Dynamic analysis of rectangular plates with stepped thickness subjected to moving loads including additional mass

This paper presents a simplified analytical method for rectangular plates with arbitrarily- and eccentrically-stepped thickness, such as building slabs, subjected to moving loads, including the effect of the additional mass. The discontinuous variation of the bending stiffness and mass of the plate due to the variation of the thickness can be expressed continuously by means of a characteristic function, which is defined as a Dirac function existing continuously in a prescribed region, as proposed by the author's previous work. Since the bending stiffness used here is given exactly by the actual bending stiffness at each point, a modification of the bending stiffness used in an equivalent plate analogy is unnecessary. It is clarified from numerical computations that the effect of the additional mass due to moving loads is significant for heavy-weight additional mass but is negligible for usual additional mass with 65 kg. Then, approximate but accurate solutions for a current plate subjected to stationary and moving loads are proposed by excluding the effect of additional mass. The numerical results obtained from the proposed theory for simply-supported and clamped plates with stepped thickness, excluding the effect of additional mass, show good agreement with results obtained from the finite element method using FEM code NASTRAN.