scholarly journals Approximate solution of homotopic mapping for nonlinear vibration problem of transmission line

2011 ◽  
Vol 60 (6) ◽  
pp. 068802
Author(s):  
Wu Qin-Kuan
Keyword(s):  
Approximate Solution ◽  
Transmission Line ◽  
Nonlinear Vibration ◽  
Vibration Problem ◽  
Homotopic Mapping

Forced Vibration of Systems With Nonlinear, Nonsymmetrical Characteristics

1957 ◽  
Vol 24 (3) ◽  
pp. 435-439
Author(s):  
S. Mahalingam
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Nonlinear Vibration ◽  
Forced Vibration ◽  
Free Vibrations ◽  
Frequency Function ◽  
Vibration Absorber ◽  
Single Degree Of Freedom ◽  
Nonlinear Vibration Absorber ◽  
Single Degree

Abstract A one-term approximate solution is given for the amplitudes of steady forced vibration of a single-degree-of-freedom system with a nonlinear (nonsymmetrical) spring characteristic. The method is similar to that of Martienssen (1), but the construction uses a modified curve (or “frequency function”) in place of the actual spring characteristic, the curve being so chosen that it gives the correct frequency for free vibrations. The method is extended to deal with a nonlinear vibration absorber fitted to a linear system.

Solution of Nonlinear Vibration Problem of a Prestressed Membrane by Adomian Decomposition

AIAA Journal ◽  
2012 ◽  
Vol 50 (8) ◽  
pp. 1796-1800 ◽  
Author(s):  
Mohammed R. Sunny ◽  
Rakesh K. Kapania ◽  
Cornel Sultan
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Problem ◽  
Adomian Decomposition

scholarly journals Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

2022 ◽  
Vol 2160 (1) ◽  
pp. 012072
Author(s):  
Ziyu Guo ◽  
Jing Li ◽  
Shaotao Zhu ◽  
Hui Geng
Keyword(s):  
Approximate Solution ◽  
Nonlinear Vibration ◽  
Bifurcation Analysis ◽  
Dynamic Behaviour ◽  
Averaging Method ◽  
Singularity Theory ◽  
Nonlinear Oscillators ◽  
Dynamical Analysis ◽  
Dimensional System ◽  
Coupled Nonlinear Oscillators

Abstract The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging method and Krylov-Bogoliubov (KB) transformation presented by new notations of matrices. The bifurcation function is derived to investigate its dynamic behaviour by singularity theory. The results obtained provide guidance for the nonlinear vibration of symmetric coupled nonlinear oscillators model with clearance.

scholarly journals Nonlinear Dynamic Analysis of High-Voltage Overhead Transmission Lines

2018 ◽  
Vol 2018 ◽  
pp. 1-35 ◽  
Author(s):  
Meng Zhang ◽  
Guifeng Zhao ◽  
Jie Li
Keyword(s):  
Transmission Line ◽  
Nonlinear Vibration ◽  
Transmission Lines ◽  
Internal Resonance ◽  
Nonlinear Dynamic Analysis ◽  
Primary Resonance ◽  
Vibration Energy ◽  
Overhead Transmission Lines ◽  
Out Of Plane ◽  
Plane Direction

According to a generalized Hamilton’s principle, three-dimensional (3D) nonlinear vibration equations for overhead transmission lines that consider geometric nonlinearity are established. Based on the characteristics of an actual transmission line, the 3D equations are simplified to two-dimensional equations, and the nonlinear vibration behavior of transmission lines is investigated by combining theoretical analysis with numerical simulation. The results show that transmission lines have inherently nonlinear vibration characteristics. When in free vibration, a transmission line can undergo nonlinear internal resonance, even when its initial out-of-plane energy is relatively low; as its initial out-of-plane energy increases, the coupling of in-plane and out-of-plane vibration becomes stronger. When forced to vibrate by an external excitation, due to the combined action of internal and primary resonance, the vibration energy of a transmission line transfers from the out-of-plane direction to the in-plane direction that is not directly under the excitation, resulting in an increase in the dynamic tension and the displacement amplitude of the transmission line. Increasing damping can consume the vibration energy of a transmission line but cannot prevent the occurrence of internal resonance.

Composite right/left-handed transmission line with array of thermocouples for generating terahertz radiation

2020 ◽  
Vol 92 (2) ◽  
pp. 20502
Author(s):  
Behrokh Beiranvand ◽  
Alexander S. Sobolev ◽  
Anton V. Kudryashov
Keyword(s):  
Transmission Line ◽  
Terahertz Radiation ◽  
Transmission Lines ◽  
Software Package ◽  
Optical Pulses ◽  
Capacitively Coupled ◽  
Voltage Difference ◽  
Left Handed ◽  
Microwave Transmission ◽  
Commercial Software Package

We present a new concept of the thermoelectric structure that generates microwave and terahertz signals when illuminated by femtosecond optical pulses. The structure consists of a series array of capacitively coupled thermocouples. The array acts as a hybrid type microwave transmission line with anomalous dispersion and phase velocity higher than the velocity of light. This allows for adding up the responces from all the thermocouples in phase. The array is easily integrable with microstrip transmission lines. Dispersion curves obtained from both the lumped network scheme and numerical simulations are presented. The connection of the thermocouples is a composite right/left-handed transmission line, which can receive terahertz radiation from the transmission line ports. The radiation of the photon to the surface of the thermocouple structure causes a voltage difference with the bandwidth of terahertz. We examined a lossy composite right/left-handed transmission line to extract the circuit elements. The calculated properties of the design are extracted by employing commercial software package CST STUDIO SUITE.

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