Lagrangianlized Nonlinear Dynamic Equation of Timoshenko Beam and Application

Abstract

Base on Hamilton's principle, under the continuity conditions of generalized coordinator, generalized force and the deformation, provide nonlinear deformation problem of Timoshenko beam’s Lagrangianlized basic elastic equation and its generalized boundary condition. Lagrangianlized basic elastic equation makes it possible to avoid indirect problem for the variation principle of continuum, which not only simplify the solving of direct problem but also stylize the solving process. The YUQING ancient bridge (in ShangHai) is taken as an example, calculating the kinetics characteristics and making damage diagnosis combined with the pulsation experimental result data.