Determining the velocity of a moving rod and the thickness of its coating using natural frequencies of flexural vibrations

2016 ◽  
Vol 11 (1) ◽  
pp. 10-15
Author(s):  
A.G. Khakimov
Keyword(s):  
Coating Thickness ◽  
Textile Industry ◽  
Natural Frequencies ◽  
Neutral Line ◽  
Research Work ◽  
Longitudinal Force ◽  
Wire Drawing ◽  
Constant Length ◽  
Velocity Parameter ◽  
Flexural Vibrations

Research has been performed on natural transverse vibrations of a portion of a constant length in a straight thin coated rod moving along the neutral line of a non-deformed state. The movement takes place between two rigidly fixed coaxial guides (clamps), the distance between them equalling the length of the rod moving portion. The longitudinal force is assumed to constantly act along the neutral line. It has been found that a decrease in the natural frequencies of flexural vibrations of the rod occurs with an increase in the velocity parameter. It is also shown that a decrease in the natural frequencies of flexural vibrations of the rod occurs with an increase of the coating thickness. Using two frequencies of flexural vibrations, we can determine the velocity parameter of the moving rod and the thickness of its coating. The results of the research work can find technological use in the problems on dynamics and strength of machines and mechanisms in manufacturing the coated products: in textile industry, wire manufacturing process, metallurgy (especially for rolling metal bars and strips), wire drawing, plastic products and paper rolls manufacturing and can be used to determine the velocity and the coating thickness of a moving rod, strip or wire using two frequencies of flexural vibrations.

Determining the velocity of a moving three-layered plate and the thickness of its filler using natural frequencies of flexural vibrations

2017 ◽  
Vol 12 (1) ◽  
pp. 109-114
Author(s):  
A.G. Khakimov
Keyword(s):  
Natural Frequencies ◽  
Neutral Line ◽  
Research Work ◽  
Longitudinal Force ◽  
Layered Plate ◽  
Constant Length ◽  
Transverse Vibrations ◽  
Deformed State ◽  
Flexural Vibrations ◽  
Natural Transverse

Research has been performed on natural transverse vibrations of a portion of a constant length in a straight threelayered plate with a filler moving along the neutral line of a non-deformed state. The movement takes place between two rigidly fixed coaxial guides (clamps), the distance between them equalling the length of the vibrating portion. The longitudinal force is assumed to constantly act along the neutral line. It has been found that an increase in the natural frequencies of flexural vibrations of the plate occurs with an increase in the thickness of the filler. Using two frequencies of flexural vibrations, we can determine the velocity of the moving three-layered plate and the thickness of its filler. The results of the research work can find technological use in the problems on dynamics and strength of machines and mechanisms in manufacturing three-layered plate with fillers and can be used to determine the velocity of a plate and the thickness of its filler using two frequencies of flexural vibrations.

Flexural vibrations of the pipeline on elastic supports with moving fluid

2019 ◽  
Vol 14 (1) ◽  
pp. 10-16
Author(s):  
A.G. Khakimov ◽  
A.A. Yulmukhametov
Keyword(s):  
Natural Frequencies ◽  
Neutral Line ◽  
Unit Length ◽  
Fluid Pressure ◽  
Density Parameter ◽  
Liquid Density ◽  
Bending Vibrations ◽  
Technical Application ◽  
Elastic Supports ◽  
Flexural Vibrations

In the work investigated the flexural vibrations of the pipeline. Parts of the pipeline on both sides of the sagging section have elastic supports. It is assumed that a constant longitudinal force acts along the neutral line. An incompressible fluid flows through the pipe at a constant average speed. The influence of internal pressure in the pipe on these oscillations is taken into account. The direct problem of determining the eigenfrequencies of flexural vibrations of the pipeline by the Kirchhoff model using Ferrari formulas is solved. The frequency spectrum is determined depending on the fluid pressure, the elasticity of the supports, the velocity of the fluid through the pipe. Particular and limiting cases are considered, for example, when the stiffness of the supports is very large and when they are very small. Graphs of the dependence of the first and second eigenfrequencies on the velocity of the transported liquid at different values of the liquid density parameter are constructed. It is shown that with the growth of the velocity parameter there is a decrease in the natural frequencies of flexural vibrations of the pipeline, and the faster the higher the density parameter of the liquid. It is determined that with an increase in the mass of the liquid per unit length of the pipeline there is a decrease in the natural frequencies of bending vibrations of the pipe. It is found that with the increase in the mass flow through the pipe, the natural frequencies of bending oscillations also decrease. It is confirmed that the frequencies of flexural vibrations of the pipeline are the same for the cases of pipe fastening “rigid fixing — rigid fixing” and “free end — free end”. The results of the study will contribute to the development of methods of acoustic diagnostics and non-destructive testing and can find technical application for monitoring and diagnostics of pipeline systems.

Free Flexural Vibrations Response of Composite Mindlin Plates or Panels With a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint)

2005 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Solution Technique ◽  
Shear Stresses ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Present Solution ◽  
Flexural Vibrations ◽  
Support Conditions ◽  
Interpolation Polynomials

The present study is concerned with the “Free Flexural Vibrations Response of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint). The plate “adherends” and the plate “doublers” are considered as dissimilar, orthotropic “Mindlin Plates” with the transverse and the rotary moments of inertia. The relatively, very thin adhesive layers are taken into account in terms of their transverse normal and shear stresses. The mid-center of the bonded region of the joint is at the mid-center of the entire system. In order to facilitate the present solution technique, the dynamic equations of the plate “adherends” and the plate “doublers” with those of the adhesive layers are reduced to a set of the “Governing System of First Order ordinary Differential Equations” in terms of the “state vectors” of the problem. This reduced set establishes a “Two-Point Boundary Value Problem” which can be numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the adhesive layers, the “hard” and the “soft” adhesive cases are accounted for. It was found that the adhesive elastic constants drastically influence the mode shapes and their natural frequencies. Also, the numerical results of some parametric studies regarding the effects of the “Position Ratio” and the “Joint Length Ratio” on the natural frequencies for various sets of support conditions are presented.

scholarly journals Cantilever Beam Metastructure for Active Broadband Vibration Suppression

2020 ◽  
Author(s):  
Ratiba Fatma Ghachi ◽  
Wael Alnahhal ◽  
Osama Abdeljaber
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Research Work ◽  
Peak Frequency ◽  
Experimental Frequency ◽  
Transmission Frequency ◽  
Vibration Attenuation ◽  
The Masses ◽  
Zigzag Structure

This paper presents a beam structure of a new metamaterial-inspired dynamic vibration attenuation system. The proposed experimental research presents a designed cantilevered zigzag structure that can have natural frequencies orders of magnitude lower than a simple cantilever of the same scale. The proposed vibration attenuation system relies on the masses places on the zigzag structure thus changing the dynamic response of the system. The zigzag plates are integrated into the host structure namely a cantilever beam with openings, forming what is referred to here as a metastructure. Experimental frequency response function results are shown comparing the response of the structure to depending on the natural frequency of the zigzag structures. Results show that the distributed inserts in the system can split the peak response of the structure into two separate peaks rendering the peak frequency a low transmission frequency. These preliminary results provide a view of the potential of research work on active-controlled structures and nonlinear insert-structure interaction for vibration attenuation.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

Steel Wire Grinding Testing Based on New Type Abrasive Belt Grinding Machine

2012 ◽  
Vol 602-604 ◽  
pp. 2273-2278
Author(s):  
Ping Zhang ◽  
Jia Chun Li
Keyword(s):  
Metal Removal ◽  
Removal Rate ◽  
Steel Wire ◽  
Research Work ◽  
Wire Drawing ◽  
Belt Grinding ◽  
Abrasive Belt ◽  
New Type ◽  
Working Principle ◽  
Grinding Machine

As a new process, the abrasive belt grinding plays an increasingly important role in the field of machining. It meets a variety of processing requirements. The concept of abrasive belt grinding and its working principle were introduced, and a new type of abrasive belt grinding equipment for removing the rust on steel wire surface was designed. Some key experiments for testing grinding force，the metal removal rate，belt wear rate、grinding ratio，grinding depth and wire speed were studied. The research work provides rational parameters for the pretreatment of rust removal in metal wire drawing processing.

Flexural Vibrations of a Multi-Material Microhydraulic Hose Subjected to External Excitation. Experimental Research and Theoretical Description

2021 ◽  
Author(s):  
Marek Lubecki ◽  
Michał Stosiak ◽  
Mirosław Bocian ◽  
Kamil Urbanowicz
Keyword(s):  
Experimental Research ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Classical Equation ◽  
Analytical Description ◽  
Theoretical Description ◽  
Laser Vibrometer ◽  
Flexural Vibrations ◽  
Stiffness And Damping ◽  
Mathematica Software

Abstract The paper presents experimental research and mathematical modeling of flexural vibrations of a composite hydraulic microhose. The tested object was a Polyflex 2020N-013V30 hydraulic microhose, consisting of a braided aramid layer placed in a thermoplastic matrix. The vibrations were induced with an external electromagnetic exciter in the range from 0 Hz to 100 Hz using the sweep function. Using a laser vibrometer, the exciter’s displacement was measured in the above-mentioned range. Long exposure photographs were taken to identify the form of microhose’s vibrations as well as to measure it’s amplitude. The existence of considerable non-linearity in subsequent natural frequencies was shown. At the same time, mathematical simulations were carried out using the Mathematica software. For the analytical description of the object’s vibrations partial differential equations based on the string equation were used. A part responsible for damping in the material was added to the classical equation of the string. The dependence of the values of the stiffness and damping coefficients a on the excitation frequency made it possible to model nonlinearities manifested by the upward shift of higher natural frequencies and the suppression of the amplitudes of successive modes. Further development of the proposed model will allow for modeling the internal pressure in the hose and its effect on transverse vibrations. It will also allow to design of vibrations of composite microhoses and avoid the coupling of these vibrations with external excitations.

Joint order allocation and transportation planning under uncertainty within a socially responsible supply chain

2019 ◽  
Vol 15 (2) ◽  
pp. 531-565 ◽  
Author(s):  
R. Ghasemy Yaghin ◽  
P. Sarlak
Keyword(s):  
Supply Chain ◽  
Social Responsibility ◽  
Transportation Planning ◽  
Textile Industry ◽  
Research Work ◽  
Planning Under Uncertainty ◽  
Market Demand ◽  
Order Allocation ◽  
Total Contribution ◽  
Content Type

Purpose This paper aims to propose an integrated supplier selection, order allocation, transportation planning model, along with investment planning for corporate social responsibility (CSR), over a given multi-period horizon under uncertainty. Furthermore, a customer’s behavior to pay more money for items with CSR attributes is considered in the total market demand. Design/methodology/approach The objective functions, i.e. social value of purchasing, total profit (TP), total delivery lead-time, total air pollution, total water pollution and total energy consumption with regard to a number of constraints are jointly considered in a multi-product system. It is worth noting that operational- and sustainable-related parameters are usually vague and imprecise in this area. Therefore, this paper develops a new fuzzy multi-objective optimization model to capture this inherent fuzziness in critical data. Findings Through the numerical examples in the textile industry, the application of the model and usefulness of solution procedures are carried out. The numerical results obtained from the proposed approach indicate the efficiency of the solution algorithm in different instances. Moreover, the authors observe that social investment of the buyer, to stimulate market demand, can affect the TP and also involve the total contribution of suppliers in social responsibility. Originality/value This research work concentrates on providing a procurement and inventory model through the lens of sustainability to enable textile supply chain managers and related industries to apply the approach to their inventory control and supply management. Totally, the proposed methodology could be applied by many fabric buyers of textile industry tackling purchasing issues and attempting to perfect understanding of social supply chains.

Natural Frequencies of Plate Systems using the Edge Effect Method

1967 ◽  
Vol 9 (4) ◽  
pp. 318-324 ◽  
Author(s):  
S. M. Dickinson ◽  
G. B. Warburton
Keyword(s):  
Natural Frequency ◽  
Edge Effect ◽  
Series Solution ◽  
Natural Frequencies ◽  
Rectangular Plates ◽  
Form Part ◽  
Approximate Frequency ◽  
Flexural Vibrations ◽  
Effect Method ◽  
Partial Success

In this paper the Bolotin edge effect method is used to consider the free flexural vibrations of systems built up from rectangular plates. The constituent plates of the systems are considered either to lie in the same plane and form part of a plate continuous over line supports or to lie in planes at right angles to each other, as in box constructions. The application of the edge effect method to single-and multi-plate systems is described and the approximate frequency equations for two two-plate systems are given. The first 10 natural frequency parameters for these two systems for particular side ratios are compared with those obtained using a series solution and agreement is shown to be good. A few frequency parameters for a closed box computed using the edge effect method and the series solution are also compared. The range of plate systems to which the edge effect method may be applied with complete success and the range to which it may be applied with only partial success are indicated. The sources of errors in the edge effect solutions are indicated.

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