Establishment of the original frequency of the continual section of the interreson research machine Rayleigh–Ritz method

: 5-15
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University
Hetman Petro Sahaidachny National Army Academy

Aim. Is to establish the first natural frequency of the continuum in the form of a rod (body with distributed parameters) of the interresonant vibrating machine. Method. The work is based on fundamental methods of mechanics, in particular the theory of mechanical oscillations. The natural frequencies and reactions in the supports of the continuum were found using the method of initial parameters, using the Krylov functions and the Rayleigh-Ritz method. Results. The paper considers a discrete model of an interresonant vibrating machine and establishes the partial frequency of its reactive mass, which is the initial parameter that the continuous section must provide. The frequency equation of the continuum section is formed using analytical methods. The value of its first natural frequency was found, which practically coincided with the partial frequency of the discrete model. The continuous section in the form of a rod was modeled in the software product SOLIDWORKS Simulation. Scientific novelty. For the first time, the most optimal scheme of fastening the continuous section in the form of an elastic rod mounted on two hinged supports, one of the ends of which is cantilevered, and the other is driven by an eccentric. For the first time using the Rayleigh-Ritz method, the natural frequency of the continuum section was analytically found, which is a determining parameter for the synthesis of interresonant discrete-continuum vibrating machines in which the partial frequency of the discrete model was matched with the value of the first natural frequency of the rod. Practical significance. The established analytical expressions will allow to form the effective concept of construction of an engineering technique of calculation of discrete-continuous vibrating technological equipment of various technological purpose, capable to realize effectively interresonant operating modes. Sufficient accuracy of the proposed analytical expressions contributes to their widespread use in practice.

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