On the Bolotin's reduced beam model versus various boundary conditions.

• Simplified beam equations with inertial terms and nonlinear curvatures are derived. • They can be treated as the first approximation to the Kirchhoff nonlinear equations. • Simplified equations versus boundary conditions are illustrated and discussed. • Nonlinear modes of beam vibrations are constructed for various boundary conditions. This paper is devoted to the construction of asymptotically correct simplified models of nonlinear beam equations for various boundary conditions. V.V. Bolotin mentioned that in some cases (e.g., if compressed load is near the buckling value), the so-called "nonlinear inertia" must be taken into account. The effect of nonlinear inertia on the oscillations of the clamped-free beam is investigated in many papers. Bolotin used some physical assumption and did not compare the order of nonlinear terms in original equations. Below we propose our method for deriving those, which we will named "Bolotin's equations". This approach is based on fractional analysis of original boundary value problems. [ABSTRACT FROM AUTHOR]