- Shiota I. and Miyamoto Y. eds., Functionally graded materials 1996. Elsevier, 1997.
- Fazelzadeh S.A. and Hosseini M., Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials. Journal of fluids and structures, Vol. 23, No.8, 1251-1264, 2007.
- Aydin K., Free vibration of functionally graded beams with arbitrary number of surface cracks. European Journal of Mechanics-A/Solids, Vol. 42, 112-124, 2013.
- Xue X. and Tang J., Vibration control of nonlinear rotating beam using piezoelectric actuator and sliding mode approach. Journal of Vibration and Control, Vol. 14, No.6, pp. 885-908, 2008.
- Tian J., Zhang Z. and Hua, H., Free vibration analysis of rotating functionally graded double-tapered beam including porosities. International Journal of Mechanical Sciences, Vol. 150, pp. 526-538, 2019.
- الهکرمی ف. و قصاب زاده سریزدی م.، تحلیل ارتعاشات آزاد پوسته استوانهای نازک و نسبتاً ضخیم مدرج تابعی دو جهتی بر اساس تئوری مرتبه اول تغییر شکل برشی. مهندسی مکانیک دانشگاه تبریز، د. 46، ش. 1، ص 15-28، 1394.
- Karamanli A., Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Composite Structures, Vol. 189, pp. 127-136, 2018.
- پیل افکن ر. و خواجه زاده س.، تحلیل ارتعاشی نانو تیر مگنتو الکترو الاستیک تیموشنکو با مدل معادلات انتگرال-دیفرانسیل. مهندسی مکانیک دانشگاه تبریز, د. 48، ش. 4، ص 67-76، 1397.
- Patil M.A. and Kadoli R., Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer. Applied Mathematical Modelling, Vol. 84, pp. 137-157, 2020.
- Panda R.K., Nayak B. and Sarangi S.K, Active vibration control of smart functionally graded beams. Procedia Engineering, Vol. 144, pp. 551-559, 2016.
- Bruant I. and Proslier L., Improved active control of a functionally graded material beam with piezoelectric patches. Journal of Vibration and Control, Vol. 21, No.10, pp. 2059-2080, 2015.
- Bodaghi M., Damanpack A.R., Aghdam M.M. and Shakeri M., Nonlinear active control of FG beams in thermal environments subjected to blast loads with integrated FGP sensor/actuator layers. Composite Structures, Vol. 94, No.12, pp. 3612-3623, 2012.
- Sheng G.G. and Wang X., Studies on dynamic behavior of functionally graded cylindrical shells with PZT layers under moving loads. Journal of Sound and Vibration, Vol. 323, No.3-5, pp. 772-789, 2009.
- Sheng G.G. and Wang X., Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads. Composite Structures, Vol. 93, No.1, pp. 162-170, 2010.
- He X.Q., Ng T.Y., Sivashanker, S. and Liew, K.M., Active control of FGM plates with integrated piezoelectric sensors and actuators. International journal of Solids and Structures, Vol. 38, No.9, pp. 1641-1655, 2001.
- Maruani J., Bruant I., Pablo, F. and Gallimard, L., A numerical efficiency study on the active vibration control for a FGPM beam. Composite Structures, Vol. 182, pp. 478-486, 2017.
- Jafari A.A. and Fathabadi M., Forced vibration of FGM Timoshenko beam with piezoelectric layers carrying moving load. Aerospace Mechanics Journal, Vol. 9, No.2, pp. 69-77, 2013.
- Kayacık Ö., Bruch Jr J.C., Sloss J.M., Adali S. and Sadek I.S., Integral equation approach for piezo patch vibration control of beams with various types of damping. Computers & structures, Vol. 86, No.3-5, pp. 357-366, 2008.
- ملکی م.، محمدی ص. و فروتن م.، بررسی ارتعاش آزاد و پاسخ استاتیکی تیر مدرج هدفمند پیزوالکتریک براساس نظریه الاستیسیته دوبعدی. مهندسی مکانیک دانشگاه تبریز, د. 48، ش. 3، ص 328-319، 1397.
- Peng X.Q., Lam K.Y. and Liu G.R., Active vibration control of composite beams with piezoelectrics: a finite element model with third order theory. Journal of sound and vibration, Vol. 209, No.4, pp. 635-650, 1998.
- Fallah N. and Ebrahimnejad M., Finite volume analysis of adaptive beams with piezoelectric sensors and actuators. Applied Mathematical Modelling, Vol. 38, No.2, pp. 722-737, 2014.
- Li F.M. and Lyu X.X., Active vibration control of lattice sandwich beams using the piezoelectric actuator/sensor pairs. Composites Part B: Engineering, Vol. 67, pp. 571-578, 2014.
- Belouettar S., Azrar L., Daya E.M., Laptev V. and Potier-Ferry M., Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach. Computers & structures, Vol. 86, No.3-5, pp. 386-397, 2008.
- Damanpack A.R., Bodaghi M., Aghdam M.M. and Shakeri M., Active control of geometrically non-linear transient response of sandwich beams with a flexible core using piezoelectric patches. Composite Structures, Vol. 100, pp. 517-531, 2013.
- Qiu Z.C., Zhang X.M., Wang Y.C. and Wu Z.W., Active vibration control of a flexible beam using a non-collocated acceleration sensor and piezoelectric patch actuator. Journal of sound and vibration, Vol. 326, No.3-5, pp. 438-455, 2009.
- Salmasi H., Fotouhi R. and Nikiforuk P.N., Vibration control of a flexible link manipulator using smart structures. IFAC Proceedings Volumes, Vol. 41, No.2, pp. 11787-11792, 2008.
- Chou J.H., Chen S.H., Chang M.Y. and Pan A.J., Active robust vibration control of flexible composite beams with parameter perturbations. International journal of mechanical sciences, 39, No.7, pp. 751-760, 1997.
- Li S., He P. and Lin X., Asymmetrical Barrier Function-Based Adaptive Vibration Control for Nonlinear Flexible Cantilever Beam with Obstacle Restriction. IEEE Access, No.9, pp. 58306-58318, 2021.
- Qiu Z.C., Wang T.X. and Zhang X.M., Sliding mode predictive vibration control of a piezoelectric flexible plate. Journal of Intelligent Material Systems and Structures, Vol. 32, No.1, pp. 65-81, 2021.
- حیدری م. و هادیان جزی ش.، کنترل فعال ارتعاشات یک تیر هوشمند دوار با استفاده از وصلههای پیزوالکتریک. مهندسی مکانیک دانشگاه تبریز, د. 48، ش. 3، ص 67-76، 1397.
- پرهام ف.، احمدی ح.، فروتن ک. و حیدری سرائی م.، کنترل ارتعاشات تیر مدرج تابعی در حضور نامعینی تحت بارگذاری پریودیک. بیست و هشتمین کنفرانس سالانه بین المللی انجمن مهندسان مکانیک ایران، تهران، ایران، 1399.
- https://learn.digilentinc.com/Documents/139.
- Djojodihardjo H., Jafari M., Wiriadidjaja S., and Ahmad K.A., Active vibration suppression of an elastic piezoelectric sensor and actuator fitted cantilevered beam configurations as a generic smart composite structure. Composite Structures, Vol. 132, pp. 848-863,
- Fu Y., Wang J. and Mao Y., Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment. Applied Mathematical Modelling, Vol. 36, No.9, pp. 4324-4340, 2012.
- Zheng Y.F., Fu Y.M. and Wang F., Nonlinear dynamic stability for piezoelectric laminated plate with damage. Applied Mathematical Modelling, Vol. 38, pp. 570-576, 2006.
- Ke L.L., Yang J. and Kitipornchai S., An analytical study on the nonlinear vibration of functionally graded beams. Meccanica, Vol. 45, No.6, pp. 743-752, 2010.
- Hagedorn Peter, and Anirvan DasGupta. Vibrations and waves in continuous mechanical systems. Chichester: Wiley, 2007.
- Slotine Jean-Jacques E., and Weiping Li. Applied nonlinear control. Vol. 199, No.1, Englewood Cliffs, NJ: Prentice hall, 1991.
Majkut L., Free and forced vibrations of Timoshenko beams described by single difference equation. Journal of Theoretical and Applied Mechanics, Vol. 47, No.1, pp. 193-210, 2009.
|