Examination of Boundary Conditions for Sixth-order Damped Beam Theory

Item

Title
Examination of Boundary Conditions for Sixth-order Damped Beam Theory
Report Number
WL-TR-91-3078 Volume I, p. BBA-1 thru BBA-15
Creator
Tate, Ralph E.
Corporate Author
LTV Aircraft Products Group
Laboratory
Wright Laboratory
Date
1991
Date Issued
1991-08
Extent
15
Contract
Laboratory Research - No Contract
DoD Project
2401
DoD Task
240104
Identifier
ADA241311
Format
1 online resource
Abstract
The purpose of sixth-order beam theory is to include the effects of core shearing due to extentional deformation in terms of the transverse displacements. The constraint to eliminate the extentional motion reduces a twelfth-order
system of equations into a single sixth-order equation. Since boundary conditions are necessary to completely specify the solution of partial differential equations, the author purposes to use this forum to present a detailed derivation of the sixth-order equation of motion using energy method techniques. The boundary conditions follow naturally as a consequence of the energy method formulation. The author show how two "natural" boundary conditions are lost, and must be replaced by two "kinematic" boundary conditions. The author interprets the boundary conditions and their consequences in the analysis of damped beams.
Description
The purpose of sixth-order beam theory is to include the effects of core shearing due to extentional deformation in terms of the transverse displacements. The constraint to eliminate the extentional motion reduces a twelfth-order
system of equations into a single sixth-order equation. Since boundary conditions are necessary to completely specify the solution of partial differential equations, the author purposes to use this forum to present a detailed derivation of the sixth-order equation of motion using energy method techniques. The boundary conditions follow naturally as a consequence of the energy method formulation. The author show how two "natural" boundary conditions are lost, and must be replaced by two "kinematic" boundary conditions. The author interprets the boundary conditions and their consequences in the analysis of damped beams.
Distribution Classification
1
Distribution Conflict
No
DTIC Record Exists
No
Illinois Tech Related
No
Photo Quality
Not Needed
Report Availability
Full text available
Type
article
Is Part Of
Proceedings of Damping '91: 13-15 February 1991 San Diego, California (Pages AAC-1 through DCC-19)
Media
article06