{"id":{"repo_id":"wvu","oai_identifier":"oai:researchrepository.wvu.edu:etd-1951"},"canonical_url":"https://search.dev.ndltd.org/etd/wvu/oai:researchrepository.wvu.edu:etd-1951","repository":{"repo_id":"wvu","name":"West Virginia University","base_url":"https://researchrepository.wvu.edu/do/oai/"},"display":{"title":"Dynamic stability of an elliptical pendulum with unilateral simple supports","abstract":"The study of rollover stability of partially filled tanker trucks often requires the use of mechanical pendulums to substitute the sloshing dynamics of the fluid. Cylindrical tanks have been effectively characterized by simple pendulums combined with some fixed masses. Just recently, a WVU team proposed the use of an elliptical pendulum to substitute the sloshing dynamics in partially filled elliptical tankers.;In this research, a trammel mechanism is configured as an elliptical pendulum with a unilaterally supported base. That is, the supports on either side can lift off the ground to allow for rollover under certain critical lateral accelerations. Two generalized coordinates are considered, one representing the angle of swing of the pendulum and a second one representing the tilt angle of the base (lift off the ground). This degree of freedom (tilt angle) is active only if the lateral accelerations are greater than certain critical value, giving rise to the unilateral support restraints at the base of the mechanism.;The initial angle of swing that made the pendulum base liftoff was determined under zero lateral acceleration. The minimum horizontal lateral acceleration that caused the base to liftoff was also calculated when the pendulum was at rest (in the vertical position). The angular displacement, angular velocity and angular acceleration were calculated with respect to time, for systems with fixed or unilateral supports.;A mathematical model was developed to simulate the dynamic response of the elliptical pendulum with unilateral constraints. A mode of instability was found in which the pendulum swings producing liftoff but not rollover, as the base \"bounces\" back-and-forth, from a one support only base to a simple supported base.","abstract_html":"The study of rollover stability of partially filled tanker trucks often requires the use of mechanical pendulums to substitute the sloshing dynamics of the fluid. Cylindrical tanks have been effectively characterized by simple pendulums combined with some fixed masses. Just recently, a WVU team proposed the use of an elliptical pendulum to substitute the sloshing dynamics in partially filled elliptical tankers.;In this research, a trammel mechanism is configured as an elliptical pendulum with a unilaterally supported base. That is, the supports on either side can lift off the ground to allow for rollover under certain critical lateral accelerations. Two generalized coordinates are considered, one representing the angle of swing of the pendulum and a second one representing the tilt angle of the base (lift off the ground). This degree of freedom (tilt angle) is active only if the lateral accelerations are greater than certain critical value, giving rise to the unilateral support restraints at the base of the mechanism.;The initial angle of swing that made the pendulum base liftoff was determined under zero lateral acceleration. The minimum horizontal lateral acceleration that caused the base to liftoff was also calculated when the pendulum was at rest (in the vertical position). The angular displacement, angular velocity and angular acceleration were calculated with respect to time, for systems with fixed or unilateral supports.;A mathematical model was developed to simulate the dynamic response of the elliptical pendulum with unilateral constraints. A mode of instability was found in which the pendulum swings producing liftoff but not rollover, as the base "bounces" back-and-forth, from a one support only base to a simple supported base.","abstract_has_math":false,"creators":["Karam, Heins Naim"],"institution":null,"degree_name":"MS","degree_level":"Thesis","degree_discipline":"Mechanical and Aerospace Engineering","degree_department":null,"school":null,"contributors":["Victor H. Mucino."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1999,"date_issued":"1999-05-01T07:00:00Z","date_published":"1999-05-01T07:00:00Z","updated_at":"2026-07-24T06:15:08Z","subjects":["Forestry"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://researchrepository.wvu.edu/etd/948"],"render_values":[{"text":"https://researchrepository.wvu.edu/etd/948","href":"https://researchrepository.wvu.edu/etd/948","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.33915/etd.948","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Victor H. 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Cylindrical tanks have been effectively characterized by simple pendulums combined with some fixed masses. Just recently, a WVU team proposed the use of an elliptical pendulum to substitute the sloshing dynamics in partially filled elliptical tankers.;In this research, a trammel mechanism is configured as an elliptical pendulum with a unilaterally supported base. That is, the supports on either side can lift off the ground to allow for rollover under certain critical lateral accelerations. Two generalized coordinates are considered, one representing the angle of swing of the pendulum and a second one representing the tilt angle of the base (lift off the ground). This degree of freedom (tilt angle) is active only if the lateral accelerations are greater than certain critical value, giving rise to the unilateral support restraints at the base of the mechanism.;The initial angle of swing that made the pendulum base liftoff was determined under zero lateral acceleration. The minimum horizontal lateral acceleration that caused the base to liftoff was also calculated when the pendulum was at rest (in the vertical position). The angular displacement, angular velocity and angular acceleration were calculated with respect to time, for systems with fixed or unilateral supports.;A mathematical model was developed to simulate the dynamic response of the elliptical pendulum with unilateral constraints. A mode of instability was found in which the pendulum swings producing liftoff but not rollover, as the base \"bounces\" back-and-forth, from a one support only base to a simple supported base."]},{"key":"dc:title","label":"Title","values":["Dynamic stability of an elliptical pendulum with unilateral simple supports"]}]}],"canonical_facts":{"dc:contributor":["Victor H. Mucino."],"dc:creator":["Karam, Heins Naim"],"dc:date.available":["2019-01-17T08:00:00Z"],"dc:description.abstract":["The study of rollover stability of partially filled tanker trucks often requires the use of mechanical pendulums to substitute the sloshing dynamics of the fluid. Cylindrical tanks have been effectively characterized by simple pendulums combined with some fixed masses. Just recently, a WVU team proposed the use of an elliptical pendulum to substitute the sloshing dynamics in partially filled elliptical tankers.;In this research, a trammel mechanism is configured as an elliptical pendulum with a unilaterally supported base. That is, the supports on either side can lift off the ground to allow for rollover under certain critical lateral accelerations. Two generalized coordinates are considered, one representing the angle of swing of the pendulum and a second one representing the tilt angle of the base (lift off the ground). This degree of freedom (tilt angle) is active only if the lateral accelerations are greater than certain critical value, giving rise to the unilateral support restraints at the base of the mechanism.;The initial angle of swing that made the pendulum base liftoff was determined under zero lateral acceleration. The minimum horizontal lateral acceleration that caused the base to liftoff was also calculated when the pendulum was at rest (in the vertical position). The angular displacement, angular velocity and angular acceleration were calculated with respect to time, for systems with fixed or unilateral supports.;A mathematical model was developed to simulate the dynamic response of the elliptical pendulum with unilateral constraints. A mode of instability was found in which the pendulum swings producing liftoff but not rollover, as the base \"bounces\" back-and-forth, from a one support only base to a simple supported base."],"dc:identifier":["https://doi.org/10.33915/etd.948","https://researchrepository.wvu.edu/etd/948"],"dc:subject":["Forestry"],"dc:title":["Dynamic stability of an elliptical pendulum with unilateral simple supports"],"thesis:degree_discipline":["Mechanical and Aerospace Engineering"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T06:15:08Z"}