Analytical modelling of a large-scale dynamic testing facility

An analytical model, which aims at reproducing the response of a large-scale dynamic testing facility, that is a system composed of the specimen/shaking table/reaction-mass/airbags/dampers/soil is developed. The Lagrangian of the system is derived, under the assumption of large displacements and rotations. A set of four nonlinear differential equations is obtained and solved with numerical methods. Preliminary verifications of the derived model are carried out by reproducing both well-known results in the literature as well as those of a lumped model employed in the design of an existing dynamic testing facility. The case-study for validating the nonlinear equations of motion is the shaking table of the EUCENTRE Laboratory.