Confinement of Vibrations in Flexible Structures Using Supplementary Absorbers: Dynamic Optimization

Abstract

We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.

Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting

“…Substituting Equation (17) into Equation (29) yields the same set of equations. This indicates that minimizing the power dissipated by the primary damping is equivalent to maximizing the power dissipated by the absorber damping for the same set of µ and ζ p .…”

“…The following literature review will focus on simultaneous VS and EH using TMD. Ouled Chtiba et al [17] optimized the locations, masses, stiffnesses, and damping coefficients of a set of TMDs to minimize the total energy of the primary structure. Later, they [18] proposed an optimal design for a set of TMDs incorporated with piezoelectric devices.…”

Optimization of Dynamic Vibration Absorbers Based on Equal-Peak Theory

“…In Viana et al (2008) uses the ant colony optimization technique to arrive at the optimal parameters of a vibration absorber. In Pennestri (1998) applied a Chebyshev's min-max criterion for finding the optimal damper parameters, and others numerical studies based on minimax optimization are reported in (Ouled Chtiba et al (2010b), Randall et al (1981), Brown and Singh (2011).…”

Optimal control of transverse vibration of Euler-Bernoulli beam with multiple dynamic vibration absorbers using Taguchi's method

“…Lin and Cho [7] investigated dynamic characteristics of a simply supported beam traversed by multiple moving loads and a practical scheme for suppressing the resulting resonant or excessive vibration by using a damped absorber. In [8] Chtiba and his colleagues have proposed a new strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibration in flexible structures. In [9] Vestroni et al studied the pedestrian-induced vibrations in suspension footbridges via multiple tuned mas dampers.…”