Free vibration and stability of thin elastic beams subjected to axial forces

Natural frequencies and buckling loads of a simply supported beam with small length-to-depth ratio and sufficiently thin rectangular cross-sections subjected to initial axial tensile and/or compressive forces are analyzed. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a one-dimensional higher order beam theory for thin rectangular beams is derived through Hamilton's principle. Several sets of truncated approximate theories which can take into account the effects of both shear deformations with depth changes and rotary inertia are applied to solve the eigenvalue problems of a thin elastic beam. The Navier solution procedure is used to satisfy the boundary conditions of a simply supported thin rectangular beam. In order to assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling load for the axial and bending problems of thin beams are examined in detail. It is noticed that the present approximate theories can predict the natural frequencies and buckling loads of thin beams with small length-to-depth ratio more accurately than other refined higher order theories and the classical beam theory. (C) 1996 Academic Press Limited