Vibration of thin pre-twisted helical beams

Leung, A.Y.T.

doi:10.1016/j.ijsolstr.2010.01.005

Cited by 9 publications

(4 citation statements)

References 28 publications

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“…With using the Frenet triad and its special differential can be derived the displacement vector gradient of an out of plane curved beam as follows 27 :…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

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RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Marvi

Ghadiri

2020

Sci Rep

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the DnA molecule is the most evolved and most complex molecule created by nature. the primary role of DnA in medicine is long-term storage of genetic information. Genetic modifying is one of the most critical challenges that scientists face. On the other hand, it is said that under the influence of acoustic, electromagnetic, and scalar waves, the genetic code of DnA can be read or rewritten. in this article, the most accurate and comprehensive dynamic model will be presented for DnA. each of the two strands is modeled with an out of plane curved beam and then by doubling this two strands with springs, consider the hydrogen bond strength between this two strands. Beams are traditionally descriptions of mechanical engineering structural elements or building. However, any structure such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contain beam structures that are designed to carry lateral loads are analyzed similarly. Also, in this model, the mass of the nucleobases in the DNA structure, the effects of the fluid surrounding the DNA (nucleoplasm) and the effects of temperature changes are also considered. finally, by deriving governing equations from Hamilton's principle method and solving these equations with the generalized differential quadrature method (GDQM), the frequency and mode shape of the DNA is obtained for the first time. In the end, validation of the obtained results from solving the governing equations of mathematical model compared to the obtained results from the coMSoL software is confirmed. By the help of these results, a conceptual idea for controlling cancer with using the DnA resonance frequency is presented. this idea will be presented to stop the cancerous cell's protein synthesis and modifying DnA sequence and genetic manipulation of the cell. on the other hand, by the presented DnA model and by obtaining DnA frequency, experimental studies of the effects of waves on DNA such as phantom effect or DNA teleportation can also be studied scientifically and precisely.

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“…With using the Frenet triad and its special differential can be derived the displacement vector gradient of an out of plane curved beam as follows 27 :…”

Section: Nonlocal Elasticity Theorymentioning

confidence: 99%

“…A.Y.T. Leung is the only reference derived from the governing equations for a helical beam with rectangular cross-sections with pre-twist 27 .…”

mentioning

confidence: 99%

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

Marvi

Ghadiri

2020

Sci Rep

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“…The governing equations and the associated natural boundary conditions of a pretwisted helical beam with noncircular cross-sections have been derived in Leung (2010) from differential geometry and variational principles. For isotropic materials, the formulation was identical to the existing literature for helical beam with circular cross-sections.…”

mentioning

confidence: 99%

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

Kobelev

2014

Multidiscipline Modeling in Materials and Structures

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Purpose -The purpose of this paper is to address the practically important problem of the load dependence of transverse vibrations for helical springs. At the beginning, the author develops the equations for transverse vibrations of the axially loaded helical springs. The method is based on the concept of an equivalent column. Second, the author reveals the effect of axial load on the fundamental frequency of transverse vibrations and derive the explicit formulas for this frequency. 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 is demonstrated. Finally, when the frequency nullifies, the side buckling spring occurs. Design/methodology/approach -Helical springs constitute an integral part of many mechanical systems. A coil spring is a special form of spatially curved column. The center of each cross-section is located on a helix. The helix is a curve that winds around with a constant slope of the surface of a cylinder. An exact stability analysis based on the theory of spatially curved bars is complicated and difficult for further applications. Hence, in most engineering applications a concept of an equivalent column is introduced. The spring is substituted for the simplification of the basic equations by an equivalent column. Such a column must account for compressibility of axis and shear effects. The transverse vibration is represented by a differential equation of fourth order in place and second order in time. The solution of the undamped model equation could be obtained by separation of variables. The fundamental natural frequency of the transverse vibrations depends on the current length of the spring. Natural frequency is the function of the deflection and slenderness ratio. Is the fundamental natural frequency of transverse oscillations nullifies, the lateral buckling of the spring with the natural form occurs. The mode shape corresponds to the buckling of the spring with moment-free, simply supported ends. The mode corresponds to the buckling of the spring with clamped ends. The author finds the critical spring compression. Findings -Buckling refers to the loss of stability up to the sudden and violent failure of seed straight bars or beams under the action of pressure forces, whose line of action is the column axis. The known results for the buckling of axially overloaded coil springs were found using the static stability criterion. The author uses an alternative approach method for studying the stability of the spring. This method is based on dynamic equations. In this paper, the author derives the equations for transverse vibrations of the pressure-loaded coil springs. The fundamental natural frequency of the transverse vibrations of the column is proved to be the certain function of the axial force, as well as the variable length of the spring. Is the fundamental natural frequency of transverse oscillations turns to be to zero, is the lateral buckling of the spring occurs.Research limi...

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“…The current study aims to examine the vibration characteristics of an out-of-plane helical nanobeam, marking the first investigation of its kind. In order to authenticate our research, we conducted a comparison of our findings with those of Leung [9] at the macro level, with the selection of ea=0 (as shown in Table 2). It is assumed that the values of τ and κ are both equal to zero.…”

Section: Convergence Investigationmentioning

confidence: 99%

Auxetic Metamaterial Pre-twisted Helical Nanobeams: Vibrational Characteristics

Ghadiri,

Ahari,

Marvi

2023

Preprint

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The current investigation pertains to the vibrational characteristics of an out of plane helical nanobeam composed of auxetic material. This study marks the first instance of such an analysis. The Frenet-triad is a mathematical tool utilized to account for the impact of curvature, allowing for the dynamic alteration of the coordinate system and the precise definition of the location vector. In order to examine this model, the governing equations are formulated utilizing Timoshenko's beam theory and Eringen's nonlocal elasticity theory, and applying Hamilton's principle. The generalized differential quadrature method (GDQM) is employed to solve the governing equations under various boundary conditions. The present study validates the precision and effectiveness of the existing model through a comparison between the outcomes obtained from the simplified approach and the benchmark results reported in the literature. The findings reveal a satisfactory level of conformity between the two sets of results. Ultimately, the numerical outcomes are derived with a focus on exploring the impact of various factors such as inclination angle, auxetic rib length, curvatures, tortuosity, and pre-twists on the helical nanobeam. The findings of this work may be used as a benchmark for further investigations.

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Vibration of thin pre-twisted helical beams

Cited by 9 publications

References 28 publications

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

RETRACTED ARTICLE: A Mathematical Model for Vibration Behavior Analysis of DNA and Using a Resonant Frequency of DNA for Genome Engineering

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

Auxetic Metamaterial Pre-twisted Helical Nanobeams: Vibrational Characteristics

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