Heuristic Thermal Postbuckling and Large-Amplitude Vibration Formulations of Beams
A = area of cross section b = maximum central deflection or amplitude E = Young’s modulus I = area moment of inertia L = length of the column or beam PL = mechanical equivalent of the thermal buckling load PNL = mechanical equivalent of the thermal postbuckling load r = radius of gyration Ta = tension developed in the beam due to large deflections TL = buckling temperature TNL = postbuckling temperature u = axial displacement w = transverse displacement x = axial coordinate = coefficient of linear thermal expansion "x = axial strain L = thermal buckling load parameter ( PNLL=EI) NL = thermal postbuckling load parameter, PLL =EI Ta = axial tension parameter, TaL =EI !L = linear radian frequency !NL = nonlinear radian frequency