Nonlinear Oscillations of an Autoparametrical System With Two Coupled Pendulums

2007 ◽  
Author(s):  
Danuta Sado
Keyword(s):  
Nonlinear Oscillations ◽  
Type System ◽  
Vertical Direction ◽  
Free Vibrations ◽  
System Response ◽  
Main Body ◽  
Bifurcation Diagrams ◽  
Damping Force ◽  
Internal Resonances ◽  
Non Linear

The nonlinear dynamics of a three degree of freedom autoparametrical vibration system with two coupled pendulums in the neighborhood internal and external resonances is presented in this work. It was assumed that the main body is suspended by an element characterized by non-linear elasticity and non-linear damping force and is excited harmonicaly in the vertical direction. The two connected by spring pendulums characterized are mounted to the main body. It is assumed, that the motion of the pendulums are damped by nonlinear resistive forces. Solutions for the system response are presented for specific values of the uncoupled normal frequency ratios and the energy transfer between modes of vibrations is observed. Curves of internal resonances for free vibrations and external resonances for exciting force are shown. In this type system one mode of vibration may excite or damp another one, and except different kinds of periodic vibration there may also appear chaotic vibration. Various techniques, including chaos techniques such as bifurcation diagrams and: time histories, phase plane portraits, power spectral densities, Poincare` maps and exponents of Lyapunov, are used in the identification of the responses. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits. The results show that the system can exhibit various types of motion, from periodic to quasi-periodic to chaotic, and is sensitive to small changes of the system parameters.

The Periodic and Chaotic Vibration of Dynamical System With Elastic Pendulum

2006 ◽  
Author(s):  
Danuta Sado
Keyword(s):  
Linear Elasticity ◽  
Vertical Direction ◽  
System Response ◽  
Main Body ◽  
Bifurcation Diagrams ◽  
Damping Force ◽  
Chaotic Vibration ◽  
Non Linear ◽  
Linear Damping ◽  
Elastic Pendulum

The nonlinear damping effect on response of coupled three degree-of-freedom autoparametric vibration system with elastic pendulum attached to the main mass is investigated numerically. It was assumed that the main body is suspended by an element characterized by non-linear elasticity and non-linear damping force and is excited harmonically in the vertical direction. The elastic pendulum characterized also by -linear elasticity and non-linear damping. Solutions for the system response are presented for specific values of the uncoupled normal frequency ratios and the energy transfer between modes of vibrations is observed. Curves of internal resonances for free vibrations and external resonances for exciting force are shown. In this type system one mode of vibration may excite or damp another one, and except different kinds of periodic vibration there may also appear chaotic vibration. Various techniques, including chaos techniques such as bifurcation diagrams and: time histories, phase plane portraits, power spectral densities, Poincare` maps and exponents of Lyapunov, are used in the identification of the responses. These bifurcation diagrams show many sudden qualitative changes, that is, many bifurcations in the chaotic attractor as well as in the periodic orbits. The results show that the system can exhibit various types of motion, from periodic to quasi-periodic to chaotic, and is sensitive to small changes of the system parameters.

NON-LINEAR VIBRATION ABSORBERS USING HIGHER ORDER INTERNAL RESONANCES

2000 ◽  
Vol 234 (5) ◽  
pp. 799-817 ◽  
Author(s):  
P.FRANK PAI ◽  
BERND ROMMEL ◽  
MARK J. SCHULZ
Keyword(s):  
Higher Order ◽  
Vibration Absorbers ◽  
Linear Vibration ◽  
Internal Resonances ◽  
Non Linear

Dynamic Model and Simulation of Flag Vibrations Modeled as a Membrane

2014 ◽  
Author(s):  
Gary Frey ◽  
Ben Carmichael ◽  
Joshua Kavanaugh ◽  
S. Nima Mahmoodi
Keyword(s):  
Constant Velocity ◽  
Cross Flow ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Mode Shapes ◽  
System Response ◽  
Wind Flow ◽  
Pressure Function ◽  
Model And Simulation ◽  
Reasonable Model

A flag is modeled as a membrane to investigate the two-dimensional characteristics of the vibration response to an uniform wind flow. Both the affecting tension and pressure functions for the wind flow with constant velocity are introduced and utilized in the modeling. In this case, the tension is caused by the weight of the flag. The pressure function is a function describing the pressure variations caused on the flag when in uniform flow. The pressure function is found by assuming that the air flow is relatively slow and that the flag is wide enough to minimize cross flow at the boundaries. An analysis of the downstream motion of the flag is necessary as well. Hamilton’s principle is employed to derive the partial differential equation of motion. The flag is oriented in the vertical direction to neglect the effect of the flag’s weight on the system’s response. Galerkin’s method is used to solve for the first four mode shapes of the system, and the system response is numerically solved. Simulations reveal a very reasonable model when the flag is modeled as a membrane.

The Analysis of Automotive Door Seal Energy Consumption

2011 ◽  
Vol 80-81 ◽  
pp. 714-718
Author(s):  
Yun Kai Gao ◽  
Da Wei Gao
Keyword(s):  
Energy Consumption ◽  
Elastic Force ◽  
Bernoulli Equation ◽  
Analysis Model ◽  
Damping Force ◽  
Total Energy Consumption ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Damping ◽  
Simplified Analysis

The seal deformation of automotive door is caused by the door compression forces, including non-linear elastic force and non-linear damping force. The working principles of them are analyzed and a new simplified analysis model is built. Based on the Bernoulli equation and the law of conservation of mass, the mathematical models are established to calculate energy consumption of the seal system. According to the analysis results, the energy consumption of non-linear elastic force and non-linear damping force are respectively 84% and 16% of the total energy consumption of the seal system. At last, the calculation data is compared with the test data and the error is less than 5%, so the calculation method proposed in this paper is observed to be accurate.

Analysis of Free Nonlinear Vibration Behavior for Curved Embedded Carbon Nanotubes on Elastic Foundation

2010 ◽  
Author(s):  
M. Rezaee ◽  
H. Fekrmandi
Keyword(s):  
Carbon Nanotubes ◽  
Dynamic Behavior ◽  
Continuum Mechanics ◽  
Nonlinear Term ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
System Response ◽  
Response Curves ◽  
Vibration Behavior ◽  
The Continuum

Carbon nanotubes (CNTs) are expected to have significant impact on several emerging nanoelectromechanical (NEMS) applications. Vigorous understanding of the dynamic behavior of CNTs is essential for designing novel nanodevices. Recent literature show an increased utilization of models based on elastic continuum mechanics theories for studying the vibration behavior of CNTs. The importance of the continuum models stems from two points; (i) continuum simulations consume much less computational effort than the molecular dynamics simulations, and (ii) predicting nanostructures behavior through continuum simulation is much cheaper than studying their behavior through experimental verification. In numerous recent papers, CNTs were assumed to behave as perfectly straight beams or straight cylindrical shells. However, images taken by transmission electron microscopes for CNTs show that these tiny structures are not usually straight, but rather have certain degree of curvature or waviness along the nanotubes length. The curved morphology is due to process-induced waviness during manufacturing processes, in addition to mechanical properties such as low bending stiffness and large aspect ratio. In this study the free nonlinear oscillations of wavy embedded multi-wall carbon nanotubes (MWCNTs) are investigated. The problem is formulated on the basis of the continuum mechanics theory and the waviness of the MWCNTs is modeled as a sinusoidal curve. The governing equation of motion is derived by using the Hamilton’s principle. The Galerkin approach was utilized to reduce the equation of motion to a second order nonlinear differential equation which involves a quadratic nonlinear term due to the curved geometry of the beam, and a cubic nonlinear term due to the stretching effect. The system response has been obtained using the incremental harmonic balanced method (IHBM). Using this method, the iterative relations describing the interaction between the amplitude and the frequency for the single-wall nanotube and double-wall nanotube are obtained. Also, the influence of the waviness, elastic medium and van der Waals forces on frequency-response curves is researched. Results present some useful information to analyze CNT’s nonlinear dynamic behavior.

The investigation of broad-absorbing tetrabenzocorrolazine dye-based black matrix of low dielectric constant

2020 ◽  
Vol 24 (10) ◽  
pp. 1198-1207
Author(s):  
Jun Choi
Keyword(s):  
Dielectric Constant ◽  
Thin Film Transistor ◽  
Vertical Direction ◽  
Critical Factor ◽  
Color Filter ◽  
Low Dielectric Constant ◽  
Main Body ◽  
Color Strength ◽  
Low Dielectric ◽  
Perylene Dye

Tetrabenzocorrolazine dyes with high color strength and broad absorbance derived from a phthalocyanine moiety were designed and synthesized for a color filter on an array-mode black matrix of low dielectric constant. The prepared tetrabenzocorrolazine dyes focused the absorbance of phthalocyanine further into the visible light range so that the color was considerably closer to black, while making it easier to introduce an axial substituent in the vertical direction to the dye main body, thereby markedly improving its solubility in industrial solvents. Upon mixing with a perylene dye of 450-550 nm absorbance and a thermosetting resin composition, dye-based black matrix films with high optical density values, associated with superior light shielding capability, were fabricated. The prepared black matrix films not only ensured thermal resistance by allowing easy intermolecular cohesion but also served as an insulating membrane that did not interfere with the thin film transistor electric signals, exhibiting a value of 3-5 when dielectricity was measured as the most critical factor for the color filter on array mode display panels.

Stochastic Resonance in Strongly Coupled Duffing and Van der pol Oscillators Under Trichotomous Noise and Bearing Fault Diagnosis

2019 ◽  
Vol 19 (03) ◽  
pp. 2050023
Author(s):  
Gang Zhang ◽  
Xia Wu ◽  
Tianqi Zhang
Keyword(s):  
Stochastic Resonance ◽  
Coupling Coefficient ◽  
Damping Coefficient ◽  
System Response ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
Strongly Coupled ◽  
Force Coupling ◽  
Trichotomous Noise

Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

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