Response Determination of a Beam with Moderately Large Deflection Under Transverse Dynamic Load Using First Order Shear Deformation Theory

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive equation. These equations which are a system of nonlinear partial differential equations with constant coefficients are derived by using the Hamilton’s principle. The eigenfunction expansion method and the perturbation technique are applied to obtain the response. The results are compared with the finite elements method.