YAPAY SİNİR AĞLARI YAKLAŞIMI İLE BOYLAMASINA TİTREŞİMİN TRANSENDENTAL DENKLEMİN ÇÖZÜMÜ

Abstract

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.

Keywords

• Yapay Sinir Ağları (YSA),Boyuna Titreşim,Sonlu Elemanlar Yöntemi

An Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal Vibration

Abstract

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.

 

Keywords

• Artificial Neural Network (ANN),Longitudinal Vibration,Finite Element Method(FEM)

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