Finding closed-form solutions of beam vibration

Maróti, György

doi:10.1556/pollack.6.2011.1.13

Cited by 8 publications

(2 citation statements)

References 2 publications

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“…Remarkably, three different mode shapes were shown to be associated with the same buckling load in the clamped-free column case, whereas a single mode shape was presented with any other boundary condition. Ayadoglu [2], Ece et al [3], Calió' and Elishakoff [4], Li [5], Maroti [6], and Calio' et al [7] obtained other novel results inspired by the closed-form solution by Elishakoff and Endres [1].…”

Section: Introductionmentioning

confidence: 97%

Some Intriguing Results Pertaining to Functionally Graded Columns

Elishakoff

Miglis

2013

Journal of Applied Mechanics

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Some intriguing results are reported in conjunction with closed form solutions obtained for a clamped-free vibrating inhomogeneous column under an axial concentrated load using the semi-inverse method. Fourth order polynomial is postulated for both the vibration mode shape and buckling displacement. Solution is provided for the flexural rigidity and the natural fi'equency. It is shown that, for each level of axial loading, there may exist up to five flexural rigidities satisfying the governing differential equation and boundary conditions.

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Section: Introductionmentioning

confidence: 97%

Some Intriguing Results Pertaining to Functionally Graded Columns

Elishakoff

Miglis

2013

Journal of Applied Mechanics

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“…Only one exception has to be made, because the capital I in Maple is reserved for the imaginary unit, so the capital J is used instead. The detailed description of usage and programming of Maple can be found in [3] and [4], while [5] and [6] give examples of how Maple can be used in engineering calculations.…”

Section: Introductionmentioning

confidence: 99%

On buckling of axially functionally graded beams

Maróti¹,

Elishakoff²

2012

Pollack Periodica

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Abstract:In his study Aydogdu analyzed the vibration and buckling of axially functionally graded simply supported beams. By using pre-defined frequency and buckling loads he determined the Young's modulus in axial direction as a function of axial coordinate. In this study it is demonstrated that there is error in his calculation; moreover, corrected computation is presented and the right solution of the ODE is visualized. It is pointed out that the method used by Aydogdu is apparently not applicable for the solution of the problem at hand.

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Hysteresis in column systems

Iványi

2015

J. Phys.: Conf. Ser.

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Finding closed-form solutions of beam vibration

Cited by 8 publications

References 2 publications

Some Intriguing Results Pertaining to Functionally Graded Columns

Some Intriguing Results Pertaining to Functionally Graded Columns

On buckling of axially functionally graded beams

Hysteresis in column systems

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