Effect of static axial compression on the natural frequencies of helical springs

Kobelev, Vladimir

doi:10.1108/mmms-12-2013-0078

Cited by 14 publications

(12 citation statements)

References 36 publications

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“…He derived the explicit formulas for the fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring. The reduction of frequency with the load was demonstrated by Kobelev (2014). In this study, similar to the Reference (Yıldırım, 2009a), it was shown that when the frequency nullifies the spring buckling occurs.…”

Section: Introductionsupporting

confidence: 84%

“…As it is well known, the critical buckling loads may also be determined in a dynamic manner (Yıldırım, 2012;Kobelev, 2014). In this method, for a given static axial load, from 0 P to cr P at which the fundamental frequency of the spring becomes zero, the fundamental frequencies of the spring are searched.…”

Section: Numerical Example For Buckling and Free Vibration With A Stamentioning

confidence: 99%

“…Kacar and Yıldırım (2016) presented natural frequencies and buckling loads of barrel, hyperboloidal and conical unidirectional composite helical springs with circular and rectangular sections. Kobelev (2014) studied the load dependence of transverse vibrations for helical springs by developing equations, which were represented by two coupled second order differential equations. Kobelev's (2014) method was based on the concept of an equivalent column.…”

Section: Introductionmentioning

confidence: 99%

“…Kobelev (2014) studied the load dependence of transverse vibrations for helical springs by developing equations, which were represented by two coupled second order differential equations. Kobelev's (2014) method was based on the concept of an equivalent column. He derived the explicit formulas for the fundamental natural frequency of the transverse vibrations of the spring depends on the variable length of the spring.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Axial Static Load Dependence Free Vibration Analysis of Helical Springs Based on the Theory of Spatially Curved Bars

Yıldırım¹

2016

Lat. Am. j. solids struct.

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This work addresses an accurate and detailed axial static load dependence linearly elastic free vibration analysis of cylindrical helical springs based on the theory of spatially curved bars and the transfer matrix method. For a continuous system, governing equations comprise coupled vibration modes namely transverse vibrations in two orthogonal planes, torsional and axial vibrations. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory and their effects on the frequencies are investigated. The effects of the initial stress resultants on the frequencies are also studied. After buckling, forward-shifting phenomenon of higher frequencies is noticeably demonstrated. It is also revealed that a free/forced vibration analysis with an axial static load should not be performed individually without checking buckling loads.

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Section: Introductionsupporting

confidence: 84%

Section: Numerical Example For Buckling and Free Vibration With A Stamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Axial Static Load Dependence Free Vibration Analysis of Helical Springs Based on the Theory of Spatially Curved Bars

Yıldırım¹

2016

Lat. Am. j. solids struct.

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“…[33]. The Haringx model was also used in study [34] to determine the natural frequencies of transverse vibrations of a simply supported spring. It was pointed out, in [35], that the above-mentioned equivalent rod concept, proposed in [22] for the analysis of elastic stability of helical springs, can also be applied in the analysis of natural transverse vibrations of helical springs.…”

Section: Introductionmentioning

confidence: 99%

Natural transverse vibrations of helical springs in sections covered with elastic coatings

Michalczyk

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. It has been demonstrated in previous studies that local elastomer coatings covering the end coils of helical springs can efficiently reduce the amplitudes of circum-resonant vibrations in such springs. The analysis of the influence that elastic coatings have on the frequencies and modes of natural transverse vibrations of springs is presented in this paper. The concept of the equivalent beam of the Timoshenko type is utilized in calculations of the frequencies and modes of transverse vibrations. The model developed allows users to determine the frequencies and modes of symmetric as well as antisymmetric vibrations of axially loaded springs with elastic coatings of arbitrary length. A comparison of the results obtained using FEM analysis, in which the model represented the actual spring geometry, with the results obtained by means of the presented model indicates its high accuracy. model of a spatially curved rod, the model of an equivalent rod or beam, and the model in which a continuous system, such as a spring, is substituted by a discrete-periodic system consisting of concentrated masses joined by a mass-less stiffness, jointly representing one spring coil or its fragment. Equations of motion are written for an elementary fragment of a spring wire in the first model. Such a formulation of the problem [12, 13] allows arbitrary modes and frequencies of spring vibrations to be determined, however, solving it by analytical methods is very difficult and therefore such a solution is not suitable in practical applications. These difficulties mean that in several studies concerning the analysis of spring vibrations treated as a spatially curved rod, the authors use numerical methods. New finite elements, capable of modeling spring coils or their fragments were proposed in [14]. They are suitable for application in static problems as well as when looking for natural frequencies of helical springs. Mottershead provided, in the above-mentioned paper, experimental results later utilized by other authors. A similar approach to the problems of helical springs was presented in [15][16][17]. Pearson expanded -in [18] -equations provided by Wittrick [13], taking into account the influence of a static axial force. For determining natural vibrations, he applied the transfer matrix method. The same method was used in [19], concerning the analysis of parameters influencing natural frequencies of helical springs (utilizing the Cayley-Hamilton theorem), and in [20]. In this last paper, the authors compared their results with the results obtained on the basis of the Haringx model [21]. They pointed out that, in the case of helical springs with geometrical parameters, typical of springs used in machine buildings, the conformity between the results obtained by them and the results obtained using the Haringx model is high. In the numerical example quoted by them, for which the first 16 natural frequencies were determined, the maximum difference between their results and the ones from the Haringx model did not exceed 1.3%. In ...

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“Equivalent Columns” for Helical Springs

Kobelev¹

2021

Durability of Springs

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Effect of static axial compression on the natural frequencies of helical springs

Cited by 14 publications

References 36 publications

Axial Static Load Dependence Free Vibration Analysis of Helical Springs Based on the Theory of Spatially Curved Bars

Axial Static Load Dependence Free Vibration Analysis of Helical Springs Based on the Theory of Spatially Curved Bars

Natural transverse vibrations of helical springs in sections covered with elastic coatings

“Equivalent Columns” for Helical Springs

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