Yıl: 2018 Cilt: 8 Sayı: 2 Sayfa Aralığı: 496 - 504 Metin Dili: İngilizce İndeks Tarihi: 10-02-2020

Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method

Öz:
Piezoelectric materials, which have fast response and low energy usage features, are widely used in sensors and actuators. Due to theactive role of their working principle, it is important to know the vibration characteristic of each piezoelectric material. In this paper,forced vibration analysis of arbitrary non-uniform piezoelectric rod has been performed. The governing differential equations havevariable coefficients which are functions of mechanical and electrostatic properties. Analytical solution of these linear differentialequations is limited to specific cross-section area models, so numerical method is inevitable. Numerical model of the forced vibrationof cantilever piezoelectric (PZT-4) rod with an arbitrary non-uniform cross-section area is obtained in the Laplace space and thensolved numerically by the Complementary Functions Method (CFM). Solutions were transformed from the Laplace domain to thetime domain by applying modified Durbin’s procedure. The technique is validated for a uniform piezoelectric rod that can also besolved analytically. In order to demonstrate the effect of arbitrary geometry on the dynamic feature of the rod, numerical examples areemployed.
Anahtar Kelime:

Değişken Kesitli Piezoelektrik Çubuğun Tamamlayıcı Fonksiyonlar Yöntemi ile Zorlanmış Titreşim Analizi

Öz:
Sahip oldukları hızlı tepki verme ve düşük enerji gereksinimi gibi özellikleri sayesinde piezoelektrik özelliğe sahip malzemeler algılayıcı ve uyarıcı olarak sıklıkla kullanılmaktadır. Çalışma prensiplerinde titreşim özellikleri etkin rol oynadığından, piezoelektrik malzemelerin titreşim karakteristiklerini bilmek önemlidir. Bu çalışmada kesiti keyfi olarak değişen piezoelektrik bir çubuğun zorlanmış titreşim analizi yapılmıştır. Problemi ifade eden diferansiyel denklem, mekanik ve elektrostatik özelliklerin fonksiyonu olan değişken katsayılara sahiptir. Bu tür bir lineer diferansiyel denklemin analitik çözümü bazı özel kesit alanları ile sınırlı olduğundan sayısal çözümleme kaçılmazdır. Keyfi kesit alanına sahip konsol piezoelektrik çubuğun (PZT-4) zorlanmış titreşimi için matematiksel model Laplace uzayında elde edilmiş ve Tamamlayıcı Fonksiyonlar Yöntemi ile sayısal olarak çözülmüştür. Çözümlerin zaman uzayına dönüşümü modifiye Durbin yöntemi uygulanarak gerçekleştirilmiştir. Çözüm yöntemi, analitik olarak da çözülebilen üniform piezoelektrik çubuk için de geçerlidir. Keyfi kesit değişiminin çubuğun dinamik davranışına etkisini göstermek için sayısal örnekler verilmiştir.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Abrate, S. 1995. Vibration of non-uniform rods and beams. J. Sound V., 185(4):703-716.
  • Agarwal, RP. 1982. On the method of complementary functions for nonlinear boundary-value problems. J. Optimiz. Theory App., 36(1):139-144.
  • Aktaş, Z. 1972. Numerical Solutions of Two-Point Boundary Value Problems. Metu, Ankara.
  • Calim, FF. 2016. Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation. Composites Part B, 103:98-112.
  • Calim, FF. 2016. Transient analysis of axially functionally graded Timoshenko beams with variable cross-section. Composites Part B, 98:472-483.
  • Celebi, K., Keles, I. 2011. Analysis of one-dimensional response of an elastic body under dynamic loads, 6th International Advanced Technologies Symposium, 16-18 May, Elazığ, Turkey.
  • Celebi, K., Keles, I., Tutuncu, N. 2011. Exact solution for forced vibration of non-uniform rods by Laplace transformation. GU J. Sci., 24(2):347-353.
  • Chapra, SC., Canale, RP. 1998. Numerical Methods for Engineers, 2nd ed., New York, USA:McGraw-Hill, 760-766.
  • Chen, WQ., Zhang, CL. 2009. Exact analysis of longitudinal vibration of a nonuniform piezoelectric rod. Proc. Spie. Int. Soc. Optics Photo., 749307.
  • Ding, HJ., Chen, WQ. 2001. Three Dimensional Problems of Piezoelasticity, New York, USA: Nova Science Publishers.
  • Durbin, F. 1974. Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J., 17(4):371-376.
  • Eisenberger, M. 1991. Exact longitudinal vibration frequencies of a variable cross-section rod. Appl. Acoust., 34(2):123-130.
  • Eker, M., Celebi, K., Yarımpabuç, D. 2015. Free Vibration Analysis of Nonuniform Piezoelectric Rod by Complementary Functions Method. European Conference on Numerical Mathematics and Advanced Application; 14-18 September, Ankara, Turkey.
  • Kumar, BM., Sujith, RI. 1997. Exact solutions for the longitudinal vibration of non-uniform rods. J. Sound V., 207(5):721-729.
  • Li, QS. 2000. Exact solutions for longitudinal vibration of multi-step bars with varying cross- section. J. Vib. Acoust., 122(2):183-187.
  • Li, QS. 2000. Free longitudinal vibration analysis of multi-step non-uniform bars based on piecewise analytical solutions. Eng. Struct., 22(9):1205-1215.
  • Nadal, C., Pigache, F. 2009. Multimodal electromechanical model of piezoelectric transformers by Hamilton’s principle. IEEE T. Ultrason. Ferr., 56(11):2530-2543.
  • Przybylski, J. 2015. Static and dynamic analysis of a flextensional transducer with an axial piezoelectric actuation. Eng. Struct., 84:140-151.
  • Roberts, SM., Shipman, JS. 1979. Fundamental matrix and two-point boundary-value problems. J. Optimiz. Theory App., 28(1):77-88.
  • Shi, ZF., Chen, Y. 2004. Functionally graded piezoelectric cantilever beam under load. Arch. Appl. Mech., 74(3):237-247.
  • Temel, B., Yıldırım, S., Tütüncü, N. 2014. Elastic and viscoelastic response of heterogeneous annular structures under Arbitrary Transient Pressure. Int. J. Mech. Sci., 89:78-83.
  • Tutuncu, N., Temel, B. 2009. A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres. Compos. Struct., 91:385-390.
  • Tutuncu, N., Temel, B. 2013. An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness. Mech. Adv. Mat. Struct., 20:38-46.
  • Yang, JS., Fang, HY. 2003. A piezoelectric gyroscope based on extensional vibrations of rods. Int. J. Appl. Electrom., 17(4):289-300.
  • Yang, L., Zhifei, S. 2009. Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature. Compos. Struct., 87(3):257-264.
  • Yardimoglu, B., Aydın, L. 2011. Exact longitudinal vibration characteristics of rods with variable cross-sections. Shock Vib., 18(4):555-562.
  • Yarımpabuç, D., Eker, M., Çelebi, K. 2016. Free Vibration Analysis of Nonuniform Piezoelectric Rod by Chebyshev Pseudospectral Method. 1st International Mediterranean Science and Engineering Congress, 26-28 September, Adana, Turkey.
  • Zhang, CL., Chen, WQ., Li, JY., Yang, JS. 2009. One-dimensional equations for piezoelectromagnetic beams and magnetoelectric effects in fibers. Smart Mater. Struct., 18(9).
APA YARIMPABUÇ D, EKER M, ÇELEBİ K (2018). Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. , 496 - 504.
Chicago YARIMPABUÇ Durmuş,EKER MEHMET,ÇELEBİ KERİMCAN Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. (2018): 496 - 504.
MLA YARIMPABUÇ Durmuş,EKER MEHMET,ÇELEBİ KERİMCAN Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. , 2018, ss.496 - 504.
AMA YARIMPABUÇ D,EKER M,ÇELEBİ K Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. . 2018; 496 - 504.
Vancouver YARIMPABUÇ D,EKER M,ÇELEBİ K Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. . 2018; 496 - 504.
IEEE YARIMPABUÇ D,EKER M,ÇELEBİ K "Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method." , ss.496 - 504, 2018.
ISNAD YARIMPABUÇ, Durmuş vd. "Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method". (2018), 496-504.
APA YARIMPABUÇ D, EKER M, ÇELEBİ K (2018). Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. Karaelmas Fen ve Mühendislik Dergisi, 8(2), 496 - 504.
Chicago YARIMPABUÇ Durmuş,EKER MEHMET,ÇELEBİ KERİMCAN Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. Karaelmas Fen ve Mühendislik Dergisi 8, no.2 (2018): 496 - 504.
MLA YARIMPABUÇ Durmuş,EKER MEHMET,ÇELEBİ KERİMCAN Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. Karaelmas Fen ve Mühendislik Dergisi, vol.8, no.2, 2018, ss.496 - 504.
AMA YARIMPABUÇ D,EKER M,ÇELEBİ K Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. Karaelmas Fen ve Mühendislik Dergisi. 2018; 8(2): 496 - 504.
Vancouver YARIMPABUÇ D,EKER M,ÇELEBİ K Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method. Karaelmas Fen ve Mühendislik Dergisi. 2018; 8(2): 496 - 504.
IEEE YARIMPABUÇ D,EKER M,ÇELEBİ K "Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method." Karaelmas Fen ve Mühendislik Dergisi, 8, ss.496 - 504, 2018.
ISNAD YARIMPABUÇ, Durmuş vd. "Forced Vibration Analysis of Non-Uniform Piezoelectric Rod by the Complementary Functions Method". Karaelmas Fen ve Mühendislik Dergisi 8/2 (2018), 496-504.