*Robert W. Leonard, Bernard Budiansky*

*naca-report-1173*

*1954*

The basic equations of Timoshenko for the motion of vibrating nonuniform beams, which allow for effects of transverse shear deformation and rotary inertia, are presented in several forms, including one in which the equations are written in the directions of the characteristics. The propagation of discontinuities in moment and shear, as governed by these equations, is discussed. Numerical traveling-wave solutions are obtained for some elementary problems of finite uniform beams for which the propagation velocities of bending and shear discontinuities are taken to be equal. These solutions are compared with modal solutions of Timoshenko's equations and, in some cases, with exact closed solutions.

*An Adobe Acrobat (PDF) file of the entire report:*

http://naca.central.cranfield.ac.uk/reports/1954/naca-report-1173.pdf