scholarly journals Zero and root loci of disturbed spring–mass systems

2014 ◽  
Vol 470 (2164) ◽  
pp. 20130751 ◽  
Author(s):  
Christophe Lecomte
Keyword(s):  
Complex Systems ◽  
Frequency Domain ◽  
Dynamic Responses ◽  
Local Disturbance ◽  
Broad Category ◽  
Analytical Properties ◽  
Discrete Values ◽  
Atomic Lattices ◽  
Elliptical Region

Models consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering.

Dynamic Response of 3D Surface/Embedded Rigid Foundations of Arbitrary Shapes on Multi-Layered Soils in Time Domain

2019 ◽  
Vol 19 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Zejun Han ◽  
Mi Zhou ◽  
Xiaowen Zhou ◽  
Linqing Yang
Keyword(s):  
Dynamic Response ◽  
Frequency Domain ◽  
Time Domain ◽  
Dynamic Stiffness ◽  
Dynamic Responses ◽  
Rigid Foundation ◽  
Layered Soils ◽  
Stiffness Matrices ◽  
The Time Domain ◽  
Arbitrary Shapes

Significant differences between the predicted and measured dynamic response of 3D rigid foundations on multi-layered soils in the time domain were identified due to the existence of uncertainties, which makes the issue a complicated one. In this study, a numerical method was developed to determine the dynamic responses of 3D rigid surfaces and embedded foundations of arbitrary shapes that are bonded to a multi-layered soil in the time domain. First, the dynamic stiffness matrices of the rigid foundations in the frequency domain are calculated via integral domain transformation. Secondly, a dynamic stiffness equation for rigid foundations in the time domain is established via the mixed variables formulation, which is based on the discrete dynamic stiffness matrices in the frequency domain. The proposed method can be applied to the treatment of systems with multiple degrees of freedom without losing the true information that concerns the coupling characteristics. Numerical examples are presented to demonstrate the accuracy of the proposed method for predicting the horizontal, vertical, rocking, and torsional vibrations. Further, a parametric study was carried out to provide insight into the dynamic behavior of the soil–foundation interaction (SFI) while considering soil nonhomogeneity. The results indicate that the elastic modulus of the soil has a significant impact on the dynamic responses of the rigid foundation. Finally, a numerical example of a rigid foundation resting on a six-layered, semi-infinite soil demonstrates that the proposed method can be used to deal with multi-layered media in the time domain in a relatively easy way.

scholarly journals Analysis and optimization of the effects of frictional and viscous dampers on dynamical systems

2019 ◽  
Vol 38 (2) ◽  
pp. 255-269
Author(s):  
Marlon Wesley Machado Cunico ◽  
Jennifer Desiree Medeiros Cavalheiro
Keyword(s):  
Frequency Domain ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Mechanical Systems ◽  
Static Friction ◽  
Coulomb Force ◽  
Dynamic Responses ◽  
Dynamical Response ◽  
Viscous Dampers ◽  
Three Degrees Of Freedom

Over the last several years, the complexity of products has been increasing in parallel to the product cost thus becoming one of main focal points for development. On the other hand, although several applications struggle to fix vibration problems, highlighting the importance of damper design, literature that compares the benefits and disadvantages between of dry-frictional, viscous, and Coulomb–viscous dampers is still rare. Owing to this, the main goal of this work is to present a study that compares the dynamical response of mechanical systems against several damper types. For this research, we analyzed the effects of three types of damper (viscous, Coulomb–viscous, and dry-frictional dampers) on two mechanical systems. The first system consists of a mass-spring-damper with one degree of freedom, while the second system is a rotational machine with three degrees of freedom. The sensibility analyses of each damper were also studied, where the viscosity, Coulomb force, static friction, and Stribeck decay were the variables. In this work, mechanical systems were studied in a forced vibration condition and analyzed in the time and frequency domain in addition to identifying the main transfer functions in the frequency domain. In this analysis, the displacement, receptance, and force reaction were considered to be the study responses. After analyzing the main effect of damper coefficients on the general dynamic responses, we performed an optimization study in order to evidence the optimal configurations of either majorly viscous or frictional damper. Lastly, we analyzed the main behavior of this optimized damper on three-degrees-of-freedom rotational dynamic system.

scholarly journals FRICTIONAL EFFECTS ON THE DYNAMIC RESPONSES OF A SINGLE-STAGE SPUR GEAR SYSTEMS

2021 ◽  
Vol 03 (02) ◽  
pp. 191-203
Author(s):  
Tareq Z HAMAD ◽  
Khaldoon F. BRETHEE ◽  
Ghalib R IBRAHIM
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Spur Gear ◽  
Industrial Applications ◽  
Single Stage ◽  
Dynamic Responses ◽  
Mechanical Equipment ◽  
Gear Mesh ◽  
The Time Domain ◽  
Complex Matter

Gears are paramout rotary mechanical equipment as its used in many industrial applications, for example in cars, industrial compressors and other applications. Therefore, monitoring the development of its condition is very important to prevent the aggravation of defects and stopping production. Friction between gears is causes of vibration but its representation in modeling and the analysis of its effect on the dynamic response is a very complex matter. In this study, the friction effect was studied by relying on equal load sharing formula and by relying on the sliding velocity direction of single-stage spur gears. The time domain was converted to the frequency domain, depending on the Fast Fourier Transform ( FFT ) method. Dynamic modeling results indicate that the friction between gears has a significant effect on the Vibration response of gearbox. This effect can be noticed by increasing the vibration amplitude in the time domain. It can also be seen by increasing the gear mesh frequency (GMF) amplitude and by increasing the amplitude of its harmonics in the frequency domain.

The Frequency Research of Fractional Order PIλDμ Controller

2013 ◽  
Vol 278-280 ◽  
pp. 1521-1524
Author(s):  
Hai Qun Wang ◽  
Ling Meng
Keyword(s):  
Complex Systems ◽  
Frequency Domain ◽  
Control Systems ◽  
Fractional Order ◽  
Industrial Production ◽  
Pid Controller ◽  
Time Analysis ◽  
Integer Order ◽  
Integral Order

Since most of the control systems in real industrial production are fractional，there is necessery to propose fractional order PIλDμ controller, which extend the traditional integer-order PID controller to fractional order, it has increased two free degree: Integral-order λ and differential-order μ, to more accurately control those complex systems. At the same time analysis the performance of fractional order PIλDμ controller in frequency domain. Especially,the two degrees’ effect to controller.

scholarly journals Dynamic Responses of the Metro Train’s Bogie Frames: Field Tests and Data Analysis

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xuhui He ◽  
Kehui Yu ◽  
Chenzhi Cai ◽  
Yunfeng Zou
Keyword(s):  
Frequency Domain ◽  
Dynamic Characteristics ◽  
Field Tests ◽  
Dynamic Responses ◽  
Discrete Wavelet ◽  
Bogie Frame ◽  
Time Frequency ◽  
Acceleration Signal ◽  
Track Irregularity ◽  
Acceleration Signals

This paper focuses on the dynamic characteristics of the metro train’s bogie frames based on the field test data. The acceleration signals of both motor bogie frame and trailer bogie frame of a standard B-type metro train were measured. Running tests on the Metro line 21 of Guangzhou (China) were carried out. The acquired acceleration signals of bogie frames were analyzed through several methods to identify the dynamic characteristics of the motor and trailer bogies in the time-frequency domain. The spectral analysis and time-frequency representations show that noise components exist in the high-frequency domain of the original signal, especially for the acceleration signal of the motor bogie frame. Then, the soft thresholding process and discrete wavelet transform decomposition process are conducted to obtain a denoised version of the original signals in the time-frequency domain. The vibration frequency domain and energy distribution of bogie frames under different train speeds are analyzed. The track irregularity wavelength of the metro line is calculated and analyzed based on the measured bogie frames’ acceleration signals. The dynamic characteristics of the metro train’s bogie frames in this paper can be adopted as a reference in the track diagnosis of the elevated metro line.

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