scholarly journals A hybrid algorithm for solving inverse boundary problems with respect to intermediate masses on a beam

2021 ◽  
Vol 104 (4) ◽  
pp. 4-13
Author(s):  
A.A. Aniyarov ◽  
◽  
S.A. Jumabayev ◽  
D.B. Nurakhmetov ◽  
R.K. Kussainov ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Analysis ◽  
Hybrid Algorithm ◽  
Natural Frequencies ◽  
Boundary Problems ◽  
Inverse Boundary ◽  
The Third ◽  
Uniform Beam ◽  
Analytical Relations ◽  
The Masses

The inverse problem of determining the weight of three intermediate masses on a uniform beam from the known three natural frequencies has been solved. The performed numerical analysis allows restoring the value of only the second mass in a unique way. The inverse problem of determining the weight of three intermediate masses is solved uniquely except in the case when the first and the third masses are located geometrically symmetric relative to the middle of the beam. The hybrid algorithm for the unique solving inverse problem of determining the weight of three intermediate masses has been developed. The first three natural frequencies of the beam are calculated numerically by using the Maple computer package. Analytical relations between the masses are found.

150 Years of Das Kapital and No End in Sight. Unsystematic Remarks on a Never-Ending Story

2019 ◽  
Vol 29 (6) ◽  
pp. 23-46
Keyword(s):  
Political Economy ◽  
Formal Structure ◽  
Monetary Theory ◽  
Economic Crises ◽  
General Introduction ◽  
The Third ◽  
Social Forms ◽  
Adequate Understanding ◽  
Theory Of Value ◽  
The Masses

Michael Heinrich, one of the leading Marx scholars, provides a general introduction into Das Kapital with emphasis on the latest interpretations of it. The circumstances surrounding its writing and publication are shown to have interfered with an adequate appreciation of it. The formal structure and organization of the first volume are obstacles to readers and demand much from their education and intellect. The article summarizes the basic trajectories of Marx’s criticisms of political economy, including the critique of naturalizing social forms arising under capitalism and Marx’s original monetary theory of value. The author disentangles Marx’s Das Kapital from views mistakenly ascribed to it, such as the idea that value is determined solely by labor and the prediction of pauperization of the masses. First, Marx’s theory of value goes well beyond explaining prices under capitalism. Second, his main prophecy concerned the inevitable growth of inequality between the masters of capital and the employed classes and did not forecast impoverishment. The paper also points out that the sequence of publication of different volumes of Das Kapital caused lacunae in interpreting Marx’s oeuvre. For instance Engels’ efforts made the third volume more accessible to readers but also obscured the overall pattern of Marx’s thinking. the article shows that Das Kapital was a dynamic and fluctuating project to such an extent that Marx himself several times revisited his views of the causes of economic crises and falling profits and also intended to deal extensively with ecological issues. Reaching an adequate understanding of the theory contained in Das Kapital cannot depend on the manuscripts of those volumes alone. Marx’s notebooks, which have only recently published, are an indispensable aid to understanding it.

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

Effect of compact inclusion on the natural frequencies of vibrations of a pipe string in a well

2021 ◽  
pp. 73-77
Author(s):  
A.M. Svalov ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Natural Frequencies ◽  
Oscillation Period ◽  
Drill String ◽  
Analytical Relation ◽  
Longitudinal Vibrations ◽  
Bottom Hole ◽  
Tubing String ◽  
Analytical Relations

The influence of small-size inclusion of pipes in a well column on the natural frequency of its longitudinal vibrations is investigated. Using the asymptotic expansion in a small parameter, an analytical relation is obtained that describes the change in the period of the column oscillations in the form of some additional small term to the period of the homogeneous column oscillations. Numerical calculations show that the obtained analytical relations almost accurately describe the oscillation period of a column with a massive compact inclusion, while its difference from the oscillation period of a homogeneous column is within ~20%. The results obtained can be useful for preventing resonant phenomena in the drill string when drilling wells, as well as for optimal use of the longitudinal vibrations of the tubing string to influence the bottom-hole zones of producing wells.

Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight

1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
Simplified Model ◽  
Main Rotor ◽  
Numerical Examples ◽  
The Masses

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.

Exploiting Hitler’s Magic

2017 ◽  
Author(s):  
Eric Kurlander
Keyword(s):  
Case Studies ◽  
Third Reich ◽  
National Socialist ◽  
Book Of Revelation ◽  
Objective Reality ◽  
The Third ◽  
Political Campaigning ◽  
The Third Reich ◽  
The Masses ◽  
The Relationship

This chapter illustrates how the National Socialist Workers' Party (NSDAP) appropriated supernatural ideas in order to appeal to ordinary Germans, enlisting the help of occultists and horror writers in shaping propaganda and political campaigning. By exploiting the supernatural imaginary, Hitler tied his political mission into something out of the Book of Revelation, as one ‘divinely chosen’ to create the Third Reich. The chapter then looks at three case studies. The first assesses Hitler's approach to politics through his reading of Ernst Schertel's 1923 occult treatise, Magic: History, Theory, Practice. The second considers the NSDAP's propaganda collaboration with the horror writer, Hanns Heinz Ewers. The third delves into the relationship between the NSDAP and Weimar's most popular ‘magician’, Erik Hanussen. In coopting Schertel's magic, enlisting Ewers, and forming an alliance with Hanussen, the Nazis diverted the masses from objective reality and toward the coming Third Reich.

scholarly journals Convolution and deconvolution: two mathematical tools to help performing tests in research and industry

2021 ◽  
Vol 12 ◽  
pp. 6
Author(s):  
Jean-Pierre Fanton
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Electrical Energy ◽  
Integral Transforms ◽  
Physical Measurement ◽  
Photographic Images ◽  
Test Standards ◽  
Energy Networks ◽  
The Third ◽  
The Subject

The concepts of convolution and deconvolution are well known in the field of physical measurement. In particular, they are of interest in the field of metrology, since they can positively influence the performance of the measurement. Numerous mathematical models and computer developments dedicated to convolution and deconvolution have emerged, enabling a more efficient use of experimental data; this in sectors as different as biology, astronomy, manufacturing and energy industries. The subject finds today a new topicality because it has been made accessible to a large public for applications such as processing photographic images. The purpose of this paper is to take into account some recent evolutions such as the introduction of convolution methods in international test standards. Thus, its first part delivers a few reminders of some associated definitions. They concern linear systems properties, and integral transforms. If convolution, in most cases, does not create major calculation problems, deconvolution on the contrary is an inverse problem, and as such needs more attention. The principles of some of the methods available today are exposed. In the third part, illustrations are given on recent examples of applications, belonging to the domain of electrical energy networks and photographic enhancement.

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 Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

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