A Practical Method for the Dynamic Analysis of Non-Uniform Piezoelectric Rod

Year 2019, , 181 - 186, 01.03.2019

Durmuş Yarımpabuç , Mehmet Eker , Kerimcan Çelebi

https://doi.org/10.19113/sdufenbed.438009

Abstract

In this paper, a unified approach for the dynamic analysis of non-uniform piezoelectric rod is presented. It is assumed that the cross sectional area of the rod is varying along the longitudinal axis, arbitrarily. Therefore, the partial differential equations that govern the non-uniform piezoelectric isotropic rod in a forced vibration analysis are obtained with a variable coefficient taking into account mechanical and electrostatic equations. Analytical solutions of these equations are only possible for simple crosssection areas. First, the governing equations are transformed to the Laplace space and then solved numerically by pseudospectral Chebyshev approach for arbitrary cross-section area under four different load functions. The final results are transformed to the time domain using modified Durbin’s procedure. The technique is validated for simple cross-section area results that can also be solved analytically.

Keywords

Forced vibration, Piezoelectric rod, Laplace transform, Pseudospectral Chebyshev method

Düzgün Olmayan Piezoelektrik Çubuğun Dinamik Analizi için Pratik Bir Yöntem

Abstract

Bu çalışmada, düzgün olmayan piezoelektrik çubuğun dinamik analizi için birleşik bir yaklaşım sunulmaktadır.  Çubuğun enine kesit alanının rastgele olarak uzunlamasına eksen boyunca değiştiği varsayılmaktadır.  Bu nedenle, zorlanmış titreşim analizinde düzgün olmayan piezoelektrik izotropik çubuğu idare eden kısmi diferansiyel denklemler, mekanik ve elektrostatik denklemler dikkate alınarak değişken bir katsayılı olarak elde edilirler.  Bu denklemlerin analitik çözümleri sadece basit kesit alanları için mümkündür. İlk olarak, sistemi idare eden denklemler Laplace uzayına dönüştürülür ve daha sonra dört farklı yük fonksiyonu altında rastgele kesit alanı için pseudospektral Chebyshev yaklaşımı ile sayısal olarak çözülür. Nihai sonuçlar, modifiye edilmiş Durbin prosedürü kullanılarak zaman uzayına dönüştürülür. Yöntem, analitik olarak da çözülebilen basit kesit alanına sahip piezoelektrik çubuk sonuçları ile doğrulanmıştır.

Keywords

Zorlanmış titreşim, Piezoelektrik çubuk, Laplace dönüşümü, Pseudospectral Chebyshev yöntemi

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