The Natural Characteristics of Fluid Conveying Pipe under Different Supporting Conditions

2013 ◽  
Vol 372 ◽  
pp. 612-619 ◽  
Author(s):  
Ri Dong Bao
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Fluid Pressure ◽  
Vertical Vibration ◽  
Elastic Coefficient ◽  
Pipe Section ◽  
Mode Function ◽  
Constrained Coefficients ◽  
Natural Characteristics

The natural characteristics of fluid conveying pipe with its ends under different supporting conditions were investigated. The expression of vertical vibration mode-function of pipe beam was derived from the boundary conditions of similarly supported beam. The effect of different supporting elastic coefficient, fluid pressure, flowrate, and axial force of pipe section on its natural characteristics was calculated and analyzed based on the eigenequation of motion. The numerical computation results showed that its natural frequency was proportional to elastic supporting coefficient and axially pressed force of pipe section, but was proportional conversely to fluid flowrate, fluid pressure and axially sectional drawn force of pipe. The natural frequency of different modes can be coupled with each other, the primarily mode and secondly mode would change either. In order to improve the natural frequency of fluid conveying pipe, the elastically constrained coefficients should be extended and the axially pressed force of pipe section should be avoided.

Study on Hydromechanics with Critical Instability Flowrate of Two Ends Supported Pipe Conveying Fluid

2013 ◽  
Vol 387 ◽  
pp. 77-84
Author(s):  
Ri Dong Bao
Keyword(s):  
Boundary Conditions ◽  
Vibration Mode ◽  
Fluid Pressure ◽  
Engineering Application ◽  
Vertical Vibration ◽  
Pipe Conveying Fluid ◽  
Pipe Section ◽  
Mode Function ◽  
Critical Instability ◽  
Conveying Fluid

The expression of vertical vibration mode-function of fluid conveying pipe supported elastically on two ends was derived from the boundary conditions of similarly supported beam. The dynamic stability of pipe conveying fluid with the same supporting conditions was invesigated and the expression of its critical instability flowrate was obtained. The effects of fluid pressure and axial force of pipe section on critical instability flowrate were calculated and analyzed based on the eigenequation. The numerical results showed that the critical instability flowrate were proportional to axial drawn force, but proportional conversely to fluid pressure and axial pressed force of pipe section. The critical instability flowrate of fluid conveying pipe varied greatly with its supporting conditions. In order to improve its value at engineering application, the axial pressed force of pipe section should be avoided.

The Influence of Supported and Restrained Elastic Coefficient on the Stability of Fluid Conveying Pipe

2012 ◽  
Vol 479-481 ◽  
pp. 292-298 ◽  
Author(s):  
Ri Dong Bao
Keyword(s):  
Flow Velocity ◽  
Vibration Mode ◽  
Fluid Pressure ◽  
Vertical Vibration ◽  
Piping System ◽  
Elastic Coefficient ◽  
Dynamical Simulation ◽  
Mode Function ◽  
Linear Spring ◽  
The Stability

The dynamic stability of fluid conveying piping system under different supporting conditions, considering the fluid structures interaction, was investigated. The expression of vertical vibration mode-function of commonly supported piping system was derived from its boundary condition of the similar beam. Firstly, considering the effects of Kelvin-Voigt visco-elastic coefficient of pipe, fluid pressure and axially sectional force of pipe, the motion equation of the piping system was established. Secondly, the equation was discretized by Galerkin method according with its similar supporting conditions of beam. Thirdly, the expression of critically instable flow velocity was obtained. Lastly, the stability of the piping system was analyzed by using the dynamical simulation methods. The numerical results showed that the critically instable flow velocity is proportional conversely to supported linear spring coefficients, but is proportional to restrained torsion spring coefficients.

Vibration Analysis of the Load on Helicopter Swashplate Rod

2012 ◽  
Vol 226-228 ◽  
pp. 119-123
Author(s):  
Fang Wang ◽  
Ming Chen
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Vibration Mode ◽  
Rotor Speed ◽  
Helicopter Control ◽  
Flight Experiment ◽  
Control Precision ◽  
Mode Function

The swashplate rod is a key component of helicopter control system. The vibration environment of helicopter is quite complex. The natural frequency of the swashplate rod is generally low. So resonance occurs easily. Resonance could reduce control precision or even damage the whole control system. Established dynamic and mathematical model of swashplate rod. Analyzed the vibration characteristics. Obtained the natural frequency and vibration mode function of the rod. In the compression, tension and free state, the natural frequency of the rod is basically the same. Made flight experiment with a developing helicopter as object. Measured the load of the swashplate rod in flight conditions. Make Fourier analysis to the load. Obtained the frequencies of the load on the rod. The frequencies coincide with 1 and 2 times of the rotor speed.

scholarly journals Fluid-Structure Interaction Vibration of Hydraulic Pipe System

2011 ◽  
Vol 2-3 ◽  
pp. 822-827
Author(s):  
Jun Zhe Lin ◽  
Lei Qin ◽  
En Tao Zhou ◽  
Bang Chun Wen
Keyword(s):  
Natural Frequency ◽  
Fluid Pressure ◽  
Driving Frequency ◽  
Mass Ratio ◽  
Elastic Coefficient ◽  
Vibration Equation ◽  
Pipe System ◽  
Structure Interaction ◽  
Dimensionless Equation ◽  
Aero Engine

Based on Newton method, the nonlinear differential equation of FSI vibration of hydraulic pipe on aero-engine has been established. The equation include visco-elastic coefficient, and the dimensionless equation was got. The influence of mass ratio, velocity of fluid and axial force on natural frequency of the pipe was researched by analyzing the FSI vibration equation of the pipe. The influence of fluid pressure on natural frequency was verified by experiment. And vibration response of the pipe was obtained by experiment at different driving frequency. The conclusion of the experiment was consistent with the result of the theory.

scholarly journals The Influence of Shaft’s Bending on the Coupling Vibration of a Flexible Blade-Rotor System

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Chao-feng Li ◽  
Hou-xin She ◽  
Wen Liu ◽  
Bang-chun Wen
Keyword(s):  
Natural Frequency ◽  
Critical Speed ◽  
Vibration Mode ◽  
Rotor System ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Coupling Vibration ◽  
Mode Function ◽  
Coupling Mode ◽  
Supporting Condition

The influence of shaft bending on the coupling vibration of rotor-blades system is nonignorable. Therefore, this paper analyzed the influence of shaft bending on the coupling vibration of rotor-blades system. The vibration mode function of shaft under elastic supporting condition was also derived to ensure accuracy of the model as well. The influence of the number of blades, the position of disk, and the support stiffness of shaft on critical speed of system was analyzed. The numerical results show that there were two categories of coupling mode shapes which belong to a set where the blade’s first two modes predominate in the system: shaft-blade (SB) mode and interblade (BB) mode due to the coupling between blade and shaft. The BB mode was of repeated frequencies of (Nb-2) multiplicity for number blades, and the SB mode was of repeated frequencies of (2) multiplicity for number blades. What is more, with the increase of the number of blades, natural frequency of rotor was decreasing linearly, that of BB mode was constant, and that of SB mode was increasing linearly. Natural frequency of BB mode was not affected while that of rotor and SB mode was affected (changed symmetrically with the center of shaft) by the position of disk. In the end, vibration characteristics of coupling mode shapes were analyzed.

scholarly journals Vibrations Analysis of Rectangular Plates with Clamped Corners

2018 ◽  
Vol 8 (1) ◽  
pp. 275-283
Author(s):  
Mohammad A. Gharaibeh ◽  
Amr M. Obeidat
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Mode Shape ◽  
Current Problem ◽  
Vibration Mode ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Fundamental Natural Frequency

AbstractThis paper discusses the fundamental natural frequency of a thin elastic rectangular, isotropic and orthotropic, plates with clamped corners. Rayleigh’s method was used to analytically calculate the plate lowest natural frequency. In this solution, the vibration mode shape was assumed in a form that certifies the displacement as well as the rotational boundary conditions of the current problem. Finally, this paper provides useful information for evaluating the natural frequency of a plate with fixed corners with different mass attachments configurations.

Modal Analysis of Circular Diamond Saw-Blade for Deep Sawing of Granite

2006 ◽  
Vol 315-316 ◽  
pp. 348-351 ◽  
Author(s):  
Yuan Li ◽  
Xi Peng Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Factors Influencing ◽  
Nature Frequency ◽  
Diamond Saw ◽  
Rotary Speed ◽  
Saw Blade ◽  
Natural Characteristics

In this paper, finite element method (FEM) was applied to analyze the natural characteristics of a diamond saw-blade for deep sawing of natural granite. The vibration mode and nature frequency of the saw-blade were theoretically studied by a commercial FEM software. The factors influencing the natural characteristics of the saw-blade were also discussed. It was found that the natural frequency of the saw-blade increases with its thickness, rotary speed and clamping ratio, but decreases with its diameter.

Differential Quadrature Method to Analyze Natural Characteristics of Buried Pipelines in Liquefaction Soil

2013 ◽  
Vol 765-767 ◽  
pp. 749-754
Author(s):  
Ri Dong Bao
Keyword(s):  
Natural Frequency ◽  
Differential Quadrature Method ◽  
Seismic Effect ◽  
Differential Quadrature ◽  
Theoretical Research ◽  
Quadrature Method ◽  
Buried Pipeline ◽  
Buried Pipelines ◽  
Elastic Coefficient ◽  
Natural Characteristics

On the basis of fluid-structure-interaction of the liquefaction soil, pipeline and the conveying fluid, in this paper, the differential vibration equations of the buried pipeline are deduced. The differential quadrature method (DQM) was tried to use to analyze the natural frequency of buried pipeline in liquefaction soil under the effect of flow velocity, fluid density, pressure in pipe, viscosity of pipe, axial force, elastic coefficient of the soil. Some preliminary conclusions concerning with the natural frequency of buried pipeline are also obtained. The theoretical research of the seismic effect on the pipeline in the liquefaction soil is presented.

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

Component Rearrangement on Printed Wiring Boards to Maximize the Fundamental Natural Frequency

1993 ◽  
Vol 115 (3) ◽  
pp. 312-321 ◽  
Author(s):  
Tien-Sheng Chang ◽  
E. B. Magrab
Keyword(s):  
Simulated Annealing ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Printed Wiring Board ◽  
Computationally Efficient ◽  
Additional Increase ◽  
Simulated Annealing Method ◽  
Fundamental Natural Frequency ◽  
Rearrangement Algorithm ◽  
Annealing Method

A methodology to attain the highest fundamental natural frequency of a printed wiring board by rearranging its components has been developed. A general two-dimensional rearrangement algorithm is developed by which the rearrangement of the component-lead-board (CLB) assemblies is performed automatically for any combination of equal size, unequal size, movable and immovable CLBs. This algorithm is also capable of incorporating two design restrictions: fixed (immovable) components and prohibited (non-swappable) areas. A highly computationally efficient objective function for the evaluation of the automatic rearrangement process is introduced, which is a linear function of the size of the individual CLBs that have been selected for each interchange. The simulated annealing method is adapted to solve the combinatorial rearrangement of the CLBs. Using 61 combinations of boundary conditions, equal and unequal sized CLBs, movable and immovable CLBs, various CLB groupings and sets of material properties, it is found that, when compared to the exact solution obtained by an exhaustive search method, the simulated annealing method obtained the highest fundamental natural frequency within 1 percent for 87 percent of the cases considered, within 0.5 percent for 72 percent of the cases and the true maximum in 43 percent of them. To further increase the fundamental natural frequency the introduction of a single interior point support is analyzed. Depending on the boundary conditions an additional increase in the maximum fundamental natural frequency of 44 to 198 percent can be obtained.

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