The combined motion of a rigid cylindrical tank filled with a fluid with a free surface and a moving platform attached to the tank by a spring is simulated mathematically. The nonlinear oscillations of this system caused by a harmonic force applied to the platform are studied Keywords: rigid cylindrical tank, fluid with free surface, moving platform, nonlinear oscillations, variational algorithmIntroduction. The technological advancement motivates solving the dynamic problem for structures partially filled with a fluid and subjected to different boundary conditions. Fluid-filled tanks on a moving platform are used as components of engineering structures in mechanical engineering, rocket technology, aircraft construction, fluid carriers and storages [1,13,14]. Various aspects of the behavior of such systems without elastic elements were addressed in [3-9, 13, 14, 16-20]. The influence of the elastic properties of structures contacting with a fluid are studied in [10-12, 15, 21] with, however, little attention given to the motion of a fluid with free surface. Mathematically, such problems are described by inhomogeneous equations (a coupled nonlinear system of ordinary differential equations and a nonlinear boundary-value problem with free boundary). The analytic solutions of such nonstationary nonlinear boundary-value problems have not yet been found. Therefore, approximate methods mainly based on variational algorithms and methods of nonlinear mechanics are used. Here we study the nonlinear coupled oscillations of a perfectly rigid cylindrical tank partially filled with a fluid and attached by a spring to a platform exerting harmonic loading on the tank.1. Problem Formulation. Subject of Analysis. Consider a perfectly rigid cylindrical tank partially filled with a fluid and attached by a spring to a platform moving over a horizontal plane. The platform-tank-fluid system is initially at rest. A harmonic force F A t = cos( ) w (w = 3.8, 4.0, 4.14, 4.3, 5.2, A = 662 N) is applied to the platform. A general view of this
