Apparently First Closed-Form Solution for Vibration of Functionally Graded Rotating Beams

Elishakoff, Isaac; Zaza, N.; Curtin, J.; Hashemi, Javad

doi:10.2514/1.j053033

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2022

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Cited by 7 publications

(1 citation statement)

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“…The solutions reported in this study can be extended to additional problems dealing with aerospace applications [35][36][37][38][39][40]. Specifically, this study extends the previous investigations reported in papers [7,[41][42][43]. It is hoped that some of the reported solutions could be extended to the nonlocal case as was conducted in Storch and Elishakoff [44].…”

Section: Discussionsupporting

confidence: 75%

Buckling of a column made of the functionally graded material with high-order polynomial mode shape

Elishakoff

Chotpatthamanon

Reddy

2022

Mathematics and Mechanics of Solids

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In this study, we investigate the buckling of a column made of functionally graded materials in axial direction. The column is simply supported at both ends. The mode shape is represented by a polynomial whose power is increased from four to nine; this power only restricted by the possibility of the hand- or symbolic-manipulation. It is shown that the solutions stemming from lower-order polynomial are all contained in the solution associated with higher-order polynomials. Numerous novel solutions are uncovered that could be used as benchmark solutions versus numerous approximate techniques available for eigenvalue problems.

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