Free Vibrtions of Timoshenko Beams on Rigid Blocks
The aim of the paper is to analyze the vibration of Timoshenko beam resting on the most arbitrary elastically flexible supports. The boundary conditions are defined by means of a 2 x 2 flexibility matrix, and the structure is discretized according to the so-called cell procedure. The Lagrangian coordinates are selected to be the vertical displacements of the end points of the rigid bars, plus the four possible displacements of the external constraints. A numerical example is worked out in which the obtained results are compared with some known results.
References
A.RAITHEL and C.FRANCIOSI, The stability of arches in the Lagrangian approach, J. Struci. Engng., ASCE, 847-858, 1984.
V.FRANCIOSI and N.M. AUCIELLO, Analisi modale degli archi su imposte elastiche comunque cedevoli, Industria Italiana del Cemento, 706-711, 1988.
C.FRANCIOSI and M.A.DE ROSA, A new approach to the Timoshenko beam theory (to be published), 1991.
N.M.AUCIELLO, The effect of the support flexibilities on arch-beam system, Struct. Engng. Rev., 8, 1-6, 1991.
J.C.BRUCH and T.P.MITCHELL, Vibrations of mass-loadedclamped-free Timoshenko beam, J. Sound Vib., 114, 341-345, 1987.
H.ABRAMOVICH and O.HAMBURGER, Vibration of a cantilever Timoshenko beam with a tip mass, J. Sound Vib., 148, 162-170, 1991.