# Vibration analysis of a magneto-elastic beam with general boundary conditions subjected to axial load and external force

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### Cites methods from "Vibration analysis of a magneto-ela..."

...(1998) and Liu and Chang (2005). Here the approximate solution of this equation is obtained using the first-order method of multiple scales as given later....

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7,315 citations

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...Generation of characteristic orthogonal polynomials Given a polynomial f1ðxÞ, an orthogonal set of polynomials in the interval apxpb can be generated by using a Gram–Schmidt process stated below [10,11]: f2ðxÞ 1⁄4 ðx B2Þf1ðxÞ, (3) fkðxÞ 1⁄4 ðx BkÞfk 1ðxÞ Ckfk 2ðxÞ, (4) Bk 1⁄4 Z L...

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3,151 citations

### Additional excerpts

...Generation of characteristic orthogonal polynomials Given a polynomial f1ðxÞ, an orthogonal set of polynomials in the interval apxpb can be generated by using a Gram–Schmidt process stated below [10,11]: f2ðxÞ 1⁄4 ðx B2Þf1ðxÞ, (3) fkðxÞ 1⁄4 ðx BkÞfk 1ðxÞ Ckfk 2ðxÞ, (4) Bk 1⁄4 Z L...

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805 citations

432 citations

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...Mathematical modeling Hamilton’s principle [9] is adopted to derive the equation of motion [8] of the beam as follows: m qy qt2 þ Cd qy qt þ EI q y qx4 þ ky þ P q y qx2 1⁄4 f ðx; tÞ þ qc qx þ q qx Z x...

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315 citations