Dynamic Response of Pavement Plates to the Positive and Negative Phases of the Friedlander Load

The dynamic response of pavement plates to a localized Friedlander load based on the three-parameter foundation model with the account of soil inertia is analyzed. The pavement plate is represented by a thin orthotropic plate of finite dimensions, which can rotate and transfer deformation along the contour. The subgrade is simulated with the Pasternak foundation model, including the inertia soil factor, the localized dynamic load is simulated with the Friedlander decay function allowing for the positive and negative phases; with the time distribution described by the Dirac function. The governing equation of the problem is solved with the modified Bolotin method for determining the natural frequencies and mode numbers of the system. The Mathematica program is used to define the natural frequencies of the system from the transcendental equations. Analysis results for several parameters related to the dynamic response of plates to a localized dynamic load, which includes both positive and negative phases, are presented. The impact of the Friedlander load with the negative phase added on the response of the pavement plate is numerically simulated.