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

Yıl 2018, Cilt: 8 Sayı: 2, 496 - 504, 01.06.2018

Durmuş Yarımpabuç Mehmet Eker Kerimcan Çelebi

Öz

Piezoelectric materials, which have fast response and low energy usage features, are widely used in sensors and actuators. Due to the active 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 have variable coefficients which are functions of mechanical and electrostatic properties. Analytical solution of these linear differential equations is limited to specific cross-section area models, so numerical method is inevitable. Numerical model of the forced vibration of cantilever piezoelectric PZT-4 rod with an arbitrary non-uniform cross-section area is obtained in the Laplace space and then solved numerically by Complementary Functions Method CFM . Solutions were transformed from Laplace domain to the time domain by applying modified Durbin’s procedure. The technique is validated for a uniform piezoelectric rod that can also be solved analytically. In order to demonstrate the effect of arbitrary geometry on the dynamic feature of the rod, numerical examples are employed.

Anahtar Kelimeler

Forced Vibration, Piezoelectric rod, Laplace transform, Complementary Functions Method

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 Kelimeler

Tamamlayıcı fonksiyonlar yöntemi, Durbin yöntemi, Zorlanmış titreşim, Laplace dönüşümü, Piezoelektrik çubuk

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