Dynamic stability of short cantilever columns subjected to distributed axial loads

Shastry, B.P.; Rao, G. Venkateswara

doi:10.1016/0045-7949(86)90166-5

Cited by 17 publications

(5 citation statements)

References 3 publications

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“…By using the finite element method, Shastry and Rao [8][9] investigated the dynamic stability of bars considering shear deformation and rotator inertia, and dynamic stability of short cantilever columns subjected to distributed loads. Briseghella et al [10] studied the dynamic stabilities of several simple-beam structures.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

Shen

Que

2023

Preprint

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The parametric resonance of a frame structure may lead to a disastrous consequence. Structural engineers need a straightforward and practical method to calculate the large nonlinear parametric resonance responses of the frame structure for assessing structural safety. This paper reports on a new Vector Form Intrinsic Finite Element (VFIFE) method to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a relationship between internal nodal forces and deformation components is firstly established based on the VFIFE principle and the parametric resonance mechanism of frame structures. The VFIFE scheme is then developed to analyse the nonlinear parametric resonance of frame structures. To demonstrate the efficacy of this approach, a simply-supported beam is used as a numerical example, and the resulting VFIFE calculations are compared to the solutions obtained by current analytical methods. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that this approach can overcome the limitations of existing analytical methods, well simulate the nonlinear phenomena of parametric resonances, and produce predictions that are consistent with experimental observations. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE method is a simple and effective means of analyzing the stability and nonlinear responses of parametric resonance of planar beam structures.

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Section: Introductionmentioning

confidence: 99%

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

Shen

Que

2023

Preprint

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“…In fact, the majority of works on the dynamic stability of structures have been founded on a finite element approach (Brown et al, 1968). Some improvements, always using the finite element method, can be found in Shastry and Rao (1984), where shear deformation and rotatory inertia of the beam were taken into account, and in Shastry and Rao (1986), where the effect of distributed axial load was included.…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of elastically constrained beams: an exact approach

Majorana

Pellegrino

1997

Engineering Computations

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In this paper a simple and exact procedure that allows the exact solution of the equation of boundary frequencies to be found, i.e. to integrate in an exact form the equation of the motion of beams subject to dynamic loads, is shown. With this procedure the regions of instability of beams generically restrained at the end cross-sections are found. Analysing the results obtained, it can be clearly observed that if the stiffness of the springs increases, the regions of instability shift to higher frequencies of vibration, in accordance with the results obtained previously. The method is a valuable tool for knowing in advance or for verifying the regions of instability of complex structures analysed by a finite element method, reduced to simple beams with springs at the end cross-sections

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“…For any other nondimensionalization of these basic quantities, a series of dynamic stability curves will be obtained and are relatively difficult for proper understanding of the dynamic stability behavior. A few studies on the dynamic stability for some column boundary conditions based on [3] can be seen [4,5] with the same nondimensionalization and obtain the master dynamic instability regions in either the analog or digital forms. The numerical results presented in these studies [3][4][5] show the near invariance of the dynamic instability boundaries.…”

mentioning

confidence: 99%

“…A few studies on the dynamic stability for some column boundary conditions based on [3] can be seen [4,5] with the same nondimensionalization and obtain the master dynamic instability regions in either the analog or digital forms. The numerical results presented in these studies [3][4][5] show the near invariance of the dynamic instability boundaries. Some recent studies on this topic for plates and shells can be seen with different nondimensionalizations [6,7] and hence the problem of analyzing a number of dynamic instability curves as follows.…”

mentioning

confidence: 99%

“…1) To prove rigorously the similarity of the mode shapes required in arriving at the intuitive nondimensionalization [3] followed in [4,5], 2) to derive a simple and accurate formula (master dynamic stability formula) for predicting the dynamic stability behavior of most of the structural members where the mode shapes of the fundamental frequency and the buckling load are the same or nearly the same, subjected to an end or edge periodic axial or in-plane loads, respectively, 3) to show the effectiveness of the master dynamic stability formula with reference to the column, plate, and shell problems, and 4) to establish the invariance of the stability regions, using the nondimensional parameters derived here in the clear mathematical sense.…”

mentioning

confidence: 99%

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Master Dynamic Stability Formula for Structural Members Subjected to Periodic Loads

Rao¹,

Ratnam

Janardhan

2008

AIAA Journal

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Nomenclature G = system geometric stiffness matrix K = system stiffness matrix M = system mass matrix N = axial or in-plane compressive periodic load N cr = buckling load N s = constant part of N N t = periodic part of N = N s =N cr = N t =N cr fg = as given in Eq. (7) f 1 g = eigenvector of the dynamic stability problem f 2 g = eigenvector of the free vibration problem f 3 g = eigenvector of the buckling problem = radian frequency of N t = as defined in Eq. (12) = =! ! = natural radian frequency

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Dynamic stability of short cantilever columns subjected to distributed axial loads

Cited by 17 publications

References 3 publications

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

Dynamic stability of elastically constrained beams: an exact approach

Master Dynamic Stability Formula for Structural Members Subjected to Periodic Loads

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