Dynamic stiffness and variational iterative stiffness methods for free
vibration analysis of Touratier beams
Abstract
A new procedure introduced as variational iterative stiffness method
(VISM) to overcome the difficulties of the application of variational
iteration method to free vibration analysis of higher order beams
consist of sixth order differential equation with complex boundaries. A
higher order trigonometric shear deformation theory denoted Touratier
beam which is considering rotary inertia is used for the mathematical
model to perform free vibration analysis of beams with a uniform
cross-section, subjected to a compressive axial load, resting on Winkler
and Pasternak foundations with various boundary conditions, in this
study. Circular frequencies obtained by using VISM are compared with DSM
and analytical method (ANM) results based on Touratier and Timoshenko
beam theories where a very good agreement is observed. In addition to
the obtained circular frequency values, normalised lateral
displacements, bending rotation, rotation of the normal to the axis,
shear forces and bending moments diagrams of first modes are represented
in graphics.