Fizikalno utemeljen pojednostavljeni model ćelije aktivnog metamaterijala

undergraduate thesis

• Title (english): Physics-based reduced model of an active metamaterial cell
• Author: Daniel Krivačić
• Mentor: Neven Alujević (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2020-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering

Abstract

U radu su analizirani i diskutirani rezultati dobiveni pojednostavljenim diskretnim modelom jedne ćelije aktivnog metamaterijala. Pretpostavljena je ćelija aktivnog metamaterijala geometrije pogodne za 3D ispis jednostavnim uređajem: cijev pravokutnog poprečnog presjeka koja je naizmjence isprekidana dvostrukim membranama. Izvedene su jednadžbe gibanja i odgovarajuće prijenosne funkcije za diskretni linearni dinamički model za cijev s dva para membrana i dva aktuatora pretpostavljajući da se dinamika svake od membrana i pravokutnih akustičkih šupljina između njih može aproksimirati njihovim prvom formom vibriranja tj. sustavom masa-opruga za membranu, a opruga-prigušivač za akustičku šupljinu. Tako dobiveni model s četiri stupnja slobode je analiziran i diskutiran obzirom na stabilnost para povratnih veza koristeći Routh-Hurwitzov kriterij stabilnosti. Određeni su parametri pasivnog sustava koji jamče stabilnost aktivnog sustava s dvije povratne veze. Nadalje, za stabilne sustave je pokazan i kvantificiran gubitak akustičke recipročnosti u širokom spektru frekvencija uspoređujući odgovarajuće parove od ukupno 16 izvedenih prijenosnih funkcija između sila i brzina vibriranja svake od četiriju masa u diskretnom mehaničkom sustavu. Zato se očekuje da bi i rezultati dobiveni simulacijama na sustavu s distribuiranim parametrima, kao i eksperimentalno dobiveni rezultati, potvrdili značajan gubitak akustičke recipročnosti.

Abstract (english)

In this thesis results obtained by a simplified discrete model of a single cell of an active metamaterial are analysed and discussed. The active metamaterial cell of geometry suitable for 3D printing with a simple device is assumed: a tube of rectangular cross-section periodically intermitted by a number of double membranes. Equations of motion and the corresponding transfer functions for the discrete linear dynamic model for a tube with two double membranes and two actuators are derived, assuming that the dynamics of each of the membranes and rectangular acoustic cavities between them can be approximated by their first vibration mode only, i.e. by a mass-spring system for the membrane and a spring-damper system for the acoustic cavity. The obtained four DOF (degree of freedom) model is analysed and discussed with respect to the stability of the feedback loop using the Routh-Hurwitz stability criterion. Parameters of the passive system which guarantee the stability of the active system when the two feedback loops are closed have been determined. Furthermore, for stable systems, a loss of acoustic reciprocity in a wide range of frequencies is shown. The reciprocity loss is quantified by comparing the corresponding pairs of a total of 16 derived transfer functions between forces and vibration velocities of each of the four masses in the discrete mechanical system. Therefore, it is expected that the future results obtained by simulations on an active vibroacoustic system with distributed parameters, as well as experimentally obtained results, would confirm a significant loss of acoustic reciprocity.

• Keywords: Zvuk; Vibracije; Akustički metamaterijali; Aktivni akustički metamaterijali; Automatska regulacija zvuka i vibracija
• Keywords (english): Sound; Vibration; Acoustic Metamaterials; Active Acoustic Metamaterials; Active Control of Sound and Vibration.
• Language: croatian
• URN:NBN: urn:nbn:hr:235:054938
• Study programme: Title: Mechanical Engineering; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka strojarstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-09-17 10:37:55