Non-Linear Vibrations of a Floating Beam Under Harmonic Excitation

1994 ◽  
Vol 172 (5) ◽  
pp. 689-696
Author(s):  
F. Zhu
Keyword(s):  
Harmonic Excitation ◽  
Non Linear ◽  
Linear Vibrations

scholarly journals Application of a Novel Picard-Type Time-Integration Technique to the Linear and Non-Linear Dynamics of Mechanical Structures: An Exemplary Study

2021 ◽  
Vol 11 (9) ◽  
pp. 3742
Author(s):  
Evgenii Oborin ◽  
Hans Irschik
Keyword(s):  
Time Integration ◽  
Harmonic Excitation ◽  
Free Vibrations ◽  
Observation Time ◽  
Double Pendulum ◽  
Integration Technique ◽  
Linear Dynamics ◽  
Non Linear ◽  
Linear Vibrations ◽  
Numerical Time Integration

Applications of a novel time-integration technique to the non-linear and linear dynamics of mechanical structures are presented, using an extended Picard-type iteration. Explicit discrete-mechanics approximations are taken as starting guess for the iteration. Iteration and necessary symbolic operations need to be performed only before time-stepping procedure starts. In a previous investigation, we demonstrated computational advantages for free vibrations of a hanging pendulum. In the present paper, we first study forced non-linear vibrations of a tower-like mechanical structure, modeled by a standing pendulum with a non-linear restoring moment, due to harmonic excitation in primary parametric vertical resonance, and due to excitation recordings from a real earthquake. Our technique is realized in the symbolic computer languages Mathematica and Maple, and outcomes are successfully compared against the numerical time-integration tool NDSolve of Mathematica. For out method, substantially smaller computation times, smaller also than the real observation time, are found on a standard computer. We finally present the application to free vibrations of a hanging double pendulum. Excellent accuracy with respect to the exact solution is found for comparatively large observation periods.

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.

Non-linear vibrations of thick composite plates

1987 ◽  
Vol 115 (2) ◽  
pp. 367-371 ◽  
Author(s):  
G. Singh ◽  
Y.V.K. Sadasiva Rao
Keyword(s):  
Composite Plates ◽  
Non Linear ◽  
Linear Vibrations

Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

2016 ◽  
Vol 693 ◽  
pp. 318-323 ◽  
Author(s):  
Xin Liao ◽  
Jian Run Zhang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Joint Interface ◽  
Damping Factor ◽  
Viscous Damping ◽  
Bolted Joint ◽  
Energy Balancing ◽  
Stick Slip ◽  
Non Linear ◽  
Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

NON-LINEAR VIBRATIONS OF A SLIGHTLY CURVED BEAM RESTING ON A NON-LINEAR ELASTIC FOUNDATION

1998 ◽  
Vol 212 (2) ◽  
pp. 295-309 ◽  
Author(s):  
H.R. Öz ◽  
M. Pakdemirli ◽  
E. Özkaya ◽  
M. Yilmaz
Keyword(s):  
Elastic Foundation ◽  
Curved Beam ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Vibrations
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