SimMechanics ile Esnek Bir Yapının Modellenmesi ve Titreşim Sönümlemesi

Öz

Bu çalışmada, SimMechanics'te esnek bir kirişin modellenmesi ve simülasyonu incelenmiş ve ardından ANSYS'te sonlu elemanlar (FE) modeli ile titreşim sonuçları doğrulanmıştır. MATLAB'de SimMechanics tabanlı esnek kiriş modeli oluşturulurken, FE modeli ANSYS'de kurulmuştur. Sistemin girdileri, bir kuvvet tabanlı uyarıcı ve bozucu kuvvet olarak belirlenir. Sistemin çıkışları, esnek kirişin uç noktasındaki yer değiştirme ve ivme sinyalleri olarak seçilir. Sönümsüz doğal frekanslar, ANSYS'de modal analiz ve MATLAB'da frekans analizi ile belirlenir. Titreşim cevaplarını elde etmek için geçici analizler yapılır. Açık döngü cevapları için, yer değiştirme ve ivme titreşim sonuçları, adım ve harmonik uyarılar kullanılarak doğrulanır. Uç nokta konumunu kontrol etmek için FE ve SimMechanics modellerine PID kontrolörlü kapalı döngü kontrol uygulanır. Açık ve kapalı döngü titreşim sonuçları, farklı kontrolör kazançları için belirlenmiştir. Açık ve kapalı döngü sonuçlarının, FE modeli ve SimMechanics ile başarılı bir şekilde eşleştirildiği gözlemlenmiştir. SimMechanics tabanlı esnek kiriş modelinin doğruluğu FE modeli ile doğrulanmıştır.

Anahtar Kelimeler

• Esnek kiriş modeli
• Sonlu elemanlar modeli
• Harmonik uyarım
• SimMechanics

Modeling and Vibration Suppression of a Flexible Structure in SimMechanics

Abstract

In this work, modeling and simulation of a flexible cantilever beam are investigated in SimMechanics and then, vibration results are verified with the finite element (FE) model in ANSYS. Flexible beam model based on SimMechanics is created in MATLAB, while the FE model is established in ANSYS. In the system, inputs are determined as a force base actuator and disturbance force. Outputs of the system are selected as displacement and acceleration responses at the endpoint of flexible beam. Undamped natural frequencies are determined by modal analysis in ANSYS and frequency analysis in MATLAB. Transient analyses are achieved to obtain the vibration responses. For the open loop responses, the displacement and acceleration vibration results are verified using step and harmonic excitations. The closed-loop control with PID controller is applied to the FE and SimMechanics models to control the endpoint position. The open and closed-loop vibration results are indicated for different controller gains. It observed that open and closed-loop results are successfully matched well with the FE model and SimMechanics. The accuracy of flexible beam model based on SimMechanics is verified with the FE model.

Keywords

• Flexible beam model
• Finite element model
• Harmonic excitation
• SimMechanics

References

1. Alhazza, K. A., Nayfeh, A. H. and Daqaq, M. F. (2009) ‘On utilizing delayed feedback for active-multimode vibration control of cantilever beams’, Journal of Sound and Vibration. Academic Press, 319(3–5), pp. 735–752. doi: 10.1016/J.JSV.2008.06.052.
2. Altunışık, A. C., Okur, F. Y. and Kahya, V. (2017) ‘Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam’, Engineering Failure Analysis, 79(April), pp. 154–170. doi: 10.1016/j.engfailanal.2017.04.026.
3. Castel, A., Vidal, T. and François, R. (2012) ‘Finite-Element Modeling to Calculate the Overall Stiffness of Cracked Reinforced Concrete Beams’, Journal of Structural Engineering, 138(7), pp. 889–898. doi: 10.1061/(asce)st.1943-541x.0000520.
4. Chen, L. X., Cai, G. P. and Pan, J. (2009) ‘Experimental study of delayed feedback control for a flexible plate’, Journal of Sound and Vibration. Academic Press, 322(4–5), pp. 629–651. doi: 10.1016/J.JSV.2008.11.045.
5. Donà, M. et al. (2015) ‘An efficient two-node finite element formulation of multi-damaged beams including shear deformation and rotatory inertia’, Computers and Structures, 147, pp. 96–106. doi: 10.1016/j.compstruc.2014.10.002.
6. Lin, H. P. (2004) ‘Direct and inverse methods on free vibration analysis of simply supported beams with a crack’, Engineering Structures, 26(4), pp. 427–436. doi: 10.1016/j.engstruct.2003.10.014.
7. Meirovitch L (2001) Fundamentals ofVibrations. International Edition. New York: McGraw-Hill.
8. Mirafzal, S. H., Khorasani, A. M. and Ghasemi, A. H. (2016) ‘Optimizing time delay feedback for active vibration control of a cantilever beam using a genetic algorithm’, JVC/Journal of Vibration and Control, 22(19), pp. 4047–4061. doi: 10.1177/1077546315569863.

9. Shafiei, M. and Khaji, N. (2011) ‘Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject’, Acta Mechanica, 97, pp. 79–97. doi: 10.1007/s00707-011-0495-x.
10. Simeng, L. et al. (2016) ‘Mode-specific damage identification method for reinforced concrete beams: Concept, theory and experiments’, Construction and Building Materials, 124(2016), pp. 1090–1099.
11. Whalen, T. M. (2008) ‘The behavior of higher order mode shape derivatives in damaged, beam-like structures’, Journal of Sound and Vibration, 309(3–5), pp. 426–464. doi: 10.1016/j.jsv.2007.07.054.
12. Won, H. I., Lee, B. and Chung, J. (2018) ‘Stick-slip vibration of a cantilever beam subjected to harmonic base excitation’, Nonlinear Dynamics. Springer Netherlands, 92(4), pp. 1815–1828. doi: 10.1007/s11071-018-4164-7.
13. Zeng, J. et al. (2017) ‘Dynamic characteristic analysis of cracked cantilever beams under different crack types’, Engineering Failure Analysis. Elsevier Ltd, 74, pp. 80–94. doi: 10.1016/j.engfailanal.2017.01.005.