Termoelastik-piezoelektrik malzemelerin lineer bünye denklemlerinin formülasyonu

Bu çalı mada, termoelastik-piezoelektrik bir malzemenin elektro-termomekanik yük altındaki lineer davranı ı sistematik bir ekilde incelenmi tir. Malzemenin termoelastik-piezoelektrik anizotropiye sahip olduğu dü ünülmü tür. Malzemenin piezoelektrik özelliğe sahip olmasından dolayı, ortamın sıkı abilir olduğu kabul edilmi tir. Bu çalışmanın gerçekle tirilmesinde sürekli ortamlar mekaniğinin temel ilkeleri ve elektrostatiğin denge denklemleri belirleyici olmu tur. Termodinamik kısıtlamaların neticesi olarak gerilme potansiyelinin bir simetrik tansöre ve bir vöktöre, ısı akısı vektörü fonksiyonunun ise bir simetrik tansör ile iki vektöre bağlı olduğu görülmü tür. Bünye fonksiyonlar, bağlı oldukları argümanlarına göre bir kuvvet serisi açılımı ile temsil edilmi ve bu seri açılımında dikkate alınan terimlerin türü ve sayısı ortamın lineer mertebesini belirlemi tir. Polarizasyonun, gerilmenin ve ısı akısı vektörünün lineer bünye denklemleri, Gauss yasası denklemi, Cauchy hareket denklemi ve enerji denklemi ifadelerinde yerlerine yazılıp alan denklemleri bulunmuştur.

Formulation of the lineer constitutive equations of termoelastic piezoelectric materials

In this study, the linear behavior of a thermoelastic and piezoelectric material under electromechanical loading has been systematically analyzed. The material has a thermoelastic and piezoelectric anisotropy. Compressibility of the medium is accepted because of that material has piezoelectric feature. Basic principles of modern continuum mechanics and balance equations of Electrostatic have provided guidance and have been determining in the process of this study. As a result of thermodynamic constraints, it has been determined that the stress potantional is dependent on a symmetric tensor and a vector whereas the heat flux vector function is dependent on a symmetric tensor and two vectors. Constitutive functions have been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the linearity of the medium. The linear constitutive equations of the stress, polarization and heat flux vector are substituted in equation Coulomb#Gauss Law, in Cauchy’s equation of motion and energy equation to obtain the field equations.

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