Master formula for evaluating vibration frequencies of structural members under compressive loads

Rao, G. Venkateswara; Ratnam, B. Subba; Gunda, Jagadish Babu; Janardhana, G. Ranga

doi:10.1080/19373260.2011.555464

Cited by 7 publications

(5 citation statements)

References 15 publications

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“…The formulations used for the development of these formulae, though belong to the class of eigenvalue problems in structural mechanics, are different. For the large amplitude vibration problem, the methodology used to obtain the heuristic formula to study the initially loaded free vibrations of structural members [13], is the basis. Whereas, the procedure followed to obtain the heuristic formula for the postbuckling analysis is from the physical phenomenon involved, when the structural members are at the on set of (thermal) buckling and the effect of further increase of the (thermal) compressive load developed, by increasing the applied uniform temperature from the buckling temperature.…”

Section: Heuristic Formulaementioning

confidence: 99%

“…The development of the heuristic formula for the evaluation of the large amplitude vibration problem is based on the suitable modification of the work of Rao et al [13], in which the linear vibration behavior of the structural members with the initial end axial or normal edge inplane loads. Without going into the finer details of the work presented in Ref.…”

Section: Large Amplitude Vibration Problemmentioning

confidence: 99%

“…Without going into the finer details of the work presented in Ref. [13], the development of the heuristic formula for the large amplitude vibration problem is presented here. The formula developed for the linear vibration of the initially loaded structural member is…”

Section: Large Amplitude Vibration Problemmentioning

confidence: 99%

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Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

Venkateswara Rao,

Konda Reddy,

Subba Rao

2023

joast

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In the deign of the modern aerospace structural members, due the stringent requirement of light weight and low margins of safety, it is essential to establish the design adequacy by evaluating the stiffness related behavior, like the large lateral amplitude/deflection vibration and postbuckling, through a rigorous geometric nonlinear analysis. Though many complex formulations, either by using the continuum or numerical methods are available in the literature, the heuristic formulae developed recently, for these entirely different nonlinear problems, are similar. Hence, it is possible to unify, these simple formulae, not recognized till now. The unification of these formulae facilitates to obtain the solution for the large amplitude vibration problem from the known solution of the postbuckling of the structural members and vice versa, for a specified lateral amplitude/deflection. This novel concept of the unification is successfully demonstrated through the isotropic uniform beams/columns and thin square plates.

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Section: Heuristic Formulaementioning

confidence: 99%

Section: Large Amplitude Vibration Problemmentioning

confidence: 99%

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Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

Venkateswara Rao,

Konda Reddy,

Subba Rao

2023

joast

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“…In the novel FE formulation, the value of induced tensile load parameter λ λ λ λ t in the column, is treated as a constant initial tensile load acting along its length, and following non-dimensional matrix equilibrium equation is obtained [16], as…”

Section: Novel Fe Formulationmentioning

confidence: 99%

Thermal Postbuckling of Heated Uniform Columns Considering Green Nonlinearity: A Novel Liner Finite Element Formulation

Venkateswara Rao,

Kartikeyan,

Durga Rao

et al. 2023

joast

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Thermal postbuckling behavior of uniform, heated columns is presented, by using a novel linear Finite Element (FE) formulation. In this investigation, the general Green axial nonlinear strain- displacement relation is used, instead of the popularly used simpler von-Karman nonlinearity, which is a subset of Green nonlinearity. In the earlier complex nonlinear FE formulations, time consuming iterative or step-by-step methods are used to obtain the solution for thermal postbuckling. In the novel FE formulation, normally used FES , for performing linear buckling analysis, is proposed to obtain thermal postbuckling loads. The nodal degrees of freedom are deflection and its first derivative with respect to the axial coordinate. The geometric nonlinearity is incorporated through the tensile loads induced, with axially restrained ends of the column, due to large deflections. The effectiveness of the novel FE formulation is demonstrated, from the numerical results obtained, in terms of the ratio of thermal postbuckling to buckling loads, for specified reference deflection and slenderness ratios, of the columns with different boundary conditions. The numerical results reveal some interesting phenomena of thermal postbuckling behavior of columns.

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“…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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Master formula for evaluating vibration frequencies of structural members under compressive loads

Cited by 7 publications

References 15 publications

Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

Unification of Large Amplitude Vibration and PostBuckling Behavior of Structural Members

Thermal Postbuckling of Heated Uniform Columns Considering Green Nonlinearity: A Novel Liner Finite Element Formulation

Dynamic Stability of Beam on Elastic Foundation Including Higher Transition Foundation

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