Yıl 2019, Cilt 24 , Sayı 1, Sayfalar 161 - 170 2019-04-30

An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration
YAPAY SİNİR AĞLARI YAKLAŞIMI İLE BOYLAMASINA TİTREŞİMİN TRANSENDENTAL DENKLEMİN ÇÖZÜMÜ

Gözde Rabia AKTAŞ [1] , Abdullah EMUL [2] , Sadettin ORHAN [3]


Study of mechanical vibration is one of the major issues in engineering applications. Especially, during the design and test stages of a mechanical component or system, vibration must be considered. When a vibration issue is studied theoretically, a differential equation called characteristics equation or equation of motion (EOM) is obtained. A solution of EOM gives vibrational behavior of an object considered. When vibration of a continuous system is studied, a transcendental equation is finally obtained, whose solution by classical methods is not possible. In this study, the solution of the transcendental equation which is derived from the longitudinal vibration of a bar with one end fixed and a mass at the other end was presented. For this purpose, an ANN model was constructed and the datasets were created for the ANN model. The effects of the number of neurons, input data, and training function on the model were examined. In addition, multiple regression models were developed using the ANN data also natural frequency formulation was obtained by ANN analysis for each mode. A finite element modal analysis was performed by ANSYS software. The results obtained by ANN and ANSYS were compared with analytic calculation and it was shown that they were in enough agreement.

 

Mekanik titreşim konusu mühendislik uygulamalarındaki en önemli konulardan biridir. Özellikle, mekanik bileşenin veya sistemin dizayn ve test aşamaları boyunca titreşim dikkate alınmalıdır. Bir titreşim konusu teorik olarak çalışıldığında, özdenklem ya da diferansiyel denklem olarak isimlendirilen hareket denklemi elde edilir. Hareket denklemi, çözümü düşünülen cismin titreşim davranışını verir. Sürekli bir sistemin titreşimi çalışıldığında, sonuç olarak ‘transcendental denklem’ elde edilir. Transcendental denklemin çözümü klasik yöntemlerle mümkün değildir. Bu çalışmada, bir ucu sabitlenmiş ve diğer ucunda kütle taşıyan bir çubuğun boyuna titreşiminden elde edilen transcendental denklemin çözümü sunuldu. Bu amaçla, bir YSA modeli oluşturuldu ve bu modelde kullanılmak üzere veriler hazırlandı.  Modeldeki nöronlar, giriş verileri, eğitim fonksiyonlarının etkileri incelendi. Bununla birlikte, YSA verileri kullanılarak çoklu regresyon modelleri geliştirildi ayrıca her mod için ANN analizi ile doğal frekans formülasyonları elde edildi. Sonlu elemanlar modal analizi ANSYS kullanılarak yapıldı. YSA ve ANSYS’ten elde edilen sonuçlar analitik çözümle karşılaştırıldı ve hepsinin sonuçlarının oldukça yakın oldugu ortaya çıktı.


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Birincil Dil en
Konular Mühendislik
Bölüm Araştırma Makaleleri
Yazarlar

Orcid: 0000-0002-6087-3837
Yazar: Gözde Rabia AKTAŞ (Sorumlu Yazar)
Kurum: ULUDAĞ ÜNİVERSİTESİ
Ülke: Turkey


Orcid: 0000-0002-8151-9343
Yazar: Abdullah EMUL (Sorumlu Yazar)
Kurum: ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİ
Ülke: Turkey


Orcid: 0000-0002-9751-6665
Yazar: Sadettin ORHAN (Sorumlu Yazar)
Kurum: ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİ
Ülke: Turkey


Tarihler

Başvuru Tarihi : 27 Aralık 2018
Kabul Tarihi : 20 Şubat 2019
Yayımlanma Tarihi : 30 Nisan 2019

Bibtex @araştırma makalesi { uumfd504170, journal = {Uludağ University Journal of The Faculty of Engineering}, issn = {2148-4147}, eissn = {2148-4155}, address = {}, publisher = {Bursa Uludağ Üniversitesi}, year = {2019}, volume = {24}, pages = {161 - 170}, doi = {10.17482/uumfd.504170}, title = {An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration}, key = {cite}, author = {AKTAŞ, Gözde Rabia and EMUL, Abdullah and ORHAN, Sadettin} }
APA AKTAŞ, G , EMUL, A , ORHAN, S . (2019). An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration. Uludağ University Journal of The Faculty of Engineering , 24 (1) , 161-170 . DOI: 10.17482/uumfd.504170
MLA AKTAŞ, G , EMUL, A , ORHAN, S . "An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration". Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 161-170 <https://dergipark.org.tr/tr/pub/uumfd/issue/43494/504170>
Chicago AKTAŞ, G , EMUL, A , ORHAN, S . "An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration". Uludağ University Journal of The Faculty of Engineering 24 (2019 ): 161-170
RIS TY - JOUR T1 - An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration AU - Gözde Rabia AKTAŞ , Abdullah EMUL , Sadettin ORHAN Y1 - 2019 PY - 2019 N1 - doi: 10.17482/uumfd.504170 DO - 10.17482/uumfd.504170 T2 - Uludağ University Journal of The Faculty of Engineering JF - Journal JO - JOR SP - 161 EP - 170 VL - 24 IS - 1 SN - 2148-4147-2148-4155 M3 - doi: 10.17482/uumfd.504170 UR - https://doi.org/10.17482/uumfd.504170 Y2 - 2019 ER -
EndNote %0 Uludağ University Journal of The Faculty of Engineering An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration %A Gözde Rabia AKTAŞ , Abdullah EMUL , Sadettin ORHAN %T An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration %D 2019 %J Uludağ University Journal of The Faculty of Engineering %P 2148-4147-2148-4155 %V 24 %N 1 %R doi: 10.17482/uumfd.504170 %U 10.17482/uumfd.504170
ISNAD AKTAŞ, Gözde Rabia , EMUL, Abdullah , ORHAN, Sadettin . "An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration". Uludağ University Journal of The Faculty of Engineering 24 / 1 (Nisan 2019): 161-170 . https://doi.org/10.17482/uumfd.504170
AMA AKTAŞ G , EMUL A , ORHAN S . An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration. JFE. 2019; 24(1): 161-170.
Vancouver AKTAŞ G , EMUL A , ORHAN S . An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration. Uludağ University Journal of The Faculty of Engineering. 2019; 24(1): 170-161.