Work

Rayleigh–Ritz Approximation of the Acoustic Vibrations of Clamped Superquadrics—Application to Free Core–Shell Objects

Year: 2025

Type: article

Abstract: A numerical approach based on the Rayleigh-Ritz method and using a modification of the so-called xyz algorithm is introduced to calculate the acoustic vibrations of clamped objects whose shape is delimited by superquadrics. It is then used to improve the convergence for the free vibrations of core-shell objects. The issue in this case is first illustrated in the simpler one-dimensional case of the thickness breathing vibration of an infinite "core-shell" plate. Functions suitable for solving the clamped vibrations of the core are added to the original xyz basis of functions to improve the convergence for core-shell superquadrics. The new basis obeys the same symmetry rules as the original one, which allows calculating vibrations for individual irreducible representations when the objects are made of cubic, tetragonal, or orthorhombic materials whose principal axes are aligned with those of the superquadrics. This method is validated for an isotropic spherical core-shell system for which analytic solutions exist.

Source: Nanomaterials

DOI: 10.3390/nano15241865

Authors: Sajana S, María del Carmen Marco de Lucas, Lucien Saviot

Institutions: Centre National de la Recherche Scientifique, Laboratoire Interdisciplinaire Carnot de Bourgogne, Université Bourgogne Europe

Language: English

Topic: Acoustic Wave Phenomena Research

Subfield: Biomedical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Agence Nationale de la Recherche