Numerički model aktivne ćelije metamaterijala za nerecipročnu transmisiju zvuka

undergraduate thesis

• Title (english): Numerical model of an active metamaterial cell for non-reciprocal sound transmission
• Author: Nikola Mikšik
• Mentor: Neven Alujević (mentor)
• Granter: University of Zagreb; Faculty of Mechanical Engineering and Naval Architecture; Zagreb
• Defense date and country: 2023-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Mechanical Engineering; General Mechanical Engineering (Construction)

Abstract

U ovom radu osmišljena je ćelija aktivnog metamaterijala koja ne podliježe principu dinamičke
recipročnosti. Računalnim alatima konstruirana je cijev pravokutnog poprečnog presjeka koja
je naizmjence isprekidana dvostrukim membranama. Konstrukcija je pogodna za 3D ispis, te
se na nju mogu učvrstiti mjerni i pogonski članovi sustava za aktivnu izolaciju vibracija. Između
membrana, u pravokutnim akustičkim šupljinama, smještena su dva elektromagnetska
aktuatora koji mogu razviti silu okomito na površinu membrana, odupirući se o dvije susjedne
membrane. Na terminale aktuatora sile pričvršćeni su senzori, četiri akcelerometra, koji mogu
mjeriti brzinu vibriranja.
Postav je konstruiran tako da je dinamički odziv membrana i akustičkih šupljina dominantno
određen njihovom prvom formom vibriranja tako da se može dobro aproksimirati
matematičkim modelom za klasični linearni vibracijski sustav s četiri stupnja slobode gibanja
s koncentriranim parametrima. Izvedene su jednadžbe gibanja i ukupno 16 prijenosnih funkcija
između sila i brzina vibriranja svake od četiriju membrana u sustavu.
Signal brzine vibriranja koristi se za zatvaranje povratnih veza tako da sila razvijena aktuatorom
bude proporcionalna brzini vibriranja membrane, pri čemu parovi mjernih i pogonskih članova
povratnih veza nisu kolocirani. Ako se koristi samo jedan od dvaju senzora po aktuatoru moguće
je postići aktivno prigušenje generirano povratnom vezom takvo da matricu prigušenja sustava
čini asimetričnom. To kao rezultat ima gubitak akustičke recipročnosti kada zvuk prolazi kroz
ćeliju aktivnog metamaterijala. Analizom stabilnosti takvog sustava koristeći generalizirani
Nyquistov kriterij određeni su parametari pasivnog sustava.
Matematički model numerički je verificiran spregnutim strukturalno-akustičkim modelom
ćelije aktivnog metamaterijala pomoću alata za analizu slobodnih vibracija mehaničkih sustava
s raspodijeljenim parametrima metodom konačnih elemenata. Nadalje, pokazan je i
kvantificiran gubitak akustičke recipročnosti u širokom spektru frekvencija uspoređujući
matematički model s koncentriranim parametrima i numerički model s distribuiranim
parametrima.

Abstract (english)

In this thesis, a cell of an active metamaterial, which does not obey the principle of dynamic
reciprocity has been designed. Aided by computer tools, a rectangular cross-section tube was
constructed, which is periodically intermitted by double membranes. It is suitable for 3D
printing so that the measuring and driving members of the active vibration isolation system can
be attached to it. Between the membranes, in rectangular acoustic cavities, there are two
electromagnetic actuators that can exert a force perpendicular to the surface of the membranes.
Sensors, four accelerometers, capable of measuring the vibration velocity, are attached to the
terminals of the force actuator.
The setup is designed in such a way that the dynamic response of the membranes and the
acoustic cavities is predominantly determined by their first mode of vibration, allowing for a
good approximation with a mathematical model for a classical linear vibrational system with
four degrees of freedom and concentrated parameters. The equations of motion have been
derived together with a total of 16 transfer functions between the forces and vibration velocities
of each of the four membranes in the system.
The vibration velocity signal is used to close feedback loops, so that the force generated by the
actuator is proportional to the vibration velocity of the membrane. In this setup, the measuring
and driving members of the feedback loops are not colocated. If only one of the two sensors per
actuator is use, it is possible to achieve active damping through the feedback loop, resulting in
an asymmetric damping matrix of the system. This results in a loss of acoustic reciprocity when
the sound passes through the cell of the active metamaterial. the parameters of the passive
system were determined. By analyzing the stability of such a system using the generalized
Nyquist criterion.
The mathematical model has been numerically verified using a coupled structural-acoustic
model of the active metamaterial cell using tools for a finite element analysis of free vibration
of mechanical systems with distributed parameters. Furthermore, the loss of acoustic reciprocity
has been demonstrated and quantified across a wide frequency spectrum by comparing the
mathematical lumped parameter model and numerical distibuted parameter model.

• Keywords: aktivna kontrola vibracija; akustički metamatrijali; dinamička recipročnost; izolacija zvuka; numerički model ćelije metamaterijala; stabilnost; vibracije
• Keywords (english): active vibration isolation; acoustic metamaterials; dynamic reciprocity; stability; lumped parameter model
• Language: croatian
• URN:NBN: urn:nbn:hr:235:303891
• Project: Number: IP-2019-04-5402; Title: Dinamika Aktivnih i Rotirajućih KONstrukcija; Title: Dynamics of Active and Rotating Structures; Acronym: DARS; Leader: Neven Alujević; Jurisdiction: Croatia; Funder: HRZZ; Funding stream: IP
• 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: Embargoed access; Embargo expiration date: 2025-09-26
• Created on: 2023-09-26 09:52:04