Modal Parameter Analysis for Underdamped Mechanical Systems

Abstract

There are many ways to model and to analyze discrete event systems. In general these systems lead to a non-linear characteristic equation description in linear algebra. This paper presents an analytical method for solving the characteristic equation of higher order, which arise when solving ordinary differential equations of motion of rigid body systems with 2 ≤ p° ≤ 10 degrees of freedom. The objective of this work was to express the characteristic equation in the form of product quadratic polynomial, from which the modal components could be found. To validate the model, the modal parameters extraction technique – Ibrahim Time Domain (ITD) – was used to extract modal parameters from artificial data developed in MATLAB environment. The extracted modal components were compared to those obtained from the analytical model.

Identification of damping ratio and its influences on wind‐ and earthquake‐induced effects for large cooling towers

“…First, random decrement technique and natural excitation technique were used to extract the free response curve or cross‐correlation function from the measured responses for the structure. On this basis, three pattern recognition methods, ARMA, ITD, and STD, were applied to analyze the modal parameters. The basic theories of these methods are not detailed here due to limited space.…”

Evaluation of dynamics and running properties of rail vehicles using simulation modelling

“…Отримана система рівнянь руху складається з неоднорідних диференціальних рівнянь другого порядку [4,21], які, як правило, є нелінійними й можуть бути записані наступним чином: 𝑀𝑀 ⋅ 𝑞𝑞̈(𝑡𝑡) + (𝐵𝐵 + 𝛺𝛺 0 ⋅ 𝐺𝐺) ⋅ 𝑞𝑞̇(𝑡𝑡) + (𝐾𝐾 + 𝛺𝛺 0 2 ⋅ 𝑍𝑍) ⋅ 𝑞𝑞(𝑡𝑡) = ℎ(𝑡𝑡)…”