Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control

Abstract

This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique