{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19599"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19599","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Statistical response predictions in complex systems with dissipation","abstract":"The eigenstatistics of damped complex systems are examined for the purpose of improving statistical response predictions such as those formulated in statistical energy analysis and statistical room acoustics. Both the statistical distribution of modal decay rates and the effect of dissipation on the intermodal correlations of natural frequency spectra are explored. It is found that for moderate damping the modal decay rates of complex systems are distributed according to a modified chi square distribution whose degree depends on the spatial distribution of lossy material in the system and the wavelength of the disturbance. In addition the intermodal correlations of the natural frequency spectra are found to correspond with the predictions of the Gaussian orthogonal ensemble (GOE) provided the system remains reverberant.","abstract_html":"The eigenstatistics of damped complex systems are examined for the purpose of improving statistical response predictions such as those formulated in statistical energy analysis and statistical room acoustics. Both the statistical distribution of modal decay rates and the effect of dissipation on the intermodal correlations of natural frequency spectra are explored. It is found that for moderate damping the modal decay rates of complex systems are distributed according to a modified chi square distribution whose degree depends on the spatial distribution of lossy material in the system and the wavelength of the disturbance. In addition the intermodal correlations of the natural frequency spectra are found to correspond with the predictions of the Gaussian orthogonal ensemble (GOE) provided the system remains reverberant.","abstract_has_math":false,"creators":["Burkhardt, John Albert"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Science","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T12:12:38Z","date_published":"2011-05-07T12:12:38Z","updated_at":"2026-07-22T22:25:14Z","subjects":["Applied Mechanics","Engineering, Mechanical"],"languages":["eng"],"rights":["Copyright 1995 Burkhardt, John Albert"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543545","(UMI)AAI9543545"],"render_values":[{"text":"AAI9543545","href":null,"code":true},{"text":"(UMI)AAI9543545","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19599","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Burkhardt, John Albert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T12:12:38Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied Mechanics","Engineering, Mechanical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Burkhardt, John Albert"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543545","(UMI)AAI9543545","http://hdl.handle.net/2142/19599"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The eigenstatistics of damped complex systems are examined for the purpose of improving statistical response predictions such as those formulated in statistical energy analysis and statistical room acoustics. Both the statistical distribution of modal decay rates and the effect of dissipation on the intermodal correlations of natural frequency spectra are explored. It is found that for moderate damping the modal decay rates of complex systems are distributed according to a modified chi square distribution whose degree depends on the spatial distribution of lossy material in the system and the wavelength of the disturbance. In addition the intermodal correlations of the natural frequency spectra are found to correspond with the predictions of the Gaussian orthogonal ensemble (GOE) provided the system remains reverberant.","The effect of dissipation on statistical response estimates was explored by considering the transmission function, and the resulting energy density, of irregularly shaped damped membranes. In particular, analytical expressions estimating the variation in energy densities were developed which included a statistical distribution of modal decay rates. The introduction of a distribution of modal decay rates was found to increase expected response variations. Numerical experiments were performed on irregularly shaped damped membranes which confirmed the calculated effect of a distribution of modal decay rates on energy density variations.","The possible failure of statistical response estimates due to ignored correlations between modal amplitudes was also demonstrated. It was shown that, due to modal coherence, the mean energy density in a complex system is enhanced at the source point relative to other points in the field. The enhancement factor was found to rise from a factor of two at early times to a factor of three at times on the order of the inverse of the mean modal spacing. It was additionally demonstrated that the evolution of the enhancement factor in time from a value of two to a value of three is the same in damped systems as in undamped systems provided the simple decay of the damped reverberant field is accounted for.","Made available in DSpace on 2011-05-07T12:12:38Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543545.pdf: 6700043 bytes, checksum: fcefb50b390cec69598cc5d4c481b743 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:38:08Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:15:51-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Statistical response predictions in complex systems with dissipation"]}]}],"canonical_facts":{"dc:creator":["Burkhardt, John Albert"],"dc:date":["2011-05-07T12:12:38Z","10000-01-01","1995"],"dc:description":["The eigenstatistics of damped complex systems are examined for the purpose of improving statistical response predictions such as those formulated in statistical energy analysis and statistical room acoustics. Both the statistical distribution of modal decay rates and the effect of dissipation on the intermodal correlations of natural frequency spectra are explored. It is found that for moderate damping the modal decay rates of complex systems are distributed according to a modified chi square distribution whose degree depends on the spatial distribution of lossy material in the system and the wavelength of the disturbance. In addition the intermodal correlations of the natural frequency spectra are found to correspond with the predictions of the Gaussian orthogonal ensemble (GOE) provided the system remains reverberant.","The effect of dissipation on statistical response estimates was explored by considering the transmission function, and the resulting energy density, of irregularly shaped damped membranes. In particular, analytical expressions estimating the variation in energy densities were developed which included a statistical distribution of modal decay rates. The introduction of a distribution of modal decay rates was found to increase expected response variations. Numerical experiments were performed on irregularly shaped damped membranes which confirmed the calculated effect of a distribution of modal decay rates on energy density variations.","The possible failure of statistical response estimates due to ignored correlations between modal amplitudes was also demonstrated. It was shown that, due to modal coherence, the mean energy density in a complex system is enhanced at the source point relative to other points in the field. The enhancement factor was found to rise from a factor of two at early times to a factor of three at times on the order of the inverse of the mean modal spacing. It was additionally demonstrated that the evolution of the enhancement factor in time from a value of two to a value of three is the same in damped systems as in undamped systems provided the simple decay of the damped reverberant field is accounted for.","Made available in DSpace on 2011-05-07T12:12:38Z (GMT). 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