Principal Component Analysis in the Nonlinear Dynamics of Beams

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

A. V. Krysko, Jan Awrejcewicz, Irina V. Papkova, Olga Szymanowska, V. A. Krysko

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Article number3038179
JournalAdvances in Mathematical Physics
Volume2017
DOIs
Publication statusPublished - 1 Jan 2017

Fingerprint

principal components analysis
Purification
purification
Principal component analysis
Nonlinear Dynamics
Principal Component Analysis
Differential equations
Vibration
nonlinearity
Nonlinearity
Mathematical models
vibration
mathematical models
differential equations
Mathematical Model
Geometric Nonlinearity
Continuous System
Bernoulli
Linear differential equation
Mechanical Systems

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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.

In: Advances in Mathematical Physics, Vol. 2017, 3038179, 01.01.2017.

Research output: Contribution to journalArticle

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