CALCULATION-EXPERIMENTAL METHOD FOR DEFINITION OF LOWEST FREQUENCY IN BENDING VIBRATIONS OF COACH CAR BODY IN VERTICAL PLANE BASED ON IDENTIFICATION OF ITS BENDING STIFFNESS

2020 ◽  
Vol 2020 (9) ◽  
pp. 35-46
Author(s):  
Aleksandr Skachkov ◽  
Viktor Vasilevskiy ◽  
Aleksey Yuhnevskiy
Keyword(s):  
Least Squares Method ◽  
Vertical Plane ◽  
Bending Stiffness ◽  
Dimensional Problem ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Car Body ◽  
Variable Function ◽  
Experimental Values ◽  
Definition Of

The consideration of existing methods for a modal analysis has shown a possibility for the lowest frequency definition of bending vibrations in a coach car body in a vertical plane based on an indirect method reduced to the assessment of the bending stiffness of the one-dimensional model as a Bernoulli-Euler beam with fragment-constant parameters. The assessment mentioned can be obtained by means of the comparison of model deflections (rated) and a prototype (measured experimentally upon a natural body) with the use of the least-squares method that results in the necessity of the solution of the multi-dimensional problem with the reverse coefficient. The introduction of the hypothesis on ratability of real bending stiffness of the prototype and easily calculated geometrical stiffness of a model reduces a multi-dimensional problem incorrect according to Adamar to the simplest search of the extremum of one variable function. The procedure offered for the indirect assessment of bending stiffness was checked through the solution of model problems. The values obtained are offered to use for the assessment of the lowest frequency of bending vibrations with the aid of Ritz and Grammel methods. In case of rigid poles it results in formulae for frequencies into which there are included directly the experimental values of deflections.

CALCULATION-EXPERIMENTAL METHOD FOR DEFINITION OF LOWEST FREQUENCY IN BENDING VIBRATIONS OF COACH CAR BODY IN VERTICAL PLANE BASED ON IDENTIFICATION OF ITS BENDING STIFFNESS

2020 ◽  
Vol 2020 (9) ◽  
pp. 35-46
Author(s):  
Aleksandr Skachkov ◽  
Viktor Vasilevskiy ◽  
Aleksey Yuhnevskiy
Keyword(s):  
Least Squares Method ◽  
Vertical Plane ◽  
Bending Stiffness ◽  
Dimensional Problem ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Car Body ◽  
Variable Function ◽  
Experimental Values ◽  
Definition Of

The consideration of existing methods for a modal analysis has shown a possibility for the lowest frequency definition of bending vibrations in a coach car body in a vertical plane based on an indirect method reduced to the assessment of the bending stiffness of the one-dimensional model as a Bernoulli-Euler beam with fragment-constant parameters. The assessment mentioned can be obtained by means of the comparison of model deflections (rated) and a prototype (measured experimentally upon a natural body) with the use of the least-squares method that results in the necessity of the solution of the multi-dimensional problem with the reverse coefficient. The introduction of the hypothesis on ratability of real bending stiffness of the prototype and easily calculated geometrical stiffness of a model reduces a multi-dimensional problem incorrect according to Adamar to the simplest search of the extremum of one variable function. The procedure offered for the indirect assessment of bending stiffness was checked through the solution of model problems. The values obtained are offered to use for the assessment of the lowest frequency of bending vibrations with the aid of Ritz and Grammel methods. In case of rigid poles it results in formulae for frequencies into which there are included directly the experimental values of deflections.

scholarly journals Dynamic model substantiation of elastic body in bilevel car

2015 ◽  
Vol 2015 (4) ◽  
pp. 50-53
Author(s):  
Владимир Лебедев ◽  
Vladimir Lebedev ◽  
Дмитрий Антипин ◽  
Dmitriy Antipin ◽  
Владимир Кобищанов ◽  
...  
Keyword(s):  
Element Model ◽  
Test Subject ◽  
Test Results ◽  
Bending Vibrations ◽  
Car Body ◽  
Vibration Tests ◽  
Definition Of ◽  
Mass Position ◽  
Use Of Models ◽  
Actual Test

The aim of this work consists in choosing a rational way for the definition of selfresonant frequency in car body bending vibrations of a bilevel car. A test subject is the car body of a bilevel car of the model 61-4465 manufactured by the Company «Tver Wagon Works». The vibration tests of a bilevel car were modeled. Test results were compared to the data of actual test and a computation on the recommendations of regulations. There is developed a lamellar finite-element model of a bilevel car carcass with its stiffness corresponding to a real car body. The assessment of selfresonant frequency in car body bending vibrations was carried out on basis of three variants of its model differed with the distribution of car body gross weight: uniformly throughout the whole of metalware; throughout the parts of metalware in accordance with mass position in a real car; taking into account the influence of partition rigidity in compartments and service rooms. The comparison of modeling results with the use of models described and results of actual tests shows their satisfactory correspondence that allows approaching to dynamic values of a real car body at the investigation of its loading by the methods of computer simulation.

scholarly journals Development and evaluation of a complex of studies to increase the frequency of bending vibrations of modern passenger car bodies

2021 ◽  
Vol 80 (2) ◽  
pp. 76-85
Author(s):  
A. N. Skachkov ◽  
S. L. Samoshkin ◽  
S. D. Korshunov ◽  
D. A. Nikiforov ◽  
D. A. Romashov
Keyword(s):  
Stainless Steel ◽  
Vertical Plane ◽  
Metal Structure ◽  
Bending Stiffness ◽  
The Body ◽  
Body Structure ◽  
Bending Vibrations ◽  
Experimental Complex ◽  
Calculation Results ◽  
Vertical Accelerations

Investigations of the frequency of bending vibrations of the car bodies of 61-4440 model range, which includes compartment cars, staff cars, non-compartment cars, coach cars, restaurant cars and others, are described. The bodies of all cars of this model range have the same overall dimensions and are made of corrosionresistant steels (stainless) with flat corrugated sheathing of the lower (under the window) belt.To assess the influence of the design features of stainless steel bodies on its bending stiffness and the parameters of bending vibrations in the vertical plane, a computational and experimental complex of works was carried out.After analyzing the calculation results and experimental data, proposals were developed and implemented to increase the bending stiffness of the metal body structure with stainless steel skin. To check the implemented proposals, complex tests were carried out to determine the parameters of bending vibrations of the metal structure of the experimental body. The tests were carried out according to the combined method developed by the authors. For this, a vibrator, installed in the console parts of the body, and impulse excitation were used.The results of testing the metal structure of the experimental body in comparison with the results of testing the car bodies of 61-4440 model range showed the effectiveness of the implemented proposals, namely: increasing the frequency of the first tone of bending vibrations by 18 %; decrease in the amplitude of vertical vibrations of the body structure at the frequency of the first tone from 12 to 50 %; decrease in the amplitude of the vertical accelerations of the metal structure of the body during oscillations at the frequency of the first tone approximately by 2 times; significant reduction in horizontal acceleration in the area of the middle section walls. The effectiveness of the implemented proposals for increasing the bending stiffness of the metal structure of the experimental body allows recommending them for the entire model range of 61-4440 cars.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

A NONLINEAR LEAST‐SQUARES METHOD FOR SEISMIC REFRACTION MAPPING—PART I: ALGORITHM AND PROCEDURE

Geophysics ◽  
1972 ◽  
Vol 37 (2) ◽  
pp. 260-272 ◽  
Author(s):  
Leonidas C. Ocola
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Seismic Refraction ◽  
Vertical Plane ◽  
Nonlinear Least Squares ◽  
Inversion Method ◽  
Almost Everywhere ◽  
Isotropic Media ◽  
Time Term ◽  
Nonlinear Least Squares Method

An iterative inversion method (Reframap) based on the kinematic properties of critically refracted waves is developed. The method is based on ray tracing and assumes homogeneous and isotropic media and ray paths confined to a vertical plane through each source‐detector pair. Unlike the earlier Profile or Time‐Term Methods, no restrictions are imposed on interface topography except that it be continuous almost everywhere (in the mathematical sense). As in the preexisting methods, more observations than unknowns are assumed. The algorithm and procedure, on which the Reframap Method is based, generate apparent dips for each source detector pair at the noncritical interfaces from the slope of a least‐squares line approximation to the interface functional in the neighborhood of each refraction point. In turn, the dip and path along the critical refractor is, at every iteration, pairwise approximated by a line through the critical refracting points. The incidence angles are computed recursively by Snell’s law. The solution of the overdetermined, nonlinear multiple refractor time‐distance system of simultaneous equations is sought by Marquardt’s algorithm for least‐squares estimation of critical refractor velocity and vertical thickness under each element.

scholarly journals ON EFFICIENCY OF SOME METHODS FOR DETERMINING THE AZIMUTHAL STRUCTURE OF NOISE IN CYLINDRICAL DUCT

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 130-134
Author(s):  
Vadim Palchikovskiy ◽  
Yuliy Bersenev ◽  
Ivan Korin
Keyword(s):  
Least Squares ◽  
Dynamic Range ◽  
Least Squares Method ◽  
Microphone Array ◽  
Aircraft Engine ◽  
Circular Array ◽  
Noise Measurements ◽  
Air Intake ◽  
Experimental Values ◽  
Cylindrical Duct

The determination of azimuthal sound modes propagating in a cylindrical duct is considered based on the results of noise measurements on experimental setup with a duct diameter of 1.8 m, which corresponds to the air intake of aircraft engine. The experiments were carried out in PNRPU anechoic chamber. Spinning modes were generated by a circular array of 40 acoustic drivers. Noise in duct was recorded with circular array of 100 microphones with optimized arrangement to reach maximum dynamic range. The following methods for determining the azimuthal structure of noise were compared: modal decomposition method, cross-correlation with a reference channel method; least-squares method. The mathematical foundations and specifics of these methods are briefly outlined. According to the results of the azimuthal structure extraction, it was found that the least-squares method provides the best agreement between the generated and extracted modes and the distribution of the computed and experimental values of acoustic pressures on microphone array.

scholarly journals A New Value of the von Kármán Constant: Implications and Implementation

2009 ◽  
Vol 48 (5) ◽  
pp. 923-944 ◽  
Author(s):  
Edgar L. Andreas
Keyword(s):  
Boundary Layer ◽  
Similarity Theory ◽  
Stable Stratification ◽  
Transfer Coefficients ◽  
Obukhov Length ◽  
Von Karman ◽  
Roughness Lengths ◽  
Experimental Values ◽  
Definition Of ◽  
Von Kármán

Abstract The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory. Although credible experimental evidence has appeared sporadically that the von Kármán constant is different than the canonical value of 0.40, the mathematics of boundary layer meteorology still retain k = 0.40—probably because the task of revising all of this math to implement a new value of k is so daunting. This study therefore outlines how to make these revisions in the nondimensional flux–gradient relations; in variance, covariance, and dissipation functions; and in structure parameters of Monin–Obukhov similarity theory. It also demonstrates how measured values of the drag coefficient (CD), the transfer coefficients for sensible (CH) and latent (CE) heat, and the roughness lengths for wind speed (z0), temperature (zT), and humidity (zQ) must be modified for a new value of the von Kármán constant. For the range of credible experimental values for k, 0.35–0.436, revised values of CD, CH, CE, z0, zT, and zQ could be quite different from values obtained assuming k = 0.40, especially if the original measurements were made in stable stratification. However, for the value of k recommended here, 0.39, no revisions to the transfer coefficients and roughness lengths should be necessary. Henceforth, use the original measured values of transfer coefficients and roughness lengths but do use similarity functions modified to reflect k = 0.39.

Active Damping of Vibrations of a Cantilever Beam by Axial Force Control

2007 ◽  
Author(s):  
Thomas Pumho¨ssel ◽  
Horst Ecker
Keyword(s):  
Cantilever Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Open Loop ◽  
Active Damping ◽  
Nonlinear Feedback ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Loop Control ◽  
Damping Of Vibrations

In several fields, e.g. aerospace applications, robotics or the bladings of turbomachinery, the active damping of vibrations of slender beams which are subject to free bending vibrations becomes more and more important. In this contribution a slender cantilever beam loaded with a controlled force at its tip, which always points to the clamping point of the beam, is treated. The equations of motion are obtained using the Bernoulli-Euler beam theory and d’Alemberts principle. To introduce artificial damping to the lateral vibrations of the beam, the force at the tip of the beam has to be controlled in a proper way. Two different methods are compared. One concept is the closed-loop control of the force. In this case a nonlinear feedback control law is used, based on axial velocity feedback of the tip of the beam and a state-dependent amplification. By contrast, the concept of open-loop parametric control works without any feedback of the actual vibrations of the mechanical structure. This approach applies the force as harmonic function of time with constant amplitude and frequency. Numerical results are carried out to compare and to demonstrate the effectiveness of both methods.

Vibration Analysis of a Rail Operating Vehicle

2013 ◽  
Vol 662 ◽  
pp. 591-594
Author(s):  
Wei Guo ◽  
Qian Ding
Keyword(s):  
Vibration Analysis ◽  
Reference Value ◽  
Dynamical Model ◽  
Dynamical Response ◽  
Euler Beam ◽  
Bogie Frame ◽  
Dynamic Design ◽  
Flexible Coupling ◽  
Car Body ◽  
Operating Vehicle

A simplified rigid-flexible coupling dynamical model of the rail operating vehicle, including bogie frame and car body, was built. The car body is modeled as a flexible uniform Euler beam. The dynamical response of the vehicle under the irregularity dynamic action between wheel and rail was numerically calculated and analyzed by the fast stability algorithms. Influences of the suspension on vibration and stability of the vehicle are analyzed. The results have a certain reference value on the dynamic design of multi-functional track operating vehicle.

Research on the Natural Frequency Solving Method of the Simply Supported Beam Bridge with Cracks

2013 ◽  
Vol 437 ◽  
pp. 51-55
Author(s):  
Ping Yi Sun ◽  
Yan Hua Wang ◽  
Han Bing Liu ◽  
Guo Jin Tan
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Solution Methods ◽  
Element Approach ◽  
Experimental Values ◽  
Beam Bridge

Two kinds of natural frequency solution methods for the simply supported beam bridge with cracks are presented respectively based on the Bernoulli-Euler beam model and the finite element approach. Multiple groups of crack damages are supposed on the experimental simply supported steel I-beam, and the natural frequencies of the experimental beam are measured in all the crack cases. By comparing the calculated natural frequencies respectively obtained by the above two methods with the experimental values, the characteristics of the two kinds of natural frequency solving methods are evaluated.

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