Формирование расчётных схем дополнительных связей, прицельно регулирующих спектр частот собственных колебаний упругих систем с конечным числом степеней свободы масс, у которых направления движения параллельны, но не лежат в одной плоскости часть 1: теор

For some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane (for example, rods), special methods have been developed for creating additional constraints, the introduction of each of which purposefully increases the value of only one natural frequency and does not change any from the natural modes. The method of forming a matrix of additional stiffness coefficients that characterize such targeted constraint in this problem can also be applied when solving a similar problem for elastic systems with a finite number of degrees of mass freedom, in which the directions of mass movement are parallel, but do not lie in the same plane (for example, plates). At the same time, for such systems, only the requirements for the design schemes of additional targeted constraints are formulated, and not the methods for their creation. The distinctive paper proposes an approach that allows researcher to create computational schemes for additional targeted constraints for such systems. A variant of the computational scheme, represented by a rod system with one degree of activity, is considered. Some special properties of such targeted constraints are revealed. When forming the computational scheme, the material consumption for creating a constraint is minimized, and design restrictions are taken into account. Particular attention is paid to the modification of the computational scheme of the constraint, when, during its formation, rods appear that “pass” through the original system.