scholarly journals Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications

2014 ◽  
Vol 05 (19) ◽  
pp. 3018-3025 ◽  
Author(s):  
Safarov Ismail Ibrahimovich ◽  
Teshaev Muhsin Hudoyberdievich ◽  
Madjidov Maqsud
Keyword(s):  
Mechanical Systems ◽  
Natural Oscillations

Methods for Determinning Critical Values of Nonconservative Loads in Problems of Stability of Mechanical Systems

2019 ◽  
pp. 3-13 ◽  
Author(s):  
V.P. Radin ◽  
V.P. Chirkov ◽  
A.V. Shchugorev ◽  
V.N. Shchugorev
Keyword(s):  
Complex Function ◽  
Mechanical Systems ◽  
Critical Values ◽  
The Finite Element Method ◽  
Natural Oscillations ◽  
Flowing Liquid ◽  
Stability Problems ◽  
Distributed Parameters ◽  
The Stability ◽  
Systems With Distributed Parameters

Methods for determining critical values of nonconservative loads in stability problems of mechanical systems with distributed parameters are considered in this work. Based on a dynamic approach to stability problems, the method of direct integration of the linearized equation of perturbed motion is proposed, and the problem of determining critical loads is reduced to the problem of minimizing a complex function of several variables. As a second method, the method of decomposition of the solution of the equation of perturbed motion in the forms of natural oscillations is presented. The fundamentals of the application of the finite element method to the problems of stability under the action of non-conservative loads are also described. The methods are illustrated on classical problems: the stability of the cantilever rod under the action of potential and tracking forces and the stability of the pipeline section with flowing liquid. The accuracy and convergence of the latter two methods are analyzed depending on the number of members in the series and the number of finite elements.

scholarly journals Random oscillations of nonlinear systems with distributed Parameter

2021 ◽  
pp. 084-091
Author(s):  
Gavasheli Levan ◽  
Gavasheli Anri
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Mechanical Systems ◽  
Sharp Decrease ◽  
Damping Capacity ◽  
Pass Band ◽  
Natural Oscillations ◽  
Disturbing Force ◽  
Vibration Effect ◽  
Vibration Protection ◽  
The Creation

The article analyzes random vibrations of nonlinear mechanical systems with distributed parameters. The motion of such systems is described by nonlinear partial differential equations with corresponding initial and boundary conditions. In our case, the system as a whole is limited, so any motion can be considered as the sum of the natural oscillations of the system, i.e. in the form of an expansion of the boundary value problem in terms of own functions. The use of the theory of random processes in the calculation of mechanical systems is a prerequisite for the creation of sound design methods and the creation of effective vibration protection devices, these methods allow us to investigate dynamic processes, to determine the probabilistic characteristics of displacements of points of the system and their first two derivatives. In the work established these conditions are met, they provide effective vibration protection of the system under study with wide changes in the pass band of the frequencies of the random vibration effect, and the frequency of the disturbing force is much greater than the natural frequency of the system as a whole, in addition, with an increase in the damping capacity of the elastic-damping link of the system, the intensity of the random process significantly decreases, which in turn leads to a sharp decrease in the dynamic coefficient of the system.

Phase space of mechanical systems with a gauge group

1991 ◽  
Vol 161 (2) ◽  
pp. 13-75 ◽  
Author(s):  
Lev V. Prokhorov ◽  
Sergei V. Shabanov
Keyword(s):  
Phase Space ◽  
Gauge Group ◽  
Mechanical Systems
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