Matematički model ćelije aktivnog metamaterijala za nerecipročnu transmisiju zvuka uz upotrebu povratnih veza po pomaku i brzini vibriranja

undergraduate thesis

• Title (english): Mathematical model of an active metamaterial cell for non-reciprocal sound transmission using displacement and velocity feedback loops
• Author: Dina Suton
• Mentor: Neven Alujević (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2022-03-03, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering; General Mechanical Engineering (Construction)

Abstract

U ovom radu analizirani su i diskutirani rezultati dobiveni pojednostavljenim diskretnim modelom jedne ćelije aktivnog metamaterijala uz upotrebu povratnih veza po pomaku i po brzini vibriranja. Pretpostavljena je ćelija aktivnog metamaterijala geometrije pogodne za 3D ispis jednostavnim uređajem: cijev pravokutnog poprečnog presjeka periodično isprekidana dvostrukim membranama. Pretpostavljeno je da se dinamika svake od membrana i pravokutnih akustičnih šupljina između njih može aproksimirati njihovom prvom formom vibriranja tj sustavom masa-opruga za membranu, a opruga-prigušivač za akustičku šupljinu. Izvedene su jednadžbe gibanja i odgovarajuće prijenosne funkcije za diskretni linearni dinamički model cijevi s dva para membrana i dvije povratne veze. Provedena je analiza stabilnosti tako dobivenog aktivnog sustava s četiri stupnja slobode s dvije povratne veze. Korišten je Routh-Hurwitz kriterij stabilnosti. Određeni su parametri pasivnog sustava koji jamče stabilnost aktivnog sustava. Nadalje, za stabilne sustave pokazan je i kvantificiran gubitak recipročnosti u širokom spektru frekvencija uspoređivanjem odgovarajućeg para prijenosnih funkcija između sila i brzina vibriranja u diskretnom mehaničkom sustavu.

Abstract (english)

In this thesis, the results obtained by a simplified discrete model of a single cell of active metamaterial with the use of both position and velocity feedbacks are analyzed and discussed. The geometry of the active metamaterial cell is suitable for 3D printing with a simple device is envisaged: a rectangular pipe periodically intermitted by a pair of membranes. It is assumed that the dynamics of each of the membranes and rectangular acoustic cavities between them can be approximated by their first vibration mode, i.e. a mass-spring system for the membrane and a spring-damper system for the acoustic cavity. The equations of motion and the corresponding transfer functions for the discrete linear dynamic model of a pipe with two pairs of membranes and two feedback loops are derived. The resulting four DOF (degree of freedom) model is analysed and discussed with respect to the stability of the two feedback loops using the Routh-Hurwitz stability criterion. Parameters of the passive system that guarantee the stability of the active system are determined. Furthermore, for stable systems, the loss of reciprocity in a broad band of frequencies has been quantified by comparing the corresponding pair of transfer functions between forces and vibration velocities in a discrete mechanical system.

• Keywords: Akustika; Zvuk; Vibracije; Akustički metamaterijali; Aktivni akustički metamaterijali; Gubitak recipročnosti
• Keywords (english): Acoustics; Sound; Vibration; Acoustic Metamaterials; Active Acoustic Mrtamaterials; Loss of Reciprocity
• Language: croatian
• URN:NBN: urn:nbn:hr:235:491492
• Study programme: Title: Mechanical Engineering; specializations in: Design, Process and Energy Engineering, Production Engineering, Engineering Modelling and Computer Simulation, Marine Engineering, Industrial Engineering and Management, Materials Engineering; Course: Engineering Modelling and Computer Simulation; 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; Embargo expiration date: 2024-03-02
• Created on: 2022-03-02 11:19:09