Thermal post-buckling &Â large amplitude free vibration analysis of Timoshenko beams: Simple closed-form solutions

In present work, thermal post-buckling and large amplitude free vibration (including the effect of rotary inertia) behavior of prismatic, shear flexible Timoshenko beams is expressed in the form of simple closed-form solutions by making use of the Rayleigh-Ritz method. The total cross-section rotation field (θ) variable of the shear flexible beam based on Timoshenko beam theory is expressed as function of lateral displacement field (w) variable of the beam by appropriately making use of the homogeneous form of governing static differential equations of the Timoshenko beam. Numerical accuracy of the proposed closed-form solutions obtained from the Rayleigh-Ritz method are compared to the available literature values which indicates simplicity, accuracy and robustness of the proposed approach.