Dynamic Stability Analysis of Bi-Directional Functionally Graded Beam with Various Shear Deformation Theories Under Harmonic Excitation and Thermal Environment

In this article, dynamic stability analysis of bi-directional functionally graded materials (BDFGMs) beam rested on visco-Pasternak foundation under harmonic excitation is studied. Also, BDFGMs beam is subjected to a transversely uniformly distributed temperature rising and it is assumed that the material properties to be temperature-dependent. According to the exponential and power law distributions, thermo-mechanical properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions. Based on various shear deformation theories (e.g. Euler-Bernoulli, Timoshenko, third order shear deformation and sinusoidal shear deformation theories), the stability equations of BDFGMs beam is derived by applying the Hamilton's principle. The generalized differential quadrature method (GDQM) in conjunction with the Bolotin method is utilized to solve the differential stability equations under SS, SC and CC boundary conditions. To validate the present analysis, a comparison study is carried out with the results found in the literature and a good agreement is observed compared to the reported results. Finally, numerical results are presented to study the influences of the gradient index, length-to-thickness ratio, temperature rise and foundation parameters on the dynamic stability region of BDFGMs beam. The results of presented paper can be used to the optimal design and assessment of the structural failure.