Aimed control of the frequency spectrum of eigenvibrations of elastic plates with a finite number of degrees of freedom of masses by superimposing additional constraints

As is known, for some elastic systems with a finite number of degrees of freedom of masses, for which the directions of motion of the masses are parallel and lie in the same plane, methods have been developed for creating additional constraints that purposefully change the spectrum of natural frequencies. In particular, theory and algorithm for the formation of aimed additional constraints have been developed for the rods, the introduction of each of which does not change any of the modes of natural vibrations, but only increases the value of only one frequency, without changing the values of the remaining frequencies. The distinctive paper is devoted to the method of forming a matrix of additional stiffness coefficients corresponding to such aimed constraint in the problem of natural vibrations of rods. This method can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of motion of the masses are parallel, but not lie in the same plane. In particular, such systems include plates. However, the algorithms for the formation of aimed additional constraints, developed for rods and based on the properties of rope polygons, cannot be used without significant changes in a similar problem for plates. The method for the formation of design constraint schemes that purposefully change the spectrum of frequencies of natural vibrations of elastic plates with a finite number of degrees of freedom of masses, will be considered in the next work. © 2021, ASV Publishing House. All rights reserved.