scholarly journals Interaction between the elements characterizing the forced and parametric excitations

1998 ◽  
Vol 20 (1) ◽  
pp. 9-20
Author(s):  
Nguyen Van Dao
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Method ◽  
Special Interest ◽  
Digital Computer ◽  
Nonlinear Mechanics ◽  
First Order

In nonlinear systems, the first order of smallness terms of nonresonance forced and parametric excitations have no effect on the oscillation in the first an approximation. However, they do interact one with another in the second approximation.Using the asymptotic method of nonlinear mechanics [1] we obtain the equations for the amplitudes and phases of oscillation. The amplitude curves are drawn digital computer. The stationary oscillations and their stability are of special interest.

scholarly journals Interaction between the forced and parametric excitations with different degrees of smallness

1998 ◽  
Vol 20 (2) ◽  
pp. 11-17
Author(s):  
Nguyen Van Dao
Keyword(s):  
Nonlinear System ◽  
Parametric Excitation ◽  
Asymptotic Method ◽  
Special Interest ◽  
Second Order ◽  
First Order ◽  
First Approximation ◽  
Forced Excitation

The nonlinear system under consideration in this paper has a specification which can be stated as an interaction between the first order of smallness no resonance parametric excitation and the second order of smallness resonance forced excitation. In the first approximation these excitations have no effect. However, they do interact one with another in the second approximation.The equations for the amplitude and phase of oscillation are found by means of the asymptotic method. The stationary oscillations and their stability are of special interest.

Optimal systems and their group-invariant solutions to geodesic equations

2019 ◽  
Vol 16 (09) ◽  
pp. 1950135
Author(s):  
Bismah Jamil ◽  
Tooba Feroze ◽  
Muhammad Safdar
Keyword(s):  
Nonlinear Systems ◽  
Separation Of Variables ◽  
Noether Symmetries ◽  
Invariant Solutions ◽  
One Dimensional ◽  
Group Invariant ◽  
First Order ◽  
Geodesic Equations ◽  
Integrating Factor ◽  
Group Invariant Solutions

We find one-dimensional optimal systems of the Lie subalgebras of Noether symmetries associated with systems of geodesic equations. Further, we find invariants corresponding to each element of the derived optimal system. The derived invariants are shown to reduce systems of geodesic equations (nonlinear systems of quadratically semi-linear second-order ordinary differential equations (ODEs)) to nonlinear systems of first-order ODEs. The resulting systems are solved via known methods (e.g. separation of variables, integrating factor, etc.). In some cases, we provide exact solutions of these systems of geodesic equations.

scholarly journals Characteristic Model-Based Adaptive Control for a Class of MIMO Uncertain Nonaffine Nonlinear Systems Governed by Differential Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Duo-Qing Sun ◽  
Xiao-Ying Ma
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Linear Time ◽  
Uncertain System ◽  
Adaptive Controller ◽  
Characteristic Model ◽  
First Order ◽  
Position Tracking Control ◽  
The Stability ◽  
Nonaffine Nonlinear Systems

This paper addresses the difficulty of designing a controller for a class of multi-input multi-output uncertain nonaffine nonlinear systems governed by differential equations. We first derive the first-order characteristic model composed of a linear time-varying uncertain system for such nonaffine systems and then design an adaptive controller based on this first-order characteristic model for position tracking control. The designed controller exhibits a simple structure that can effectively avoid the controller singularity problem. The stability of the closed-loop system is analyzed using the Lyapunov method. The effectiveness of our proposed method is validated with a numerical example.

Finite Deflections and Snap-Through of High Circular Arches

1968 ◽  
Vol 35 (4) ◽  
pp. 763-769 ◽  
Author(s):  
J. V. Huddleston
Keyword(s):  
Boundary Value Problem ◽  
Cross Section ◽  
Digital Computer ◽  
Shooting Method ◽  
Point Boundary ◽  
Finite Deflections ◽  
Plane Shear ◽  
First Order ◽  
Buckling Behavior ◽  
First Order Differential Equations

The buckling behavior of two-hinged circular arches with any height-to-span ratio is studied by formulating the problem as a two-point boundary-value problem consisting of six nonlinear, first-order differential equations and appropriate boundry conditions. The theory is exact in the sense that no restrictions are placed on the size of the deflections or on the thickness of the arch. It is approximate in the sense that plane sections are assumed to remain plane, shear deformation is neglected, and the geometric properties of each cross section are assumed to remain constant during the deflection. The problem is solved on a digital computer by a shooting method that uses two levels of regula falsi and one of iteration. Selected results as plotted by the computer are shown and interpreted.

An asymptotic method applied to nonlinear systems with coupled deflection

1991 ◽  
Vol 328 (1) ◽  
pp. 71-83 ◽  
Author(s):  
L. Cveticanin ◽  
H. Yamakawa ◽  
O. Matsushita
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Method
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