Examination of Boundary Conditions for Sixth-order Damped Beam Theory
Report Number: WL-TR-91-3078 Volume I, p. BBA-1 thru BBA-15
Author(s): Tate, Ralph E.
Corporate Author(s): LTV Aircraft Products Group
Laboratory: Wright Laboratory
Date of Publication: 1991-08
Pages: 15
Contract: Laboratory Research - No Contract
DoD Project: 2401
DoD Task: 240104
Identifier: This paper is part of a conference proceedings. See ADA241311
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.
Author(s): Tate, Ralph E.
Corporate Author(s): LTV Aircraft Products Group
Laboratory: Wright Laboratory
Date of Publication: 1991-08
Pages: 15
Contract: Laboratory Research - No Contract
DoD Project: 2401
DoD Task: 240104
Identifier: This paper is part of a conference proceedings. See ADA241311
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.