<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/7985_125_1_auom_26_1.jpg"></inline-graphic> subjected to the boundary conditions <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/7985_125_2_auom_26_1.jpg"></inline-graphic> To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]). </p></abstract>

The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered  subjected to the boundary conditions  To approximate the solution of the this problem, we use the method of Newton interpolating series (see [6]) and the Taylor series method (see [8]).

Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The paper is based on the analytical and experimental results from [14], [15] and reveals, by mathematical methods, the degradation of ma- terial stifiness due...

Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

Published Online: Mar 31, 2018

Page range: 125 - 139

Received: Jan 08, 2017

Accepted: Sep 11, 2017

DOI: https://doi.org/10.2478/auom-2018-0008

Keywords
Beam, Vibration, Analytical solution

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Transverse vibrations analysis of a beam with degrading hysteretic behavior by using Euler-Bernoulli beam model

Published Online: Mar 31, 2018

Page range: 125 - 139

Received: Jan 08, 2017

Accepted: Sep 11, 2017

DOI: https://doi.org/10.2478/auom-2018-0008

KeywordsBeam, Vibration, Analytical solution

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Beam, Vibration, Analytical solution