### 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

**Principal Component Analysis in the Nonlinear Dynamics of Beams : Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations.** / Krysko, A. V.; Awrejcewicz, Jan; Papkova, Irina V.; Szymanowska, Olga; Krysko, V. A.

Research output: Contribution to journal › Article

*Advances in Mathematical Physics*, vol. 2017, 3038179. https://doi.org/10.1155/2017/3038179

}

TY - JOUR

T1 - Principal Component Analysis in the Nonlinear Dynamics of Beams

T2 - Purification of the Signal from Noise Induced by the Nonlinearity of Beam Vibrations

AU - Krysko, A. V.

AU - Awrejcewicz, Jan

AU - Papkova, Irina V.

AU - Szymanowska, Olga

AU - Krysko, V. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85011617169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85011617169&partnerID=8YFLogxK

U2 - 10.1155/2017/3038179

DO - 10.1155/2017/3038179

M3 - Article

VL - 2017

JO - Advances in Mathematical Physics

JF - Advances in Mathematical Physics

SN - 1687-9120

M1 - 3038179

ER -