Forced and free longitudinal vibrations of a regular-structure viscoelastic rod

A mutant of Bacillus licheniformis 749/C, NM 105 exhibits some notable properties, e.g., arrest of alkaline phosphatase secretion and overexpression and hypersecretion of RS protein. Although RS is known to be widely distributed in many microbes, it is rarely found, with a few exceptions, in laboratory cultures of microorganisms. RS protein is a structural protein and has the unusual properties to form aggregate. This characteristic may have been responsible for the self assembly of RS into regular tetragonal structures. Another uncommon characteristic of RS is that enhanced synthesis and secretion which occurs when the cells cease to grow. Assembled RS protein with a tetragonal structure is not seen inside cells at any stage of cell growth including cells in the stationary phase of growth. Gel electrophoresis of the culture supernatant shows a very large amount of RS protein in the stationary culture of the B. licheniformis. It seems, Therefore, that the RS protein is cotranslationally secreted and self assembled on the envelope surface.

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ANALYSIS OF SUPPRESSION OF LONGITUDINAL VIBRATIONS IN RODS WITH MATERIAL PERIODICITY

10.26678/abcm.cobem2019.cob2019-1469 ◽

2019 ◽

Author(s):

Jean Paulo Carneiro Junior ◽

Rodrigo Borges Santos ◽

Douglas Bueno

Keyword(s):

Longitudinal Vibrations

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DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

Izvestia Ufimskogo Nauchnogo Tsentra RAN ◽

10.31040/2222-8349-2020-0-4-19-24 ◽

2020 ◽

Vol 0 (4) ◽

pp. 19-24

Author(s):

I.M. UTYASHEV ◽

◽

A.A. AITBAEVA ◽

A.A. YULMUKHAMETOV ◽

◽

...

Keyword(s):

Cross Sectional Area ◽

Variable Cross ◽

Sectional Area ◽

Longitudinal Vibrations ◽

Cross Sectional ◽

Method Error ◽

Various Boundary Conditions ◽

Elastic Fixation ◽

Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

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Longitudinal oscillation of a rod with a variable cross section

Multiphase Systems ◽

10.21662/mfs2019.2.019 ◽

2019 ◽

Vol 14 (2) ◽

pp. 138-141

Author(s):

I.M. Utyashev

Keyword(s):

Cross Section ◽

Natural Frequencies ◽

Liouville Problem ◽

Variable Cross Section ◽

Variable Cross ◽

Longitudinal Vibrations ◽

Cross Sectional ◽

Independent Functions ◽

The Cross ◽

The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

International Journal of Modern Physics E ◽

10.1142/s021830130801194x ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 304-317

Author(s):

Y. M. ZHAO

Keyword(s):

Ground State ◽

Collective Motion ◽

Regular Structure ◽

Positive Parity ◽

Many Body ◽

Random Interactions ◽

Atomic Nuclei ◽

Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

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