24-unit cell network, it is possible to achieve around 40 dB vibration reduction for the first four modes tested. Further experimental testing on ring with imperfections required some additional optimization to the electrical network. Nevertheless, the resulting coupled frequency response function still verified the robustness and tunability of the broadband damping effects from the analogous network, achieving around 15 – 40 dB reduction for the first three modes.