Open AccessTHE OSCILLATIONS OF ROD CONSTRUCTIONS WITH TAKING INTO ACCOUNT THE ENERGY DISSIPATION
Author(s) -
Сергій Іванович Трубачев,
Ольга МиколаЇвна Алексейчук
Publication year - 2014
Publication title -
mehanika giroskopičeskih sistem/mehanìka gìroskopìčnih sistem
Language(s) - English
Resource type - Journals
eISSN - 2519-2272
pISSN - 0203-3771
DOI - 10.20535/0203-377127201438211
Subject(s) - dissipation , vibration , mathematical analysis , normal mode , mathematics , nonlinear system , oscillation (cell signaling) , finite element method , logarithm , polynomial , physics , acoustics , genetics , quantum mechanics , biology , thermodynamics
The paper presents a solution of the problem of beam oscillation with the energy dissipation. In studying of the dissipation of the internal energy in the materials the one of the complicated problems is the problem when the material is acting by a variable load. If the frequency of the exciting loads has definite ratios with the eigenfrequency of oscillations, the level of dynamic loads is sharply increases. If the dependence of the logarithmic decrement of the amplitude at the free vibrations, it can be used to calculate the resonant vibrations. When we solving problems for rod constructions the greatest interest has the spectrum of the natural frequencies and corresponding mode shapes. It is proposed to use a two-node finite element in the case of plane bending vibrations of the rod. In this case, the nodal unknowns are deflections and turning angles the nodes. For the approximation of displacements we use a third-order polynomial. To find the spectrum eigenfrequencies and mode shapes is suggested to use a method of increasing stiffness, which is based on the minimization of functional of the Rayleigh type. The method coordinate wise descent is applied to solve the problem of minimizing the functional, which is one of the methods of nonlinear programming. We present numerical algorithm for solving the dynamics of rod structures.