Convergence of the Rayleigh–Ritz Method for buckling analysis of arbitrarily configured I-section beam–columns

Özbaşaran, Hakan

doi:10.1007/s00419-019-01508-1

Cited by 8 publications

(5 citation statements)

References 46 publications

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“…If M � 0, equation (24) leads to expression (14), which in turn coincides with published results in the literature [3,16,20].…”

supporting

confidence: 88%

“…It is crucial to indicate that the expressions given in equations (24) and (26) can be applied not only to define the first natural frequency but also to establish the stability region based on equation f � 0 [1,2]. Considering the case of a beam with simply supported ends, from equation 24, the expression describing the stability region of the beam under end moment M and axial load F is as follows:…”

Section: Stability Of In-walled Beams Under Two External Loadsmentioning

confidence: 99%

“…is load is placed toward the tooth side at distance e from the blade axle, as illustrated in Figure 6. erefore, the saw blade (or thin-walled beam) is actually subjected to load F 0 and moment M � F • e. Substituting M � − F 0 • e and F 0 � − F equations (24) and (26), the first natural frequency of the blade can be determined appropriately.…”

Section: Application To the Vibration And Stability Analyses Of Saw Bmentioning

confidence: 99%

“…In this paper, we focus on developing analytical expressions to determine the first natural frequency of a thin-walled beam subjected to an axial load and end moment. Two problem-solving approaches are investigated; one is based on the root existence theorem and the other uses an energy method, in this case the Rayleigh method [22][23][24]. e paper shows the effects of several parameters, such as the geometry and the material properties of a beam, and the external loads on the value of the first natural frequency.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Flexural‐Torsional Vibration of Thin‐Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

Phung

Nguyen

Dang

et al. 2019

Shock and Vibration

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The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

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“…If M � 0, equation (24) leads to expression (14), which in turn coincides with published results in the literature [3,16,20].…”

supporting

confidence: 88%

Section: Stability Of In-walled Beams Under Two External Loadsmentioning

confidence: 99%

Section: Application To the Vibration And Stability Analyses Of Saw Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Flexural‐Torsional Vibration of Thin‐Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

Phung

Nguyen

Dang

et al. 2019

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…They used sine functions or cosine functions depending on the boundary conditions considered. Ozbasaran evaluated the buckling analysis of the I-section prismatic beam-columns [15]. They considered three different series of admissible functions, namely power, trigonometric, and exponential trial functions.…”

Section: Introductionmentioning

confidence: 99%

Choosing the Best Functions for the Rayleigh-Ritz Vibration Analysis of Beams

Mochida,

Eisenberger

2024

EPI-IJE

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The Rayleigh-Ritz Method is used extensively for the vibration analysis of structures. The accuracy depends on the assumed functions. In this work several different groups of functions are examined and compared for the accuracy of the resulting natural frequencies, and for the overall mode shape error norms calculated with respect to the known exact solutions. It is concluded that a set that combines low order polynomials, odd cosine and odd sine functions, or, even cosine and even sine functions, is more likely to yield the best accuracy and convergence of both frequency and mode shapes for a general beam structure.

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Rayleigh quotient and orthogonality in the linear space of boundary functions, finding accurate upper bounds of natural frequencies of non-uniform beams

Liu

2020

Arch Appl Mech

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Convergence of the Rayleigh–Ritz Method for buckling analysis of arbitrarily configured I-section beam–columns

Cited by 8 publications

References 46 publications

Flexural‐Torsional Vibration of Thin‐Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

Flexural‐Torsional Vibration of Thin‐Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

Choosing the Best Functions for the Rayleigh-Ritz Vibration Analysis of Beams

Rayleigh quotient and orthogonality in the linear space of boundary functions, finding accurate upper bounds of natural frequencies of non-uniform beams

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