The dissertation deals with the research of new classes of problems of nonlinear oscillations of complex mechanical systems, the components of which are large moving masses of liquid and reservoirs, which perform the functions of liquid transport and storage under different types of parametric perturbation, external disturbance or control.
A generalization of the classical Faraday problem is done for the following mechanical problems 1) the tank moves vertically according to a given harmonic law and can perform horizontal motion due to transverse oscillations of the fluid (additional degree of freedom is added in the system, i.e., the potential of the tank motion in the horizontal plane); 2) the tank moves vertically according to the given harmonic law and can carry out angular oscillations about the center of masses of system (additional degree of freedom is added in the system, i.e., the potential of angular motion of the tank); 3) the tank moves vertically, but not according to a given harmonic law, but under the action of a harmonic force; 4) the tank moves vertically under the action of a harmonic force and can perform horizontal motion; 5) the tank moves vertically under the action of harmonic force and can perform angular oscillations about the center of mass of the system. For the above-mentioned generalizations of the Faraday problem, domains of stability and instability are constructed, and a qualitative and spectral analysis of the oscillations of the free surface of the liquid and the reservoir is performed. It is established that dynamic processes in the system are developed as a set of parametric resonance and forced oscillations. Under the presence of additional degrees of freedom in the generalized Faraday problem the system can enter a nonlinear mode of oscillations for any frequency.
Algorithms of motion’s control of reservoir with liquid with a free surface is constructed and tested (calculation of the active external force applied to the tank), which will provide the tank motion according to a given law (prescribed motion) under the presence of constant perturbations, i.e., oscillations of the free surface of the liquid. Based on the linear model in perturbations (deviations of displacements and velocities from the program values) on the basis of modal control methods, reference model and minimization of the quadratic quality functional, feedback control algorithms are built. Feedback control based on a linear system in perturbations can be used to provide «comfortable» tank movements, without large perturbations of the free surface of the liquid. or control problems under the presence of large perturbations of the free surface of the liquid, control algorithms are constructed on the basis of compensation of the main vector of fluid pressure forces on the tank walls and the variational principle of least Gaussian coercion. It is shown that both approaches provide acceptable for practice accuracy of program motion for any high-intensity loads on the system, in addition, the control algorithm based on the Gaussian variation principle allows the minimization of energy costs for control.
The conditions and specific features of the oscillations reaching the free surface of a liquid under the action of an external force at a steady state in the absence and presence of the generalized dissipation or capillarity are studied. The research was performed for different frequency ranges of excitations of the system motion. In the absence of surface tension and dissipative forces, the steady state oscillations of the free surface of the liquid in the classical sense do not occur, the oscillations are non-stationary. Only at with the growth of the generalized dissipation in the liquid the system reaching of the steady mode is observed. It is also established that the presence of surface tension forces provides a faster output of the system to the resonant mode, but the presence of surface tension forces along the contact contour "softens" the resonance by increasing the energy contribution of axisymmetric oscillations.
