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

Subject Areas : Engineering

F Sohani ¹ , H.R Eipakchi ²

1 - Mechanical Engineering Faculty, Shahrood University
2 - Mechanical Engineering Faculty, Shahrood University

Received: 2013-07-01 Accepted : 2013-09-03 Published : 2013-12-30

Keywords: First-order shear deformation theory, Response determination, Perturbation technique, Eigenfunction expansion, Moderately large deflection,

Abstract :

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.

References:

[1] Lee K., 2002, Large deflections of cantilever beams of non-linear elastic material under a combined loading, International Journal of Non-Linear Mechanics 37:439-443.
[2] Banerjee A., Bhattacharya B., Mallik A.K., 2008, Large deflection of cantilever beams with geometric non-linearity analytical and numerical approaches, International Journal of Non-Linear Mechanics 43:366 –376.
[3] Chen L., 2010, An integral approach for large deflection cantilever beams, International Journal of Non-Linear Mechanics 45:301-305.
[4] Vega-Posada C., Areiza-Hurtado M., Aristizabal-Ochoa J., 2011, Large-deflection and post-buckling behavior of slender beam-columns with non-linear end-estraints, International Journal of Non-Linear Mechanics 46:79-95.
[5] Wang C. M., Lam K. Y., Hel X. Q., Chucheepsakul S., 1997, Large deflections of an end supported beam subjected to a point load, International Journal of Non-Linear Mechanics 32:63-72.
[6] Li L.P., Schulgasser K., Cederbaum G., 1998, Large deflection analysis of poroelastic beams, International Journal of Non-Linear Mechanics 33:1-14.
[7] Dado M., Al-Sadder S., 2005, A new technique for large deflection analysis of non-prismatic cantilever beams, Mechanics Research Communications 32:692-703.
[8] Su Y., Ma C., 2012, Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods, International Journal of Solids and Structures 49:1158-1176.
[9] Amabili M., 2008, Nonlinear Vibration and Stability of Shells and Plates, Cambridge University Press, New York.
[10] Wang C.M., Reddy J.N., Lee K.H., 2000, Shear Deformable Beams and Plates, Relationships with Classical Solutions, Elsevier, New York.
[11] Rao S.S., 2007, Vibration of Continuous Systems, John Wiley & Sons, New Jersey.
[12] Nayfeh A.H., 1993, Introduction to Perturbation Techniques, John Wiley, New York.