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Nonlinear forced vibration analysis of clamped functionally graded beams. (English) Zbl 1277.74033

The rapid growth of the research in functionally graded materials (FGM) is due to their continuously varying material properties which give great advantages over conventional homogeneous and layered materials. For example, a FGM consisting of metallic and ceramic components can improve both mechanic and thermo-mechanical properties of the system. The cracking and delamination observed in multi-layered systems are avoided due to smooth transition between the components in the FGM.
Here, the authors study free and forced vibrations of a nonlinear Euler-Bernoulli FGM beam with clamped ends. The analysis is performed using the von Kármán displacement-strain relationship. A cubic nonlinearity is involved on the first mode of vibration. The material properties vary exponentially or exhibit a power law distribution along the thickness direction. The dynamic equations of free and forced vibrations do not contain terms depending on velocity, so that the solutions cannot represent all properties of real processes because the resonance curve is limited.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E05 Inhomogeneity in solid mechanics
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References:

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