On-Line Modal Parameter Identification Applied to Linear and Nonlinear Vibration Absorbers

Abstract

A solution of the vibration attention problem on a flexible structure from a dynamic vibration absorption perspective is experimentally and numerically studied in this article. Linear and nonlinear dynamic vibration absorbers are properly implemented on a primary structure of n degrees of freedom through a modal decomposition analysis and using the tuning condition when the primary system has one single degree of freedom. A time-domain algebraic identification scheme for on-line modal parameter estimation of flexible structures is presented. A fast frequency estimation of harmonic excitation force is also obtained. A Hilbert transform analysis of the frequency response function for the case of nonlinear dynamic vibration absorption is introduced. In this way, influence of this particular passive nonlinear control device on system dynamic response can be determined. The proposed approach is validated on an harmonically perturbed building-like structure, which is discretized in a finite number of degrees of freedom. The flexible structure is subjected to resonant operational conditions, and coupled to a pendulum vibration absorber configured as a tuned mass damper as well as an autoparametric system.

Oscillation Attenuation in a Building-like Structure by Using a Flexible Vibration Absorber

“…On the other hand, configuration (c) corresponds to an autoparametric system, where the dynamic model is represented by a system of nonlinear differential equations that cannot be linearized due to the decoupling between the degree of freedom of the primary system and the dynamics of the absorber to be implemented [22,23]. This kind of configuration is not considered in the present work due to it having been widely studied in the nonlinear-vibrations literature, addressing passive and active control aspects for different hosting structures [24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Single Output and Algebraic Modal Parameters Identification of a Wind Turbine Blade: Experimental Results

“…The Hilbert transformation [18,29,30] is a popular and well-founded mathematical tool widely used to analyze the dynamic behavior of mechanical systems due to its particular properties when it is applied to experimental frequency response functions. Since the Hilbert transform maps the functions under consideration into the same domain, when applying the Hilbert transform to a FRF, let it be R(jω), then, the imaginary and the real parts of the FRF are related as follows:…”

“…where j = √ −1 and η denotes the Cauchy principal value of the integral, which is necessary to consider due to the singularity of ( 25) and ( 26) present at ω = ω c . The equations or relations (26) and ( 25) are known as the Hilbert transform pairs [18,30]. It is well known that, for non-linear systems, the pairs do not comply and the Hilbert transform will return a distorted version of R(jω).…”

“…It is important to consider that the Hilbert transform is a numerical method; then, we need to consider some linearity criterion. Therefore, as reported in [17,29,30], we can consider the set of values 0.9 ≤ σ H ≤ 1 for a linearity assumption of the dynamic behavior of the system.…”

An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients

“…An advantage of algebraic identification over other methods is that it provides identification expressions that are completely independent of the initial system conditions. Algebraic identification has been used for parameter and signal estimation in linear and non-linear vibrational mechanical systems [30][31][32][33][34][35][36][37][38][39]. Numerical and experimental results show that algebraic identification is extremely robust against parameter uncertainty, frequency variations, measurement errors and signal noise.…”