Precision control for eigen-frequency of elastic plates with finite number of mass degrees of freedom by using additional generalized connections and kinematic devices

Each generalized precision connection increases only one value of eigen-frequency prior to a specified value, without changing the remaining eigen-frequencies and all natural modes. Each generalized kinematic device reduces only one value of selected eigen-frequency prior to a specified value, without changing the remaining eigen-frequencies and all natural modes.

The methods of creating the additional connections and generalized kinematic devices that precisely change the eigen-frequency are developed for elastic systems with a finite number of degrees of freedom of masses, whose motion directions are parallel and lie in one plane. In particular, the theory and algorithm of formation of additional connections and generalized kinematic devices are developed for rods.

It is shown that the method of forming the matrix of additional stiffness coefficients describing the precision connection and a matrix of the additional inertial forces in the problem of eigen-frequency of rods, can be applied to solve a similar problem for elastic systems with a finite number of degrees of freedom of masses, whose directions of motion are parallel, but do not lie in one plane, in particular plates.

The developed algorithms for the formation of additional precision connections and generalized kinematic devices in rods based on the properties of string polygons cannot be used without significant changes in the similar problem for plates.

The development of connection schemes and kinematic devices that precisely change the eigen-frequency of elastic plates with the finite number of degrees of freedom of masses will be studies in future research.

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