The purpose of this thesis is to study the nonlinear forced vibration of an unsymmetrically laminated composite beam. Two cases are considered: unsymmetrical angle-ply and unsymmetrical cross-ply composite beams. The nonlinear governing partial differential equations of motion are obtained by taking into account the von-Karman geometrical nonlinearity. These equations are transformed into nonlinear ODE (Ordinary Differential Equations) by means of the Galerkin method. For both cases the forced Duffing equation was obtained. It is to be noted that only for the unsymmetrical cross-ply laminate simply-supported case are both quadratic and cubic nonlinearities present. The resulting equations for both cases are then solved using the Method of Multiple Scales (MMS). The boundary conditions considered here are simply-supported with immovable edges and clamped at both edges. For both cases the frequency response of the beam associated with the primary resonance was studied. In addition, the subharmonic and superharmonic resonances were analyzed for a simply-supported unsymmetrically laminated angle-ply composite beam. In order to compare the effects of different modes of vibrations, a one-mode solution and a two-mode solution were investigated.
","abstract_html":"<p>The purpose of this thesis is to study the nonlinear forced vibration of an unsymmetrically laminated composite beam. Two cases are considered: unsymmetrical angle-ply and unsymmetrical cross-ply composite beams. The nonlinear governing partial differential equations of motion are obtained by taking into account the von-Karman geometrical nonlinearity. These equations are transformed into nonlinear ODE (Ordinary Differential Equations) by means of the Galerkin method. For both cases the forced Duffing equation was obtained. It is to be noted that only for the unsymmetrical cross-ply laminate simply-supported case are both quadratic and cubic nonlinearities present. The resulting equations for both cases are then solved using the Method of Multiple Scales (MMS). The boundary conditions considered here are simply-supported with immovable edges and clamped at both edges. For both cases the frequency response of the beam associated with the primary resonance was studied. In addition, the subharmonic and superharmonic resonances were analyzed for a simply-supported unsymmetrically laminated angle-ply composite beam. In order to compare the effects of different modes of vibrations, a one-mode solution and a two-mode solution were investigated.</p>","abstract_has_math":false,"creators":["Pompei, Marie Helene"],"institution":null,"degree_name":"Master of Science in Aerospace Engineering","degree_level":"Thesis - Open Access","degree_discipline":"Graduate Studies","degree_department":null,"school":null,"contributors":["Habib Eslami","Frank Radosta","Yechiel J. Crispin"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1994,"date_issued":"1994-05-01T07:00:00Z","date_published":"1994-05-01T07:00:00Z","updated_at":"2026-07-27T19:25:16Z","subjects":["nonlinear forced vibration","laminated composite beam","Aerospace Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/db-theses/239","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Habib Eslami","Frank Radosta","Yechiel J. Crispin"]},{"key":"dc:creator","label":"Author","values":["Pompei, Marie Helene"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Graduate Studies"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Aerospace Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["nonlinear forced vibration","laminated composite beam","Aerospace Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/db-theses/239"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to study the nonlinear forced vibration of an unsymmetrically laminated composite beam. Two cases are considered: unsymmetrical angle-ply and unsymmetrical cross-ply composite beams. The nonlinear governing partial differential equations of motion are obtained by taking into account the von-Karman geometrical nonlinearity. These equations are transformed into nonlinear ODE (Ordinary Differential Equations) by means of the Galerkin method. For both cases the forced Duffing equation was obtained. It is to be noted that only for the unsymmetrical cross-ply laminate simply-supported case are both quadratic and cubic nonlinearities present. The resulting equations for both cases are then solved using the Method of Multiple Scales (MMS). The boundary conditions considered here are simply-supported with immovable edges and clamped at both edges. For both cases the frequency response of the beam associated with the primary resonance was studied. In addition, the subharmonic and superharmonic resonances were analyzed for a simply-supported unsymmetrically laminated angle-ply composite beam. In order to compare the effects of different modes of vibrations, a one-mode solution and a two-mode solution were investigated.
"]},{"key":"dc:title","label":"Title","values":["Nonlinear Forced Vibration of an Unsymmetrically Laminated Composite Beam"]}]}],"canonical_facts":{"dc:contributor":["Habib Eslami","Frank Radosta","Yechiel J. Crispin"],"dc:creator":["Pompei, Marie Helene"],"dc:description.abstract":["The purpose of this thesis is to study the nonlinear forced vibration of an unsymmetrically laminated composite beam. Two cases are considered: unsymmetrical angle-ply and unsymmetrical cross-ply composite beams. The nonlinear governing partial differential equations of motion are obtained by taking into account the von-Karman geometrical nonlinearity. These equations are transformed into nonlinear ODE (Ordinary Differential Equations) by means of the Galerkin method. For both cases the forced Duffing equation was obtained. It is to be noted that only for the unsymmetrical cross-ply laminate simply-supported case are both quadratic and cubic nonlinearities present. The resulting equations for both cases are then solved using the Method of Multiple Scales (MMS). The boundary conditions considered here are simply-supported with immovable edges and clamped at both edges. For both cases the frequency response of the beam associated with the primary resonance was studied. In addition, the subharmonic and superharmonic resonances were analyzed for a simply-supported unsymmetrically laminated angle-ply composite beam. In order to compare the effects of different modes of vibrations, a one-mode solution and a two-mode solution were investigated.
"],"dc:identifier":["https://commons.erau.edu/db-theses/239"],"dc:subject":["nonlinear forced vibration","laminated composite beam","Aerospace Engineering"],"dc:title":["Nonlinear Forced Vibration of an Unsymmetrically Laminated Composite Beam"],"thesis:degree_discipline":["Graduate Studies"],"thesis:degree_level":["Thesis - Open Access"],"thesis:degree_name":["Master of Science in Aerospace Engineering"]},"updated_at":"2026-07-27T19:25:16Z"}