טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShaban Noa
SubjectNon-Reciprocity in Non-Dispersive Waveguides with Strongly
Nonlinear Coupling
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

An acoustic diode is a device, which allows the acoustic energy to flow preferably in one direction. In this study we suggest a new design for a nonlinear acoustic diode. The proposed system consists of two non-dispersive waveguides rigidly connected to two different end masses, which are coupled by essentially a nonlinear cubic spring. This design is simple while also exhibits the non-reciprocity of the wave transmission. We analyze this system in the space of parameters to study the feasibility of this model as an acoustic diode.

Lack of dispersion in the waveguides substantially simplifies the governing equations for the displacements of the end masses to a system of linearly damped, coupled oscillators. We use the method of averaging to derive approximate analytical solutions for simple case of harmonic wave transmission and compare these results to numerical simulations with a good agreement. We define the transmission coefficient as the ratio between the transmitted and incident energies and use it to study the extent of the non-reciprocity of wave transmission in opposite directions. We show that, for appropriate selection of the parameters, the proposed system acts as an acoustical diode, allowing the transmission of acoustic waves in one direction and strongly suppressing the reverse transmission.

In order for this design to be applicative as an acoustic diode, incoming signals must maintain their form with minimal frequency distortion. In existing designs, this property is often lost for the sake of non-reciprocity. We show that the design considered in current work is capable of non-reciprocity while the transmitted waves undergo minimal frequency distortion.

Lastly, we analyze the stability of the solution using the monodromy matrix, in the space of the excitation frequency and amplitude. We find that the system maintains stability for small excitation frequencies and show that the system undergoes instability in the form of pitchfork bifurcations, in the vicinity of the resonance.

Alternative designs of the nonlinear joint are also studied. Their properties and performance are qualitatively similar to those of the purely cubic spring.