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Stochastic Models for Chladni Figures

Part of: Dynamical problems Stochastic analysis Thin bodies, structures

Published online by Cambridge University Press:  10 August 2015

Jaime Arango  and
Carlos Reyes
Jaime Arango
Affiliation:
Departamento de Matemáticas, Universidad del Valle, Calle 13, 100-00, Cali, Colombia (jaime.arango@correounivalle.edu.co)
Carlos Reyes
Affiliation:
Posgrado de Matemáticas, Universidad del Valle, Calle 13, 100-00, Cali, Colombia
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Abstract

Chladni figures are formed when particles scattered across a plate move due to an external harmonic force resonating with one of the natural frequencies of the plate. Chladni figures are precisely the nodal set of the vibrational mode corresponding to the frequency resonating with the external force. We propose a plausible model for the movement of the particles that explains the formation of Chladni figures in terms of the stochastic stability of the equilibrium solutions of stochastic differential equations.

Keywords

Chladni figuresclamped platesfree platesstabilitystochastic differential equationswave equation

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.) 74H50: Random vibrations
Secondary: 60H10: Stochastic ordinary differential equations 74K20: Plates
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 287 - 300
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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