{"id":{"repo_id":"missouri","oai_identifier":"oai:mospace.umsystem.edu:10355/98185"},"canonical_url":"https://search.dev.ndltd.org/etd/missouri/oai:mospace.umsystem.edu:10355/98185","repository":{"repo_id":"missouri","name":"University of Missouri","base_url":"https://mospace.umsystem.edu/oai/request"},"display":{"title":"Stability and vibration characteristics of skew plates","abstract":"\"Review of Literature. The deflection, stability, and vibration characteristics of rectangular plates have received considerable treatment in the literature. Solutions to the bending of rectangular plates with various boundary conditions, and under different types of loadings are available in S. P. Timoshenko and S. Woinowsky-Krieger [27]. In 1903, W. Ritz [24] proposed a method to determine approximate solutions for the eigen-frequencies and eigen-modes of transverse vibration of rectangular plates. In this approximate method, he assumed the deflection as the sum of a set of admissible functions, i.e., functions which individually satisfy all the geometric boundary conditions, with each term having an undetermined coefficient. The minimization of the energy functional with respect to these coefficients gives a frequency determinant that can be solved for the eigen-frequencies and the undetermined coefficients. This method was later adopted by other investigators, and it is shown that for many of the problems considered, it gives good approximations to the exact solutions. Young [31] and Barton [4] used this method to obtain eigen-frequencies and eigen-modes of vibration of cantilever plates. The deflection, in these investigations, was represented by the characteristic functions which define the normal modes of vibration of a uniform beam, with clamped-free, and free-free end conditions. The numerical analysis of the stability and vibration problems of skew plates, on the other hand, have not received much attention, and only a few problems of this type have been Investigated. This may be due to the difficulties that arise from the geometric configuration of these plates in the analysis. For this type of plates, therefore, new methods of approximation must be used or the available methods have to be modified to meet the requirements of the analysis. Aggawala [1] and [2], for instance, applied conformal mapping to solve bending problems of various triangular and parallelogram plates under uniform and concentrated loads.\"--Introduction.","abstract_html":""Review of Literature. The deflection, stability, and vibration characteristics of rectangular plates have received considerable treatment in the literature. Solutions to the bending of rectangular plates with various boundary conditions, and under different types of loadings are available in S. P. Timoshenko and S. Woinowsky-Krieger [27]. In 1903, W. Ritz [24] proposed a method to determine approximate solutions for the eigen-frequencies and eigen-modes of transverse vibration of rectangular plates. In this approximate method, he assumed the deflection as the sum of a set of admissible functions, i.e., functions which individually satisfy all the geometric boundary conditions, with each term having an undetermined coefficient. The minimization of the energy functional with respect to these coefficients gives a frequency determinant that can be solved for the eigen-frequencies and the undetermined coefficients. This method was later adopted by other investigators, and it is shown that for many of the problems considered, it gives good approximations to the exact solutions. Young [31] and Barton [4] used this method to obtain eigen-frequencies and eigen-modes of vibration of cantilever plates. The deflection, in these investigations, was represented by the characteristic functions which define the normal modes of vibration of a uniform beam, with clamped-free, and free-free end conditions. The numerical analysis of the stability and vibration problems of skew plates, on the other hand, have not received much attention, and only a few problems of this type have been Investigated. This may be due to the difficulties that arise from the geometric configuration of these plates in the analysis. For this type of plates, therefore, new methods of approximation must be used or the available methods have to be modified to meet the requirements of the analysis. Aggawala [1] and [2], for instance, applied conformal mapping to solve bending problems of various triangular and parallelogram plates under uniform and concentrated loads."--Introduction.","abstract_has_math":false,"creators":["Nadjafi, Hossein Z."],"institution":"University of Missouri--Columbia","degree_name":"M.S.","degree_level":"Masters","degree_discipline":"Mechanical and aerospace engineering (MU)","degree_department":null,"school":null,"contributors":[],"advisors":["Stickney, Goerge H."],"committee_chairs":[],"committee_members":[],"year":1971,"date_issued":"1971","date_published":"1971","updated_at":"2026-07-24T03:08:43Z","subjects":[],"languages":["eng","English"],"rights":["OpenAccess."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.32469/10355/98185"],"render_values":[{"text":"https://doi.org/10.32469/10355/98185","href":"https://doi.org/10.32469/10355/98185","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10355/98185","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Stickney, Goerge H."]},{"key":"dc:creator","label":"Author","values":["Nadjafi, Hossein Z."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-02-15T22:58:43Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-15T22:58:43Z"]},{"key":"dc:date.issued","label":"Date","values":["1971"]},{"key":"dc:publisher","label":"Institution","values":["University of Missouri--Columbia"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical and aerospace engineering (MU)"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Columbia"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["OpenAccess."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["https://doi.org/10.32469/10355/98185"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10355/98185"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"Review of Literature. The deflection, stability, and vibration characteristics of rectangular plates have received considerable treatment in the literature. Solutions to the bending of rectangular plates with various boundary conditions, and under different types of loadings are available in S. P. Timoshenko and S. Woinowsky-Krieger [27]. In 1903, W. Ritz [24] proposed a method to determine approximate solutions for the eigen-frequencies and eigen-modes of transverse vibration of rectangular plates. In this approximate method, he assumed the deflection as the sum of a set of admissible functions, i.e., functions which individually satisfy all the geometric boundary conditions, with each term having an undetermined coefficient. The minimization of the energy functional with respect to these coefficients gives a frequency determinant that can be solved for the eigen-frequencies and the undetermined coefficients. This method was later adopted by other investigators, and it is shown that for many of the problems considered, it gives good approximations to the exact solutions. Young [31] and Barton [4] used this method to obtain eigen-frequencies and eigen-modes of vibration of cantilever plates. The deflection, in these investigations, was represented by the characteristic functions which define the normal modes of vibration of a uniform beam, with clamped-free, and free-free end conditions. The numerical analysis of the stability and vibration problems of skew plates, on the other hand, have not received much attention, and only a few problems of this type have been Investigated. This may be due to the difficulties that arise from the geometric configuration of these plates in the analysis. For this type of plates, therefore, new methods of approximation must be used or the available methods have to be modified to meet the requirements of the analysis. Aggawala [1] and [2], for instance, applied conformal mapping to solve bending problems of various triangular and parallelogram plates under uniform and concentrated loads.\"--Introduction."]},{"key":"dc:source","label":"Dc Source","values":["Digitized a department copy."]},{"key":"dc:title","label":"Title","values":["Stability and vibration characteristics of skew plates"]}]}],"canonical_facts":{"dc:contributor.advisor":["Stickney, Goerge H."],"dc:creator":["Nadjafi, Hossein Z."],"dc:date.accessioned":["2024-02-15T22:58:43Z"],"dc:date.available":["2024-02-15T22:58:43Z"],"dc:date.issued":["1971"],"dc:description.abstract":["\"Review of Literature. The deflection, stability, and vibration characteristics of rectangular plates have received considerable treatment in the literature. Solutions to the bending of rectangular plates with various boundary conditions, and under different types of loadings are available in S. P. Timoshenko and S. Woinowsky-Krieger [27]. In 1903, W. Ritz [24] proposed a method to determine approximate solutions for the eigen-frequencies and eigen-modes of transverse vibration of rectangular plates. In this approximate method, he assumed the deflection as the sum of a set of admissible functions, i.e., functions which individually satisfy all the geometric boundary conditions, with each term having an undetermined coefficient. The minimization of the energy functional with respect to these coefficients gives a frequency determinant that can be solved for the eigen-frequencies and the undetermined coefficients. This method was later adopted by other investigators, and it is shown that for many of the problems considered, it gives good approximations to the exact solutions. Young [31] and Barton [4] used this method to obtain eigen-frequencies and eigen-modes of vibration of cantilever plates. The deflection, in these investigations, was represented by the characteristic functions which define the normal modes of vibration of a uniform beam, with clamped-free, and free-free end conditions. The numerical analysis of the stability and vibration problems of skew plates, on the other hand, have not received much attention, and only a few problems of this type have been Investigated. This may be due to the difficulties that arise from the geometric configuration of these plates in the analysis. For this type of plates, therefore, new methods of approximation must be used or the available methods have to be modified to meet the requirements of the analysis. Aggawala [1] and [2], for instance, applied conformal mapping to solve bending problems of various triangular and parallelogram plates under uniform and concentrated loads.\"--Introduction."],"dc:identifier.doi":["https://doi.org/10.32469/10355/98185"],"dc:identifier.uri":["https://hdl.handle.net/10355/98185"],"dc:language":["English"],"dc:language.iso":["eng"],"dc:publisher":["University of Missouri--Columbia"],"dc:rights":["OpenAccess."],"dc:source":["Digitized a department copy."],"dc:title":["Stability and vibration characteristics of skew plates"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mechanical and aerospace engineering (MU)"],"thesis:degree_level":["Masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Missouri--Columbia"]},"updated_at":"2026-07-24T03:08:43Z"}