Vibration Analysis of Micro-Damaged Plates with Riesz-Caputo Fractional Derivative

Year 2022, Volume: 22 Issue: 5, 989 - 997, 27.10.2022

Soner Aydınlık Ahmet Kırış

https://doi.org/10.35414/akufemubid.1070344

Abstract

In this study, with the help of Riesz Caputo fractional derivative definition, non-local analysis of micro-damaged plates are investigated by micro-elongation theory without defining the nonlocal kernels. The frequency spectrum and mode shapes of the microelongated plate with four clamped edges for different values of the fractional continua order and the material length scale parameter are carried out. 3-dimensional vibration analysis are done using the Ritz energy method. The main contribution of the study to the scientific literature is the demonstration that the nonlocal vibration analysis modeled with the concept of fractional derivative is a more suitable model than the classical theory and it fits better with the experimental results.

Keywords

Riesz-Caputo fractional derivative, Nonlocal plate vibration, Space-time fractional derivative, Microelongation theory

Mikro Hasarlı Plakların Riesz-Caputo Kesirli Türevi ile Titreşim Analizi

Abstract

Bu çalışmada Riesz Caputo kesirli türev tanımı yardımıyla, nonlokal çekirdekler tanımlamadan, mikrogenleşme teorisi ile modellenen mikro hasarlı plakların nonlokal titreşim analizi yapılmıştır. Dört ucu ankastre-“clamped” (CCCC) mikro hasarlı plağın frekans spektrumu ve mod şekilleri kesirli türev mertebesinin ve birim uyum katsayısının farklı değerleri için elde edilmiştir. 3-boyutlu titreşim analizi Ritz enerji yöntemi ile gerçekleştirilmiştir. Çalışmanın bilimsel literatüre temel katkısı, kesirli türev kavramıyla modellenen nonlokal titireşim analizinin klasik teoriye göre daha uygun bir model olduğunun ve deneysel sonuçlarla daha iyi örtüştüğünün gösterilmesidir.

Keywords

Riesz-Caputo kesirli türevi, Nonlokal plak titreşimi, Uzay-zaman kesirli türev, Mikrogenleşme teorisi

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