| | | |

## entrAn Artificial Neural Network (ANN) Approach for Solution of the Transcendental Equation of Longitudinal VibrationYAPAY 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.

• Akgöz B. and Civalek, Ö. (2013) “Longitudinal vibration analysis of strain gradient bars made of functionally graded materials,” Compos B Eng. 2013, vol. 55, pp. 263-268. doi:10.1016/j.compositesb.2013.06.035
• Avcar, M. (2010) “Free vibration of randomly and continuously non- homogenous beams with clamped edges resting on elastic foundation,” J Eng Sci Des. 2010, vol.1, pp. 33-38.
• Avcar, M. (2014) “Free vibration analysis of beams considering different geometric characteristics and boundary condition,” Int. Appl. Mech., vol.4, pp. 94-100.doi: 10.5923/j.mechanics.20140403.03
• Avcar, M., Saplıoğlu, K. (2015) “An Artificial Neural Network Application for Estimation of Natural Frequencies of Beams”, International Journal of Advanced Computer Science and Applications, Vol. 6, No. 6. doi:10.14569/IJACSA.2015.060614
• Bagdatli, S. M., Özkaya, E. Özyiğit, H. A. and Tekin, A. (2009) "Nonlinear vibrations of stepped beam systems using artificial neural networks," Struct Eng Mech., vol. 33, pp.15-30. doi:10.1177%2F1077546312463760
• Civalek, Ö. (2008) “Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT), by discrete singular convolution method,”Finite Elem Anal Des. 2008, vol. 44, pp. 725-731. doi: 10.1016/j.finel.2008.04.001
• Civalek, Ö. and Gürses, M. (2009) “Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique,” Int J Pres Ves Pip. 2009, vol. 86, pp. 677-683. doi: 10.1016/j.ijpvp.2009.03.011
• Çalışkan, M. (1993) “Modal analysis and numerical solutions of multi-degree-of-freedom vibration systems,” Graduate thesis, Trabzon.
• Ding, Z. C., Cao, M. S., Jia, H. L. , Pan, L. X. and Xu, H. (2014) “Structural dynamics-guided hierarchical neural-networks scheme for locating and quantifying damage in beam-type structures." J Vibroeng., vol. 16, pp. 3595-3608. doi: 10.1057/jors.2015.56
• Ece, M. C. ,Aydogdu, M. and V. Taskin, (2007) “Vibration of a variable cross-section beam” Mech Res Commun. 2007, vol. 34, pp. 78-84. doi: 10.1016/j.mechrescom.2006.06.005
• Flood, I., Christophilos, P. (1996) “Modeling construction processes using artificial neural networks,” Automation in Construction, Vol. 4, pp. 307-320
• Gates, R., Choi, M., Biswas, S.K., Helferty, J.J. (1993) “Stabilisation of flexible structures using artificial neural networks,” Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan), vol. 2, pp. 1817-1820. doi: 10.1109/IJCNN.1993.717007
• Hakim, S.J.S. ,Abdul Razak, H. , Ravanfar, S.A. (2014) " Adaptive Neuro Fuzzy Inference System (ANFIS) and Artificial Neural Networks (ANNs) for structural damage identification” Structural Engineering and Mechanics Volume 45, Number 6, March25 2013, pages 779-802. doi: :10.12989/sem.2013.45.6.779
• Hsieh J. C. and Plaut R. H. (1990) “Free vibrations of inflatable dams,” Acta Mech. 1990; vol. 85: pp. 207-220. doi: 10.1007/BF01181518
• Jeng, D.S. ,Cha, D. H and Blumenstein, M. (2014 ) "Application of Neural Network in Civil Engineering Problems,”
• Lazarevska, M. ,Knezevic, M.,Cvetkovska, M. ,Trombeva-Gavriloska, A. (2014)“Application of artificial neural networks in civil engineering,” Tehnički vjesnik ,21, 1353-1359.
• Leissa, A. W. and Qatu, M. S. (2011) “Vibration of Continuous Systems,” McGraw Hill Companies, 2011.
• Magrab, E. B. (1979) “Vibration of Elastic Structural Members,” Netherlands, Sijthoff and Noordhoff. doi: 10.1121/1.387167
• Nalbant, M., Gökkaya, H. , Toktaş, İ. ,Sur, G. (2009) “The experimental investigation of the effects of uncoated, PVD- and CVD-coated cemented carbide inserts and cutting parameters on surface roughness in CNC turning and its prediction using artificial neural networks,” Robotics and Computer-Integrated Manufacturing 25 (2009) 211–223. doi: 10.1016/j.rcim.2007.11.004
• Nezir, N. (2015) “Introduction to Artificial Neural Networks,”.
• Özdemir, A.T. ,Toktaş,İ. (2008) “Contemporary analyses in assessing residual stress topographic images enclosing a cold expanded hole”Canadian Metallurgical Quarterly, Vol 47, No 1 pp 59-70, doi:10.1179/cmq.2008.47.1.59
• Rao, S.S. (2007) "Vibration Of Continuous Systems " John Wiley & Sons, Inc. Isbn: 978-0-471-77171-5
• Stokey, W. F. (2002) “Vibration of systems having distributed mass and elasticity,”Harris shock and vibration handbook, Chapter 7, McGraw-Hill, 5th edition.
• Şimşek, M. and Kocatürk, T. (2007) “Free vibration analysis of beams by using a third order shear deformation theory,” Sadhana Acad Proc Eng Sci. 2007, vol. 32, pp. 167-179.
• Toktaş, İ., Başak H. (2009) “Chain Gear Design Using Artificial Neural Networks" Wiley Periodicals, Inc. Comput Appl Eng Educ 20: 38-44, doı: 10.1002/cae.20371
• Timoshenko, S. P. (1937) “Vibration Problems in Engineering,” D. Van Nostrand, Princeton, NJ.
• Yeşilce, Y. (2015) “Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and rotary inertias,” Struct Eng Mech., vol. 53, pp. 537-573. doi: 10.12989/sem.2015.53.3.537
Birincil Dil en Mühendislik Araştırma Makaleleri Orcid: 0000-0002-6087-3837Yazar: Gözde Rabia AKTAŞ (Sorumlu Yazar)Kurum: ULUDAĞ ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-8151-9343Yazar: Abdullah EMUL (Sorumlu Yazar)Kurum: ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0002-9751-6665Yazar: Sadettin ORHAN (Sorumlu Yazar)Kurum: ANKARA YILDIRIM BEYAZIT ÜNİVERSİTESİÜlke: Turkey 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 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.