Accession Number:

AD0274582

Title:

A MATRIX METHOD FOR THE DETERMINATION OF THE NATURAL VIBRATIONS OF FREE-FREE UNSYMMETRICAL BEAMS WITH APPLICATION TO LAUNCH VEHICLES

Descriptive Note:

Corporate Author:

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON D C

Report Date:

1962-04-01

Pagination or Media Count:

1.0

Abstract:

The equations for determining the undamped natural vibrations of free-free unsymmetrical beams and launch-vehicle structures are developed. The analysis treats a continuous free-free system as an equivalent discrete-mass system of a finite number of degrees of freedom. The flexure-load relationships are equated by influence coefficients which are derived by considering both flexure and deflections from local rotations. Matrix notations are used because of their suitability to the analysis of discrete-mass systems. Equations are developed for the dynamic equilibrium of the system, the natural frequencies and mode shapes and their first derivatives, the bending moments associated with the modes, and the influence coefficients. The results of an investigation on the accuracy of the natural frequencies and mode shapes in terms of the number of discrete masses employed in the solution are also included. The procedures are illustrated by a numerical analysis of a uniform beam, and the application of the matrix procedure to a typical launch vehicle is given. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE