A novel dynamic soil-structure interaction model is developed for analysis for Euler–Bernoulli beam rests on a spatially random transversely isotropic viscoelastic foundation subjected to moving and oscillating loads. The dynamic equilibrium equation of beam-soil system is established using the extended Hamilton's principle, and the corresponding partial differential equations describing the displacement of beam and soil and boundary conditions are further obtained by the variational principles. These partial differential equations are discretized in spatial and time domains and solved by the finite difference (FD) method. After the differential equations of beam and soil are discretized in the spatial domain, the implicit iterative scheme is used to solve the equations in the time domain. The solving result shows the FD method is effective and convenient for solving the differential equations of beam-soil system. The spring foundation model adopted the modified Vlasov model, which is a two-parameter model considering the compression and shear of soil. The advantage of the present foundation model is avoided estimating input parameters of the modified Vlasov model using prior knowledge. The present solution is verified by publishing solution and equivalent three-dimensional FE analysis. The present model produced an accurate, faster, and effective displacement response. A few examples are carried out to analyze the parameter variation influence for beam on spatially random transversely isotropic viscoelastic soil under moving loads.
Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads
