ABSTRACT
This chapter presents a methodology for reducing to a two-dimensional procedure the three-dimensional problem of vibration transmission from railways into buildings. The dynamic-stiffness matrix method is used to obtain a three-dimensional dynamic model of a two-dimensional structure by assembling columns and beams into repeating units. The chapter deals with a computationally efficient method for predicting the vibration response of large multi-storey structures to vibration excitation at foundation level. The dynamic-stiffness-matrix (DSM) method and an Eigenvalue procedure is used to assemble a structure of infinite length. This simplifies calculations with application to railway vibration because the source can be considered to be infinite in length. The DSM method, when applied to structures of infinite length, gives a computationally highly efficient means for calculating vibration transmission. The use of random process theory enables two-dimensional building models of infinite length to be used in conjunction with three-dimensional track and foundation models.
