{"id":775234,"date":"2021-09-15T14:29:01","date_gmt":"2021-09-15T21:29:01","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=775234"},"modified":"2021-09-15T14:29:19","modified_gmt":"2021-09-15T21:29:19","slug":"characterizing-the-vibrational-modes-of-a-cavitating-bubble-immersed-in-a-magnetic-fluid","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/characterizing-the-vibrational-modes-of-a-cavitating-bubble-immersed-in-a-magnetic-fluid\/","title":{"rendered":"Characterizing the Vibrational Modes of a Cavitating Bubble Immersed in a Magnetic Fluid"},"content":{"rendered":"
The main goal of this article is to identify the vibrational patterns of an oscillating spherical bubble immersed in<\/span><\/div>\n
a ferro\ufb02uid using Neural Networks. The gas bubble is immersed on a magnetic \ufb02uid and subjected to an harmonic pressure<\/div>\n
excitation and an applied magnetic \ufb01eld. The classical Rayleigh-Plesset equation is modi\ufb01ed and a magnetic version is<\/div>\n
proposed in order to model the radial motion of the bubble. Being a very non-linear system, the correct identi\ufb01cation of<\/div>\n
the vibrational patterns is not possible using linear system tools. In this case, fuzzy logic and neural networks are a good<\/div>\n
solution for the correct pattern identi\ufb01cation. The magnetic version of Rayleigh-Plesset equation is a second order non<\/div>\n
linear ordinary differential equation and it is solved through a \ufb01fth order Runge-Kutta scheme with adaptive time step.<\/div>\n
Four different vibrational patterns are identi\ufb01ed and proposed regarding its frequency response and Lyapunov exponets.<\/div>\n
Based on the Lyapunov exponents it is possible to analyze its non-chaotic behavior. Those Lyapunov exponents are used<\/div>\n
in a backpropagation neural network to correctly identify the bubble vibration modes what could lead to the identi\ufb01cation<\/div>\n
of the \ufb02ow physical parameters in practical applications. In order to compare the performance, another neural network<\/div>\n
is trainned with the amplitude and frequency information of the bubble motion from \u03c9<\/span>= 0 <\/span>to \u03c9<\/span>= 10<\/span>, based on its Fast<\/span><\/span><\/div>\n
Fourier Transform. The new results are compared with previous simulations made with harmonic response in frequency<\/div>\n
spectrum, in which only the \ufb01rst harmonic was considered<\/div>\n","protected":false},"excerpt":{"rendered":"

The main goal of this article is to identify the vibrational patterns of an oscillating spherical bubble immersed in a ferro\ufb02uid using Neural Networks. The gas bubble is immersed on a magnetic \ufb02uid and subjected to an harmonic pressure excitation and an applied magnetic \ufb01eld. The classical Rayleigh-Plesset equation is modi\ufb01ed and a magnetic version […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"ABCM","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"23rd ABCM International Congress of Mechanical Sciences and 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