Analysis of Vibrating Natural Frequency of Pressure Pipeline

2011 ◽  
Vol 421 ◽  
pp. 98-101
Author(s):  
Ting Yue Hao
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Flow ◽  
Physical Parameters ◽  
Beam Model ◽  
Instability Condition ◽  
Coupling Vibration ◽  
Critical Flow Velocity ◽  
Pressure Pipeline ◽  
The Mathematical Model

The pressure pipeline is simplified as the beam model with two simple supported ends. The mathematical model is established, considering influence of the fluid-solid coupling vibration. Then the critical flow velocity is obtained by calculation and solving. By analyzing the practical numerical example，the influence of physical parameters on the first three-order natural frequency is discussed. Using Matlab software for programming, the instability condition of pressure pipeline is obtained, which is consistent with the result of numerical calculation.

Simplified Adaptive Nonlinear Robust Controller for Linearized Pantagraph-Type Manipulator

1995 ◽  
Vol 7 (3) ◽  
pp. 242-249 ◽  
Author(s):  
Kiyotaka Izumi ◽  
◽  
Keigo Watanabe ◽  
Masatoshi Nakamura ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Physical Parameters ◽  
Additional Mass ◽  
Robust Controller ◽  
End Effector ◽  
Linear Controller ◽  
The Mathematical Model ◽  
Nonlinear Robust

If physical parameters are adjusted suitably in the pantagraph-type manipulator, the mathematical model becomes linear so that we can apply a linear controller. However, when the manipulator has an additional mass as an end-effector, the linear controller does not work well because the resultant model becomes nonlinear. In this paper, we propose a simplified adaptive nonlinear robust controller which we can apply to the manipulator, irrespective of the system linearity or nonlinearity. The effectiveness of the controller is illustrated by some simulations.

Vibration Analysis of a Vertical Roller Mill: Modeling and Validation

2014 ◽  
Author(s):  
Engin H. Çopur ◽  
Metin U. Salamci ◽  
Selahattin Gülbeyaz
Keyword(s):  
Mathematical Model ◽  
Vibration Analysis ◽  
Compressive Force ◽  
Vibration Characteristics ◽  
Physical Parameters ◽  
Roller Mill ◽  
Vibration Tests ◽  
Working Parameters ◽  
The Mathematical Model ◽  
Vertical Roller

In this paper, vibration characteristics of a Vertical Roller Mill (VRM) are studied by using physical parameters of an operating VRM. The mathematical model is derived and simulated for a set of working parameters. Mechanical properties of the grinding material and the physical properties of the mechanical construction are used in the vibration model in order to obtain more realistic results. Simulation results are presented which give critical frequencies of the VRM. The effects of the hydraulic compressive force to the vibration characteristics are investigated. The effects of the material feeding rate (which affects the mineral thickness to be grinded) to the vibration characteristics are also simulated. In order to validate the mathematical model, a set of experimental vibration tests are performed on the VRM. Vibrations are measured during the run-down procedure of the VRM in order to determine natural frequencies of the mill as well as excitation frequencies of the system. The measurements showed the validity of the proposed mathematical model for the vibration analysis of the VRM.

Study on Dynamic Characteristics and Dynamic Response of Woodworking Four-Side Planer

2011 ◽  
Vol 291-294 ◽  
pp. 1970-1976
Author(s):  
Shao Qun Zhang ◽  
Jun Hua ◽  
Wei Xu
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Dynamic Characteristics ◽  
Feed Rate ◽  
Reference Data ◽  
Damping Ratio ◽  
Vibration Test ◽  
Vibration Magnitude ◽  
The Mathematical Model

Through woodworking four-side planer vibration test, this article studiesits dynamic characteristics and dynamic response to identify the vibration magnitudes law of each feed roll shafts of the four-side feed beam; then finds the natural frequency and damping ratio of the feed beam and lathe bed; obtains the mathematical model of feed roll shaft vibration magnitude changing with the feed rate U under different process thicknesses. The analysis of feeding quantity and the rationality of lathe bed from the perspective of vibration design supplies the designs and operation staff with reference data.

AN ELASTICALLY SUPPORTED GEOMETRICALLY NONLINEAR SLENDER SYSTEM SUBJECTED TO A SPECIFIC LOAD IN RESPECT OF BIFURCATIONAL LOAD AND FREE VIBRATIONS

2011 ◽  
Vol 21 (10) ◽  
pp. 2983-2992 ◽  
Author(s):  
SEBASTIAN UZNY
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Characteristic Curve ◽  
Expansion Method ◽  
Free Vibrations ◽  
Geometrically Nonlinear ◽  
Internal Forces ◽  
Elastically Supported ◽  
The Mathematical Model

The formulation of and solution to the problem of stability and free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. The considered system was subjected to a follower force directed towards the positive pole (load formulated by L. Tomski). The boundary problem was formulated using Hamilton's principle and the straightforward expansion method. A series of numerical simulations were based on the mathematical model. The distribution of internal forces in the column's elements and the bifurcation load dependent on the system's parameters were determined for the tangent problem. In the case of free vibrations, the characteristic curve in the plane, load — natural frequency, was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The above research relied on modal analysis and the determination of the natural frequency of the system for the chosen values of an external load.

Thermal-Nonlocal Vibration and Instability of Single-Walled Carbon Nanotubes Conveying Fluid

2011 ◽  
Vol 27 (4) ◽  
pp. 567-573 ◽  
Author(s):  
T.-P. Chang
Keyword(s):  
Flow Velocity ◽  
Elastic Medium ◽  
Natural Frequency ◽  
Temperature Change ◽  
Nonlocal Parameter ◽  
Critical Flow ◽  
Critical Flow Velocity ◽  
Buckling Instability ◽  
Single Walled Carbon ◽  
Conveying Fluid

ABSTRACTAn elastic Bernoulli–Euler beam model is developed for thermal-mechanical vibration and buckling instability of a single-walled carbon nanotube (SWCNT) conveying fluid and resting on an elastic medium by using the theories of thermal elasticity mechanics and nonlocal elasticity. The differential quadrature method is adopted to obtain the numerical solutions to the model. The effects of temperature change, nonlocal parameter and elastic medium constant on the vibration frequency and buckling instability of SWCNT conveying fluid are investigated. It can be concluded that at low or room temperature, the first natural frequency and critical flow velocity for the SWCNT increase as the temperature change increases, on the contrary, while at high temperature the first natural frequency and critical flow velocity decrease with the increase of the temperature change. The first natural frequency for the SWCNT decreases as the nonlocal parameter increases, both the first natural frequency and critical flow velocity increase with the increase of the elastic medium constant.

The Mechanics of Spiral Springs and Its Application in Timekeeping

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Longhan Xie ◽  
Puihang Ko ◽  
Ruxu Du
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Parameter ◽  
Dynamic Deformation ◽  
Dynamic Performance ◽  
Spiral Spring ◽  
Simulation Results ◽  
Experimental Validations ◽  
The Mathematical Model ◽  
Castigliano’S Theorem

Spiral spring is widely used in mechanisms, such as mechanical watch movements and clocks where the spiral spring is used for timekeeping. According to literature, there are only a few studies on spiral springs. In this paper, the mechanics of spiral springs is analyzed in details, and its dynamic performance in mechanical watch movements is further studied to find out its natural frequency, which is the most critical parameter for mechanical watch movements. Based on Castigliano's theorem, the mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque is developed, and computer simulation with Matlab® is also conducted. Experimental validations are carried out, which confirm the simulation results. Experiments show that the analytical method in this paper can be used to guide and facilitate the design of spiral spring.

Multi-objective storage location allocation optimization and simulation analysis of automated warehouse based on multi-population genetic algorithm

2018 ◽  
Vol 26 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Yu-ling Jiao ◽  
Xiao-cui Xing ◽  
Peng Zhang ◽  
Liang-cheng Xu ◽  
Xin-Ran Liu
Keyword(s):  
Genetic Algorithm ◽  
Mathematical Model ◽  
Dynamic Simulation ◽  
Population Genetic ◽  
Physical Parameters ◽  
Location Allocation ◽  
Multi Objective ◽  
Storage Location ◽  
Population Genetic Algorithm ◽  
The Mathematical Model

Aiming at the requirement of working efficiency and security of automated warehouse and taking the operation time of outbound–inbound, the equivalent center of gravity of overall shelf and the degree of relative accumulation of related products as the multi-objective functions, the mathematical model is constructed for multi-objective storage location allocation optimization. According to the simple weighted genetic algorithm, it is easily prone to the problem of immature convergence when solving multi-objective programming problems. So, the multi-population genetic algorithm is proposed to solve the mathematical model of storage location allocation optimization. Combining with the experiment data of toy car assembly and automated warehouse, the results of the automated warehouse storage location allocation are obtained. FlexSim dynamic simulation model is established based on the storage location allocation solution, the physical parameters of automated warehouse and the experimental requirements plan of vehicle model assembly. The operation effect of the model and the utilization rate of the equipment are analyzed. The result of multi-population genetic algorithm is more reasonable and effective. It is proved that the result of multi-population genetic algorithm is superior to the result of simple weighted genetic algorithm, which provides an effective method for storage location allocation optimization and outbound–inbound dynamic simulation.

Mathematical model used for predicting arc-flash protective performance of fabrics based on physical parameters

2021 ◽  
pp. 004051752110226
Author(s):  
Wen Zhu ◽  
Hong Tang ◽  
Qilong Sun ◽  
Zhen Huang ◽  
Chengjiao Zhang
Keyword(s):  
Mathematical Model ◽  
Raw Materials ◽  
Principal Component ◽  
Thermomechanical Properties ◽  
Physical Parameters ◽  
Weave Structure ◽  
Arc Flash ◽  
Protective Fabrics ◽  
Protective Performance ◽  
The Mathematical Model

In this study, parameters that may affect the performance of arc-flash protective fabrics were systematically analyzed. Sixteen different commonly used fabrics with different configurations and grammage were produced and investigated, namely four raw materials with different configurations (93:0:5:2, 70:23:5:2, 46:47:5:2, and 23:70:5:2) and four with different grammage (180, 210, 240, and 270 g/m2). It was found that factors had different effects on the arc protective performance. Principal component analysis showed that the four plain weave fabrics of 180 g/m2 behaved differently compared with other samples, which was ascribed to the related differences in weave structure. In addition, a predicting mathematical model was developed based on the parameters that have the greatest influence on arc protective performance. The prediction parameters were not added to the structure, but replaced with physical parameters such as air permeability and thermomechanical properties. The adjusted R2 was 0.867, which demonstrated the rationality of using multiple linear regression to accurately predict arc protective performance. It was hypothesized that the construction of the mathematical model could contribute to the arc protective fabric evaluation and future researches in this field.

scholarly journals NUMERICAL METHOD OF VIBRATIONS RESEARCH IN LARGE FLEXIBLE SYSTEMS

2014 ◽  
pp. 52-59
Author(s):  
Olena Mul ◽  
Delfim Torres
Keyword(s):  
Mathematical Model ◽  
Communication Network ◽  
Numerical Method ◽  
Frequency Spectrum ◽  
Elastic System ◽  
Physical Parameters ◽  
Flexible Systems ◽  
The Real ◽  
Fundamental Systems ◽  
The Mathematical Model

The mathematical model of the real flexible elastic system is considered with the distributed and discrete parameters, which presents the equation at derivative parts with non-classical maximum terms. Complication of maximum terms makes impossible finding of exact analytical decision of such maximum task, in connection with what for researches the numerical method of the normal fundamental systems of decisions is used. Dependence of frequencies of possible vibrations is explored on different physical parameters of system. It is shown, that introduction to reverse communication network after speed with the defined values of the reverse communication coefficient allows controling the frequency spectrum in which excitation of vibrations are possible.

scholarly journals Measurement of low frequency mechanical vibrations based on an inverted magnetic pendulum

2019 ◽  
Vol 9 (5) ◽  
pp. 3480
Author(s):  
Susana V. Awad ◽  
Joaquin F Orozco ◽  
Fredy E Hoyos
Keyword(s):  
Mathematical Model ◽  
Friction Force ◽  
Low Frequency ◽  
Physical Parameters ◽  
Model Design ◽  
Frequency Meter ◽  
Adjustable Range ◽  
The Mathematical Model ◽  
Considerable Period ◽  
The Magnetic Field

<span>In this paper is presented the mathematical model, design and construction of a prototype of a  vibration frequency meter in an adjustable range of 2 Hz to 30 Hz; The experimental results and their analysis are also presented, making a comparative evaluation with the theoretical model. The device is based on the principle of resonance applied in an inverted magnetic pendulum whose natural frequency can be modified by variations of physical parameters. The oscillation of the pendulum is recorded detecting variations in the magnetic field using hall effect sensors; the data recorded with a microprocessor is analyzed and the results are simultaneously plotted in a computer interface. The data obtained were processed to be plotted in the frequency domain, facilitating its analysis. It was proved that the prototype can be used as a frequency meter and that the adjustable character of the device works according to the mathematical model. Finally, The effect of the friction force was studied, it was concluded that the friction force affects the measurement after a considerable period of time of oscillation, but not in the first moments.</span>

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