Natural oscillations of mechanical systems and the spectral theory of self-adjoint operators

1997 ◽  
Vol 86 (3) ◽  
pp. 2664-2666
Author(s):  
V. M. Babich
Keyword(s):  
Spectral Theory ◽  
Mechanical Systems ◽  
Natural Oscillations ◽  
Adjoint Operators

scholarly journals Multiparameter spectral theory of singular differential operators

1988 ◽  
Vol 31 (1) ◽  
pp. 49-66 ◽  
Author(s):  
B. P. Rynne
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Spectral Theory ◽  
Unbounded Domain ◽  
Differential Operators ◽  
Separation Of Variables ◽  
Singular Case ◽  
Ordinary Differential Operators ◽  
Adjoint Operators ◽  
Unbounded Intervals

In this paper we investigate certain aspects of the multiparameter spectral theory of systems of singular ordinary differential operators. Such systems arise in various contexts. For instance, separation of variables for a partial differential equation on an unbounded domain leads to a multiparameter system of ordinary differential equations, some of which are defined on unbounded intervals. The spectral theory of systems of regular differential operators has been studied in many recent papers, e.g. [1, 3, 6, 9, 19, 21], but the singular case has not received so much attention. Some references for the singular case are [7, 8, 10, 13, 14, 18, 20], in addition general multiparameter spectral theory for self adjoint operators is discussed in [3, 9, 19].

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 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

Spectral Theory of Compact Self Adjoint Operators

2001 ◽  
pp. 105-129
Author(s):  
Israel Gohberg ◽  
Seymour Goldberg
Keyword(s):  
Spectral Theory ◽  
Adjoint Operators
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