scholarly journals An Accurate Measurement Method for Tension Force of Short Cable by Additional Mass Block

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shuichang Li ◽  
Longlin Wang ◽  
Hua Wang ◽  
Peihua Shi ◽  
Riyan Lan ◽  
...  
Keyword(s):  
Natural Frequency ◽  
Force Measurement ◽  
Ritz Method ◽  
Added Mass ◽  
Short Length ◽  
Effective Length ◽  
Tension Force ◽  
Analytical Relationship ◽  
Test Accuracy ◽  
Additional Mass

The equivalent effective length parameter is introduced into the vibration equation of short cable; that is, the boundary condition that affects the test accuracy of short cable force is equivalent to the calculated length of cable. By attaching an additional mass block to the cable, new parameters are introduced to identify the tension force. Vibration differential equations are established for cable with and without addition mass block, taking new parameters into account, such as equivalent effective length and added mass. By solving the equations using the RITZ method, the analytical relationship between the natural frequency of cable and equivalent effective length before and after a mass block is added can be developed. It can also develop an analytical method to identify the equivalent effective length depending on whether the added mass block is attached. Then, tension force of short length cable can be evaluated by measuring its natural frequency based on equivalent effective length. The method is verified by field tests. The tests results indicate the new method mentioned in this paper is going to largely improve the accuracy of tension force measurement of short length cable.

scholarly journals Studies on Frequency Response Characteristics of High-Speed Railway Train End Relationship Test System with Flexible Bases

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6147
Author(s):  
Zhiqiang Zhang ◽  
Dacheng Cong ◽  
Zhidong Yang ◽  
Yunfei Cai ◽  
Junwei Han
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
Parallel Robot ◽  
Test System ◽  
Design Criterion ◽  
Analytical Relationship ◽  
Test Accuracy ◽  
High Speed Railway ◽  
Characteristic Model ◽  
Response Characteristics

A train end relationship test system was installed with a Stewart parallel robot on the reaction bases perpendicular to the ground, to test the fatigue and durability of train end relationship components, such as the transfixion way of a high-speed railway train. The flexibility of the reaction bases affected the test accuracy of the train end relationship components within a test frequency band range. In this paper, a coupling characteristic model was established between the flexible bases and the parallel robot. Then, the analytical relationship was analyzed between the natural frequency of the bases and the natural frequency of the parallel robot. Moreover, a design criterion was proposed for the natural frequency of the reaction bases. It was considered that when the natural frequency of the bases was not less than five times the natural frequency of the parallel robot, the influence of the flexibility of the bases on the test accuracy can be ignored. The validity of the design criterion was verified by the simulation results.

Finite Element Modeling for Steel Cord Analysis in Radial Tires

2013 ◽  
Vol 41 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Wei Yintao ◽  
Luo Yiwen ◽  
Miao Yiming ◽  
Chai Delong ◽  
Feng Xijin
Keyword(s):  
Finite Element ◽  
High Efficiency ◽  
Force Measurement ◽  
Three Dimensional ◽  
Local Stress ◽  
Tension Force ◽  
Center Line ◽  
Element Analysis ◽  
Design Variables ◽  
Steel Cord

ABSTRACT: This article focuses on steel cord deformation and force investigation within heavy-duty radial tires. Typical bending deformation and tension force distributions of steel reinforcement within a truck bus radial (TBR) tire have been obtained, and they provide useful input for the local scale modeling of the steel cord. The three-dimensional carpet plots of the cord force distribution within a TBR tire are presented. The carcass-bending curvature is derived from the deformation of the carcass center line. A high-efficiency modeling approach for layered multistrand cord structures has been developed that uses cord design variables such as lay angle, lay length, and radius of the strand center line as input. Several types of steel cord have been modeled using the developed method as an example. The pure tension for two cords and the combined tension bending under various loading conditions relevant to tire deformation have been simulated by a finite element analysis (FEA). Good agreement has been found between experimental and FEA-determined tension force-displacement curves, and the characteristic structural and plastic deformation phases have been revealed by the FE simulation. Furthermore, some interesting local stress and deformation patterns under combined tension and bending are found that have not been previously reported. In addition, an experimental cord force measurement approach is included in this article.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

scholarly journals Effect of lamination schemes on natural frequency and modal damping of fiber reinforced laminated beam using Ritz method

2021 ◽  
Vol 12 ◽  
pp. 15
Author(s):  
Somi Naidu Balireddy ◽  
Pitchaimani Jeyaraj ◽  
Lenin Babu Mailan Chinnapandi ◽  
Ch V.S.N. Reddi
Keyword(s):  
Natural Frequency ◽  
Ritz Method ◽  
Laminated Composite ◽  
High Strength ◽  
Fiber Reinforced ◽  
Modal Strain Energy ◽  
Modal Strain Energy Method ◽  
Modal Damping ◽  
Method Effects ◽  
Thin Beams

The current study focussed on analysing natural frequency and damping of laminated composite beams (LCBs) by varying fiber angle, aspect ratio, material property and boundary conditions. Ritz method with displacement field based on the shear and normal deformable theory is used and the modal damping is calculated using modal strain energy method. Effects of symmetric angle-ply and cross-ply, anti symmetric cross-ply, balanced and quasi-isotropic lay up schemes on modal damping are presented for the first time. Results revealed that influence of lay-up scheme on natural frequencies is significant for the thin beams while the modal damping of the thin beams are not sensitive to lay-up scheme. However, the lay-up scheme influences the damping significantly for the thick beams. Similarly, high strength fiber reinforced LCBs have higher natural frequency while low strength fiber reinforced LCBs have higher damping due to the better fiber-matrix interaction.

Natural Frequencies of a Railroad Track

1987 ◽  
Vol 54 (2) ◽  
pp. 299-304 ◽  
Author(s):  
S. P. Patil
Keyword(s):  
Natural Frequency ◽  
Elastic Layer ◽  
Natural Frequencies ◽  
Unit Length ◽  
Added Mass ◽  
Winkler Foundation ◽  
Railroad Track

The natural frequency of an infinite railroad track was first determined by Timoshenko as ωR = √k/m, where k is the constant for the massless Winkler foundation and m is the mass per unit length of the rail. The natural frequencies of the track are determined here by modeling the track as a beam resting on a 3-D inertial elastic layer. It is shown that the mass of the supporting foundation has a significant effect on the natural frequencies of a railroad track. Finally, the concept of “added mass” is introduced in order to determine the natural frequency in a desired mode of vibration, by modeling the track as a beam on the massless Winkler foundation and adding the mass of the foundation to the beam.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Tensile Testing Equipment and Strain Sensors

2004 ◽  
pp. 65-89
Keyword(s):  
Strain Rate ◽  
Strain Measurement ◽  
Force Measurement ◽  
Load Condition ◽  
Tensile Tests ◽  
Test Accuracy ◽  
Strain Sensing ◽  
Application Systems ◽  
Machine Stiffness ◽  
Test Diagnostics

Abstract This chapter reviews the current technology and examines force application systems, force measurement, strain measurement, important instrument considerations, gripping of test specimens, test diagnostics, and the use of computers for gathering and reducing data. The influence of the machine stiffness on the test results is also described, along with a general assessment of test accuracy, precision, and repeatability of modern equipment. The chapter discusses various types of testing machines and their operations. Emphasis is placed on strain-sensing equipment. The chapter briefly describes load condition factors, such as strain rate, machine rigidity, and various testing modes by load control, speed control, strain control, and strain-rate control. It provides a description of environmental chambers for testing and discusses the processes involved in the force verification of universal testing machines. Specimen geometries and standard tensile tests are also described.

scholarly journals Analytical method comparison on critical force of the stepped column model of telescopic crane

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880869 ◽  
Author(s):  
Fenglin Yao ◽  
Wenjun Meng ◽  
Jie Zhao ◽  
Zhanjiao She ◽  
Guoshan Shi
Keyword(s):  
Ritz Method ◽  
Method Comparison ◽  
Recursive Formula ◽  
Transcendental Equation ◽  
Critical Force ◽  
Effective Length ◽  
Deflection Curve ◽  
Stability Calculation ◽  
Column Model ◽  
The Ideal

The calculation of the critical force of the stepped column model of telescopic boom crane is the key to stability calculation of all-terrain crane. In slightly bending theory, differential equation can be built up, and then the deflection curve of ideal column can be obtained. Using this curve and the Rayleigh–Ritz method, the Euler force of the ideal column can be obtained. For n-stepped columns, Euler forces and the effective length coefficients can be acquired using the deflection curve of the ideal column and parabolic curve, respectively, combined with the Rayleigh–Ritz method. Differential equations of the n-stepped telescopic boom are established based on the vertical and horizontal buckling theory. The recursive formula of the stability of the n-stepped telescopic boom is deduced by the mathematical induction method. For the transcendental equation in the recursive formula, combined with the structural force characteristics and supplementary formulas, the Levenberg–Marquardt numerical optimization algorithm is used to solve the equations with n unknowns. Length coefficients obtained by the three methods are compared using GB3811-2008 and ANSYS 17.0. The results show that the accuracy of the numerical algorithm is the highest, and the first two algorithms will produce large errors when the stepped columns have more steps.

scholarly journals Effects of Organ-Pipe Chamber Geometry on the Frequency and Erosion Characteristics of the Self-Excited Cavitating Waterjet

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 978
Author(s):  
Tengfei Cai ◽  
Yan Pan ◽  
Fei Ma ◽  
Pingping Xu
Keyword(s):  
Mass Loss ◽  
Natural Frequency ◽  
Pressure Sensors ◽  
The Self ◽  
Effective Length ◽  
Resonance Amplitude ◽  
Equivalent Length ◽  
Contraction Ratio ◽  
Organ Pipe ◽  
The Impact

Erosion experiments were performed to uncover the impact of organ-pipe chamber geometry on the frequency and erosion characteristics of self-excited cavitating waterjets. Jets emanating from self-excited nozzles with various organ-pipe geometries were investigated. The upstream and downstream contraction ratios of the organ-pipe resonator were changed respectively from 1.5 to 6 and 2 to 12. Pressure sensors and hydrophone were used to characterize jets’ frequency characteristics. Mass loss was also obtained in each of the configurations to assess the erosion performance. By tuning the self-excited frequency, the peak resonance was achieved using the nozzles with different geometries. Accordingly, the acoustic natural frequencies of various chamber geometries were obtained precisely. Results show that with increasing upstream and downstream contraction ratio of the organ-pipe chamber, the acoustic natural frequency increases monotonically due to the reduction of equivalent length, while the resonance amplitude and mass loss first increase and then decrease. There are optimum geometric parameters to reach the largest resonance amplitude and erosion mass loss: the upstream contraction ratio being between two and four, and downstream ratio being between four and seven. The effective length of the organ pipe can be calculated by the sum of the physical length and equivalent length to accurately obtain the acoustic natural frequency. Under the optimized parameters, the equivalent length can be estimated as 0.35D.

Effects of Additional Mass on Modal Experimental Analysis of 3-Dimension and 5-Direction Braided Composites

2010 ◽  
Vol 34-35 ◽  
pp. 1467-1470
Author(s):  
Yan Gao ◽  
Jia Lu Li
Keyword(s):  
Natural Frequency ◽  
Influence Factor ◽  
Damping Ratio ◽  
Force Response ◽  
Braided Composites ◽  
Additional Mass ◽  
Response Curves ◽  
Ratio Increase ◽  
Modal Test ◽  
Relative Errors

The work of vibration test has significant meanings for the researches and applications of 3-dimension and 5-direction braided composites. This article discusses the effects of added mass with different weight on the modal test of 3-dimension and 5-direction braided composites. The comparison of the modal parameters of 3-dimension and 5-direction braided composites tested by different weight of mass reveals that the additional mass is a mostly influence factor for vibration property of 3-dimension and 5-direction braided composites. The results of frequency response and force response curves show that smaller mass accelerometer is more effective for a wider range of frequencies around the resonance frequency, a higher natural frequency and a larger peak in these points. Force-response curves show that force response amplitude increases with the increase of additional mass weight, and the larger additional mass, the shorter time taken for reaching stationary state. The errors of natural frequency and damping ratio increase when the weight of additional mass increases. With the increase of modal orders, relative errors of modal characteristics have slighter decreasing degrees. The results derived from this article will provide a useful reference for precise modal analysis of 3-dimension and 5-direction braided composites.

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