Aimed Control of the Frequency Spectrum of Eigenvibrations of Elastic Plates With a Finite Number of Degrees of Mass Freedom By Introducing Additional Generalized Kinematic Devices

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, 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, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods 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 mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods 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 mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.