Vibration of a nonlinear shear deformable beam by numerical simulation

The vibration of a uniform geometrically nonlinear shear deformable beam subjected to a transverse harmonic excitation is investigated by the method of numerical simulation. Rotatory and axial inertia are included in the model. The beam is simply supported with supports a fixed distance apart. The nonlinear partial differential equations of motion are discretized in space by the Rayleigh-Ritz method, resulting in a set of nonlinear ordinary differential equations in time. The ordinary differential equations are integrated numerically to produce a time history of the solution of the equations. Transverse displacement, axial displacement, and cross sectional rotation are approximated by series of the corresponding linear natural mode shapes of the beam. Solutions of the equations of motion are compared to corresponding solutions where shear deformation and rotatory inertia are neglected. The effect of slenderness on the difference between the shear deformable case and the non shear deformable case is investigated by considering two beam configurations. In the simulations considered, the difference between the shear deformable model and the non shear deformable model increases as excitation frequency is increased and the length to thickness ratio of the beam is decreased.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1996

Author dc:creator

• Hagmann, Christopher

Committee members dc:contributor.committeemember

• Thangjitham, Surot
• Kraige, Luther Glenn
• Heller, Robert A.

• beam
• vibration
• nonlinear
• shear-deformable
• Simulation

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-08222008-063748

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/44362