Deformation and Electrical Behaviours of Functionally Graded Piezoelectric Curved Sensors

A comprehensive analytical model is developed for a functionally graded piezoelectric (FGP) curved bar which is in a closed electrical circuit. Piezoelectric coefficient is assumed to vary in the radial direction according to a power law unlike the corresponding studies in the literature. This assumption constitutes one of the basic novelties of the present investigation. For the verification, the numerical results of the mathematical model for an FGP curved actuator are compared with those of a related study on a linear FGP curved bar in the literature. Next, the model is used to determine the deformation and electrical behaviours of an FGP curved sensor under a couple at its free end section. The presentation of the numerical results for the curved sensors is another novelty of the present study since the numerical results in the related studies in the literature were presented just for the actuators. Results are compared with bimorph piezoelectric curved sensors and the effect of the grading parameter on the mechanical and electrical fields is examined. Numerical results show that FGP curved sensor provides several advantages in terms of the mechanical behavior of the material, and the distribution and production of electric potential in the sensor are affected significantly with the variation of grading parameter.

Kapalı elektrik çevrimi içerisinde bulunan fonksiyonel derecelendirilmiş piezoelektrik (FDP) eğri eksenli kiriş için kapsamlı bir analitik model geliştirilmiştir. Literatürdeki ilgili çalışmaların aksine, piezoelektrik sabitinin radyal doğrultuda bir güç yasasına bağlı olarak değiştiği kabul edilmiştir. Bu kabul, çalışmanın temel orijinalitesinden birini oluşturmaktadır. FDP eğri eksenli bir eyleyici için modelin sayısal sonuçları, literatürdeki ilgili çalışmalar ile karşılaştırılarak, modelin sınanması sağlanmıştır. Ardından, model serbest ucundan eğilme momentine mağruz bırakılan FDP eğri eksenli sensörün mekanik ve elektrik alanını elde etmek için kullanılmıştır. Literatürdeki diğer çalışmalarda sadece eyleyiciler için sonuçlar sunulduğundan dolayı, sensör için sayısal sonuçların sunumu bu çalışmanın bir diğer orijinalliğini temsil etmektedir. Sonuçlar iki tabakalı (bimorph) piezoelektrik eğri eksenli sensör sonuçları ile karşılaştırılmış ve derecelendirme parametresinin mekanik ve elektrik alanındaki etkileri incelenmiştir. Sonuçlar göstermiştir ki, FDP eğri eksenli sensör, malzemenin mekanik davranışları açısından bir çok avantaj sergilemektedir. Elektrik potensiyelinin dağılımı ve üretimi ise derecelendirme parametresine bağlı olarak önemli ölçüde etkilenmiştir.

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