Vibration Suppression on a Hinged Three-Layer Sandwich Beam
Interactive boundary control of a layered sandwich beam with filtering and vibration suppression.
Overview
This Demonstration models a hinged three-layer sandwich beam with elastic or piezoelectric outer layers and a shear-deformable viscoelastic core. A tip sensor-controller suppresses bending vibrations; the live controls select the layer count and solver, vary the initial profile, mesh size, filtering, damping, and time, and tune each layer’s thickness, Young’s modulus, Poisson ratio, and the core shear modulus.
Mathematical model
The Mead–Marcus model couples transverse displacement $w(x,t)$ to the shear angle $v(x,t)$ of the viscoelastic core. The tip feedback uses $d_3 w_{xt}(L,t)$ to produce continuous energy decay $E(t) \leq M e^{-\omega t}E(0)$; in the finite-difference model, a viscosity term proportional to $d_2w_{xxt}$ prevents artificial high-frequency modes from obscuring that decay:
\[\begin{aligned} w_{tt} + w_{xxxx} - B v_x &= 0, \\ -C v_{xx} + P v + B w_{xxx} &= 0. \end{aligned}\]Research project
This Demonstration is part of Observability-Preserving Discretizations, specifically its work on filtering and sensing for hinged Mead–Marcus sandwich beams. It gives a visual counterpart to the project’s central question: whether a discrete model preserves the boundary information required for effective feedback control.
Reference
Aydin, Ahmet Kaan, Matthew Poynter, and Ahmet Özkan Özer. 2022. Vibration Suppression on a Hinged Three-Layer Sandwich Beam. Wolfram Demonstrations Project.