scholarly journals Non-linear vibrations of a beam with non-ideal boundary conditions and uncertainties – Modeling, numerical simulations and experiments

2018 ◽  
Vol 110 ◽  
pp. 165-179 ◽  
Author(s):  
T. Roncen ◽  
J.-J. Sinou ◽  
J-P. Lambelin
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Ideal Boundary ◽  
Non Linear ◽  
Linear Vibrations

scholarly journals Simulation of vibrations of a continuously elastic supported rod with varying boundary conditions under the action of a movable

2018 ◽  
Vol 196 ◽  
pp. 01053
Author(s):  
Sergey Gridnev ◽  
Yuriy Skalko ◽  
Ilya Ravodin ◽  
Victoria Yanaeva
Keyword(s):  
Boundary Conditions ◽  
Piecewise Linear ◽  
Moving Load ◽  
Continuous System ◽  
Basis Functions ◽  
Non Linear ◽  
Linear Vibrations ◽  
Floating Bridge ◽  
Model Equations ◽  
Elastically Supported

To simulate the non-linear vibrations of a floating bridge of a continuous system on separate floating supports with additional limiting supports at the ends with a moving load solves the most complicated problem which is the problem of describing the behavior of a span structure. A technique for simulating the vibration of an elastically supported deformable rod with limiting supports at the ends, which is a design scheme of a span structure, under the action of a moving force is developed. A computational algorithm for solving partial differential equations with varying boundary conditions is proposed, which includes boundary conditions in the model equations and does not require the subordination of basis functions to the boundary conditions. During the calculation, the basis remains constant. Piecewise linear basis functions are used to solve the differential equation. The technique is tested using a computational program Matlab, which is implemented when performing numerical studies of the behavior of the dynamic system as a function of the parameter changes. The developed technique is universal for studying the dynamics of a number of constructively non-linear systems.

scholarly journals Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 85
Author(s):  
Yasser Salah Hamed ◽  
Ali Kandil
Keyword(s):  
Time Delay ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Control Process ◽  
Control Force ◽  
Specific Level ◽  
Loop Control ◽  
Positive Displacement ◽  
Non Linear ◽  
Linear Vibrations

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

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