14 research outputs found
Experimental observation of exceptional points in coupled pendulums
The concept of exceptional point (EP) is demonstrated experimentally in the
case of a simple mechanical system consisting of two coupled pendulums.
Exceptional points correspond to specific values of the system parameters that
yield defective eigenvalues. These spectral singularities which are typical of
non-Hermitian system means that both the eigenvalues and their associated
eigenvectors coalesce. The existence of an EP requires an adequate
parameterization of the dynamical system. For this aim, the experimental device
has been designed with two controllable parameters which are the length of one
pendulum and a viscous-like damping which is produced via electromagnetic
induction. Thanks to the observation of the free response of the coupled
pendulums, most EP properties are experimentally investigated, showing good
agreements with theoretical considerations. In contrast with many studies on
EPs, mainly in the field of physics, the novelty of the present work is that
controllable parameters are restricted to be real-valued, and this requires the
use of adequate search algorithms. Furthermore, it offers the possibility of
exploiting the existence of EPs in time-domain dynamic problems
Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular duct
This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ElsevierAn analytic mode-matching method suitable for the solution of problems involving scattering in three-dimensional waveguides with flexible walls is presented. Prerequisite to the development of such methods is knowledge of closed form analytic expressions for the natural fluid–structure coupled waveforms that propagate in each duct section and the corresponding orthogonality relations. In this article recent theory [J.B. Lawrie, Orthogonality relations for fluid–structural waves in a 3-D rectangular duct with flexible walls, Proc. R. Soc. A. 465 (2009) 2347–2367] is extended to construct the non-separable eigenfunctions for acoustic propagation in a three-dimensional rectangular duct with four flexible walls. For the special case in which the duct cross-section is square, the symmetrical nature of the eigenfunctions enables the eigenmodes for a right-angled, isosceles triangular duct with flexible hypotenuse to be deduced. The partial orthogonality relation together with other important properties of the triangular modes are discussed. A mode-matching solution to the scattering of a fluid–structure coupled wave at the junction of two identical semi-infinite ducts of triangular cross-section is demonstrated for two different sets of “junction” conditions
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Mode coalescence and the Green’s function in a two-dimensional waveguide with arbitrary admittance boundary conditions
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Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide
Data accessibility: The paper contains no experimental data. All codes repositories address are available from the reference section.Copyright © 2022 The Authors. To follow