skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Derivation of the coupled equations of motion for a beam subjected to three translational accelerations and three rotational accelerations

Abstract

Equations of motion are derived to describe the coupled (axial, torsional, and lateral) dynamic response of a uniform Bernoulli--Euler beam, of constant circular cross-section, subjected to three specified translational accelerations and three specified rotational accelerations. The boundary condition equations are those for a cantilever beam with a symmetrical rigid mass attached to the free end of the beam. The resulting equations of motion (and boundary conditions) are non linear. However, for many problems, these equations can be reduced and simplified to a form more amenable to solution. An illustrative example is given where the equations are reduced and simplified to those for the coupled quasi-static response of a cantilever beam with a rigid symmetrical mass attached to its free end. Thus, the quasi-static problem corresponds to the solution of a two point, linear boundary value problem. A numerical example is also provided. The results of a computer solution for the two point, linear boundary value problem are compared with the experimental results obtained from three spinning beam experiments. The agreement between the measured and predicted beam bending strains versus angular speed is excellent. Consequently, it is concluded the mathematical model for the spinning beam and the equations associated with themore » model are accurate.« less

Authors:
Publication Date:
Research Org.:
Sandia Labs., Livermore, CA (USA)
OSTI Identifier:
6267061
Report Number(s):
SAND-79-8202
DOE Contract Number:  
EY-76-C-04-0789
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; PROJECTILES; STRUCTURAL BEAMS; STRAINS; ACCELERATION; DIAGRAMS; DYNAMIC LOADS; EQUATIONS OF MOTION; EXPERIMENTAL DATA; ROTATION; STRESSES; VARIATIONS; DATA; DIFFERENTIAL EQUATIONS; EQUATIONS; INFORMATION; MOTION; NUMERICAL DATA; 420200* - Engineering- Facilities, Equipment, & Techniques

Citation Formats

Benedetti, G.A. Derivation of the coupled equations of motion for a beam subjected to three translational accelerations and three rotational accelerations. United States: N. p., 1979. Web.
Benedetti, G.A. Derivation of the coupled equations of motion for a beam subjected to three translational accelerations and three rotational accelerations. United States.
Benedetti, G.A. Thu . "Derivation of the coupled equations of motion for a beam subjected to three translational accelerations and three rotational accelerations". United States.
@article{osti_6267061,
title = {Derivation of the coupled equations of motion for a beam subjected to three translational accelerations and three rotational accelerations},
author = {Benedetti, G.A.},
abstractNote = {Equations of motion are derived to describe the coupled (axial, torsional, and lateral) dynamic response of a uniform Bernoulli--Euler beam, of constant circular cross-section, subjected to three specified translational accelerations and three specified rotational accelerations. The boundary condition equations are those for a cantilever beam with a symmetrical rigid mass attached to the free end of the beam. The resulting equations of motion (and boundary conditions) are non linear. However, for many problems, these equations can be reduced and simplified to a form more amenable to solution. An illustrative example is given where the equations are reduced and simplified to those for the coupled quasi-static response of a cantilever beam with a rigid symmetrical mass attached to its free end. Thus, the quasi-static problem corresponds to the solution of a two point, linear boundary value problem. A numerical example is also provided. The results of a computer solution for the two point, linear boundary value problem are compared with the experimental results obtained from three spinning beam experiments. The agreement between the measured and predicted beam bending strains versus angular speed is excellent. Consequently, it is concluded the mathematical model for the spinning beam and the equations associated with the model are accurate.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1979},
month = {2}
}

Technical Report:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item. Keep in mind that many technical reports are not cataloged in WorldCat.

Save / Share: