Piezoelektrik Levha Viskoz Akışkan ve Rijit Duvardan Oluşan Sistemin Zorlanmış Titreşimine Akışkan Özelliklerinin Etkisi

Bu çalışmada piezoelektrik plak, viskoz akışkan ve rijit duvardan oluşan bir sisteme, harmonik bir mekanik kuvvet uygulandığında ortaya çıkan titreşime viskoz akışkan özelliklerinin etkisi incelenmiştir. Plağın hareketi, doğrusallaştırılmış elektro-elastisite teorisinin kesin denklemleri ile ifade edilmiştir. Akışkan akımı ise doğrusallaştırılmış Navier-Stokes denklemleri ile yazılmıştır. Plakta düzlem şekil değiştirme durumunun olduğu, akışkanın ise düzlemsel akış yaptığı varsayılmıştır. Problemin matematiksel formülasyonunu ifade eden denklemlere, sınır ve uygunluk koşullarına, plağın uzunluğu yönündeki koordinata göre Fourier dönüşümü uygulanmıştır. Ters Fourier dönüşümü ise sayısal olarak hesaplanmıştır. İncelenen hidro-piezoelektrik sistem farklı akışkanlar için ele alınmış ve akışkanın özelliklerinin, plak ve akışkan ara yüzeyindeki basınç değeri üzerindeki etkisi araştırılmıştır. Sonuçlar tartışılmış ve akışkanın viskozitesinin artmasının, ara yüzeydeki basıncı mutlak değerce arttırdığı gözlemlenmiştir. Bu araştırmanın, özellikle farklı mühendislik alanlarında yapılan enerji hasadı çalışmalarına katkıda bulunması amaçlanmıştır.

Anahtar Kelimeler:

Piezoelektrik plak, Viskoz akışkan, Zorlanmış titreşim, Rijit duvar, Ara yüzey basıncı

Effect of Fluid Properties on Forced Vibration of the System Consisting of Piezoelectric Plate, Viscous Fluid and Rigid Wall

This study investigates the mechanical forced vibration of the system which consists the piezoelectricplate, viscous fluid and rigid wall. The exact equations of motion of the linear electro-elasticity theory for piezoelectric materials are used to describe the plate motion, however, the fluid flow is described by using the linearized Navier-Stokes equations for a compressible (barotropic) viscous fluid. The plane-strain state in the plate and the plane flow of the fluid are considered in this study and the corresponding mathematical problems are solved by applying the Fourier transform with respect to the space coordinate which is on the coordinate axis directed along the plate-lying direction. The inverse Fourier transforms are determined numerically. The vibration of the examined hydro-piezoelectric system is analyzed with different fluids and the influence of fluid properties on pressure value at the plate and fluid interface is investigated. Numerical results are presented and discussed. In particular, it is established that an increase in the fluid viscosity causes to increase the amplitude of the interface normal stress. This investigation aims to contribute energy harvesting studies especially in different engineering areas.

Keywords:

Piezoelectric plate, Compressible viscous fluid, Forced vibration, Rigid wall, Interface pressure,

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