A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied to the propeller blade model lead to a radical reduction in complexity of the solution methodology.
This research is motivated by the need to obtain accurate, cost efficient propeller blade surface pressure information to be used as input to Advanced Technology Propeller Noise Prediction methods. Currently, these data are supplied by state of the art computational fluid dynamics (CFD) methods which require the calculation of the entire flow field. Though these methods yield highly accurate solutions, they are considered by the aeroacoustician to be time consuming and expensive from a computational point of view. The above integral equation method, on the other hand, involves only surface calculations, requiring much less computational expense relative to CFD methods. Results are presented that demonstrate the validity of the integral equation model and the solution procedure. Propeller noise predictions using results from the method presented here are in excellent agreement with those obtained from CFD methods.
","abstract_html":"<p>A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied to the propeller blade model lead to a radical reduction in complexity of the solution methodology.</p> <p>This research is motivated by the need to obtain accurate, cost efficient propeller blade surface pressure information to be used as input to Advanced Technology Propeller Noise Prediction methods. Currently, these data are supplied by state of the art computational fluid dynamics (CFD) methods which require the calculation of the entire flow field. Though these methods yield highly accurate solutions, they are considered by the aeroacoustician to be time consuming and expensive from a computational point of view. The above integral equation method, on the other hand, involves only surface calculations, requiring much less computational expense relative to CFD methods. Results are presented that demonstrate the validity of the integral equation model and the solution procedure. Propeller noise predictions using results from the method presented here are in excellent agreement with those obtained from CFD methods.</p>","abstract_has_math":false,"creators":["Dunn, Mark H."],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["John Tweed","John H. Heinbockel","Fereidoun Farassat","Thomas Jackson"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991-07-01T07:00:00Z","date_published":"1991-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:15Z","subjects":["Volterra integral equation","Lifting surface theory","Rotating blades","Mathematics","Structures and Materials"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/88","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["John Tweed","John H. Heinbockel","Fereidoun Farassat","Thomas Jackson"]},{"key":"dc:creator","label":"Author","values":["Dunn, Mark H."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Volterra integral equation","Lifting surface theory","Rotating blades","Mathematics","Structures and Materials"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.odu.edu/mathstat_etds/88"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied to the propeller blade model lead to a radical reduction in complexity of the solution methodology.
This research is motivated by the need to obtain accurate, cost efficient propeller blade surface pressure information to be used as input to Advanced Technology Propeller Noise Prediction methods. Currently, these data are supplied by state of the art computational fluid dynamics (CFD) methods which require the calculation of the entire flow field. Though these methods yield highly accurate solutions, they are considered by the aeroacoustician to be time consuming and expensive from a computational point of view. The above integral equation method, on the other hand, involves only surface calculations, requiring much less computational expense relative to CFD methods. Results are presented that demonstrate the validity of the integral equation model and the solution procedure. Propeller noise predictions using results from the method presented here are in excellent agreement with those obtained from CFD methods.
"]},{"key":"dc:title","label":"Title","values":["The Solution of a Singular Integral Equation Arising From a Lifting Surface Theory for Rotating Blades"]}]}],"canonical_facts":{"dc:contributor":["John Tweed","John H. Heinbockel","Fereidoun Farassat","Thomas Jackson"],"dc:creator":["Dunn, Mark H."],"dc:date.available":["2019-10-01T07:00:00Z"],"dc:description.abstract":["A technique is presented for the solution of a linear, two dimensional, singular, Volterra integral equation of the first kind. The integral equation, originally developed by Farassat and Myers, is derived from the basic equations of linearized acoustics and models the lifting force experienced by an infinitesimally thin surface moving tangent to itself. As a particular application, the motion of modern high speed aircraft propellers (Advanced Technology Propellers) is considered. The unknown propeller blade surface pressure distribution is approximated by a piecewise constant function and the integral equation is solved numerically by the method of collocation. Certain simplifying assumptions applied to the propeller blade model lead to a radical reduction in complexity of the solution methodology.
This research is motivated by the need to obtain accurate, cost efficient propeller blade surface pressure information to be used as input to Advanced Technology Propeller Noise Prediction methods. Currently, these data are supplied by state of the art computational fluid dynamics (CFD) methods which require the calculation of the entire flow field. Though these methods yield highly accurate solutions, they are considered by the aeroacoustician to be time consuming and expensive from a computational point of view. The above integral equation method, on the other hand, involves only surface calculations, requiring much less computational expense relative to CFD methods. Results are presented that demonstrate the validity of the integral equation model and the solution procedure. Propeller noise predictions using results from the method presented here are in excellent agreement with those obtained from CFD methods.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/88"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Volterra integral equation","Lifting surface theory","Rotating blades","Mathematics","Structures and Materials"],"dc:title":["The Solution of a Singular Integral Equation Arising From a Lifting Surface Theory for Rotating Blades"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:15Z"}