### Abstract

The paper discusses the impact of the von Kármán type geometric nonlinearity introduced to a mathematical model of beam vibrations on the amplitude-frequency characteristics of the signal for the proposed mathematical models of beam vibrations. An attempt is made to separate vibrations of continuous mechanical systems subjected to a harmonic load from noise induced by the nonlinearity of the system by employing the principal component analysis (PCA). Straight beams lying on Winkler foundations are analysed. Differential equations are obtained based on the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Levinson-Reddy hypotheses. Solutions to linear and nonlinear differential equations are found using the principal component analysis (PCA).

Original language | English |
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Article number | 3038179 |

Journal | Advances in Mathematical Physics |

Volume | 2017 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Advances in Mathematical Physics*,

*2017*, [3038179]. https://doi.org/10.1155/2017/3038179