Physical explanation for vibro-acoustic modulation in a structure due to local and global nonlinearities
Creators: name: Dorendorf, Lennart
Publisher: name: TUHH Universitätsbibliothek
Year: 2023
Subjects: subject: vibro-acoustic modulation
subject: structural health monitoring
subject: non-destructive testing
subject: nonlinear acoustics
subject: dynamics
classificationCode: 620
subject: Engineering and Applied Operations

description: This dissertation suggests a physical explanation revealing why any elastic nonlinearity may cause vibro-acoustic modulation (VAM) in a dynamic system that is excited by two waves simultaneously (Xω and XΩ) in case the corresponding frequencies differ significantly (ω &gt;&gt; Ω): The low frequency (LF) vibration XΩ activates the nonlinearity and varies quasi-statically the system’s natural frequency ω0 corresponding to the dominant mode shape. The amplitude and phase of the ultrasonic system response depend on the natural frequency ω0 and are therefore modulated with low frequency Ω. This analytical explanation is built upon the assumption that the system reaches a steady-state vibration (constant amplitude and phase over time) due to ultrasonic excitation Xω before the LF vibration XΩ can change the dy- namic properties of the system significantly. The fulfillment of this assumption is validated experimentally and numerically for an aluminum plate-like structure and excitation frequencies Ω = 10Hz · 2π and 180kHz · 2π &lt; ω &lt; 230kHz · 2π: It is shown that the minimum and maximum amplitudes in the modulated ultrasonic system response match the respective steady-state amplitudes under static loading with a negligible error that is &lt;1%. The beauty of the explanation is that it does not only work for the local nonlinear-elastic behavior of a defect, but also for any non-damage-induced (local or global) nonlinearity in the system which may cause modulation as well. The explanation is employed to conclude and demonstrate the following five analytical findings: 1) Any elastic nonlinearity may cause amplitude modulation and phase modulation at the same time. 2) The nonlinearity can cause envelope functions in the modulated system response with a variety of different characteristic shapes. 3) The maximum amplitude in the modulated system response in time domain can either coincide with the minimum or the maximum stress state corresponding to the LF vibration XΩ. 4) Different nonlinearities in the same system can cause contrary modulations that neutralize each other. 5) The steady-state evaluation of the ultrasonic system response allows—theoretically—VAM applications without exciting the LF vibration XΩ. Finally, three nonlinearities in the same system are investigated separately: Two non-damage-induced nonlinearities (the variation of geometric stiffness and the nonlinear-elastic material behavior of aluminum) and one damage-induced nonlinearity (the contact of fatigue crack surfaces) are considered. Numerical simulations are carried out to quantify and compare the modulation they cause individually in the system response. The results comply with the analytical findings concluded from the physical explanation and emphasize that the conventional VAM evaluation for damage monitoring is error prone.
description: Diese Dissertation stellt eine analytische physikalische Erklärung für das Auftreten Vibro- Akustischer Modulation in einer Struktur aufgrund einer elastischen Nichtlinearität vor. Es werden u.a. die folgenden Erkenntnisse daraus abgeleitet und experimentell sowie numerisch demonstriert: Eine elastische Nichtlinearität kann eine Reihe charakteristischer Einhüllender in der Systemantwort hervorrufen. Unterschiedliche Nichtlinearitäten in dem selben dynamischen System können gegenläufige Modulationen in der Systemantwort hervorrufen, die sich neutralisieren. Die statische Auswertung der Systemantwort ermöglicht VAM-Anwendungen, ohne die niedrigfrequente Vibration in der Struktur anzuregen.