Behavior of beams under transverse impact according to higher-order beam theory

Using Reissner’s principle, we formulated an equation of motion for a beam according to higher-order beam theory. We derived the Laplace transform of the equation and investigated wave-propagation behavior under transverse impact. In other words, we studied the effect of the nonlinear component of axial-warping, which cannot be determined by a conventional approach such as the Timoshenko beam theory. Specifically, we derived the transfer matrices for finite and semiinfinite beams. By choosing the appropriate state quantities, arrangement as a vector, and definition of sign convention, we were able to derive a perfect "reciprocal relation." In spite of the complicated Laplace inverse transform, we obtained an accurate and rapid solution by investigating appropriate branch points and poles and setting branch cuts. The extent of the nonlinear warping effect and its region of influence were also clearly demonstrated.