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

Abstract

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.