Ushak T. Vibration and Resistance of Resilient Systems with Discrete and Continuous Distribution of Parameters

The thesis is dedicated to the creation of the method of free vibrations and Euler loss of resistance of complex resilient systems of variable rigidity and mass taking into account point factors (point masses, disks, point supports and others). For the effective realization of such investigations modern mathematical models in the form of quasi-differential equations of the fourth degree with coefficients and measures are used, i.e. the generalized derivatives of the functions of the limited variation. In the research such theory is adapted to the mentioned investigations. For the first time the method of discretisation is used in approximate calculations of fundamental frequencies of vibrations and critical forces, which allows to find basic numerical characteristics with the preassigned accuracy. The universal programs of calculation of vibration and resistance of the resilient systems with discrete and continuous distribution of parameters are created. A number of constructions for free vibrations and resistance are investigated, graphs of corresponding forms of vibrations and loss of resistance are built.