Master Formula for Geometrically Nonlinear Dynamic Instability of Shear Flexible Beams

Ratnam, B. Subba; Rao, G. Venkateswara; Janardhana, G. Ranga

doi:10.2514/1.j051524

Cited by 1 publication

(1 citation statement)

References 17 publications

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“…In this paper, it is demonstrated intuitively that, provided the stability and vibration mode forms are same, the dynamic stability bounds derived with adequate non-dimensional parameters are the equal regardless of the boundary conditions. In [3], it is suggested that these non-dimensional parameters may be rigorously determined, and for the majority of structural members, it is shown that there are master dynamic instability curves that are valid for all structural members, regardless of boundary condition or complicating effects. If the requirement of the exactness of the mode shapes, but not the similarity as mentioned in [2], is broken while trying to get the master dynamic stability curves, the error involved in the analysis is dependent on the deviation of these mode shapes and may be evaluated by calculating the corresponding L 2 norms [4].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

Subbaratnam

2024

Civil Engineering

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A precise analytical solution has been developed using Energy Method to predict the dynamic instability bounds of simply supported beams on elastic foundation, with a focus on the impact of the higher transition foundation on dynamic stability boundaries. To determine the dynamic instability zones, a trigonometric function with a single term that meets the geometric boundary criteria to represent lateral deflection is used. For the analysis, Euler-Bernoulli beam theory is employed. Numerical results are presented in non-dimensional form in both digital and/or analogue forms, with varying foundation parameters below and above the transition foundation values of an elastic foundation. When compared to those produced using the finite element approach, the current findings exhibit a fair degree of consistency. The impact of the elastic foundation’s first and higher transition foundation values on dynamic stability behavior is amply demonstrated in the current study. According to the studies, when the elastic foundation parameter value increases, the width of the dynamically unstable zones decreases, making the beam less susceptible to the dynamic stability phenomena under periodic loads. By using the precise non-dimensional parameters for the imposed periodic load and its radian frequency, the presence of the master dynamic instability curves is demonstrated in the current work.

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Section: Introductionmentioning

confidence: 99%

Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

Subbaratnam

2024

Civil Engineering

View full text Add to dashboard Cite

show abstract

Master Formula for Geometrically Nonlinear Dynamic Instability of Shear Flexible Beams

Cited by 1 publication

References 17 publications

Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

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