Legendre Series Solution for Chinese Lantern-Type Stability Loss in a Piezoelectric Cylinder

Öz

In this study, the Chinese lantern-type stability loss of a piezoelectric cylinder under uniformly distributed axial compression is modeled for the axisymmetric case using the exact three-dimensional equations of nonlinear electroelasticity theory. The solution is reduced, through the procedures given in [1], to a series–boundary value problem involving a system of linear partial differential equations. The analytical solution employs Legendre polynomials and window functions to satisfy boundary conditions. The initial imperfection criterion is used to determine the critical parameters [1–4]. Numerical results obtained by MATLAB reveal the effects of problem parameters on the critical force causing stability loss.

Anahtar Kelimeler

• Piezoelectric
• solid cylinder
• stability loss
• Legendre polynomial
• analytical solution

Proje Numarası

FBA-2024-6604

Piezoelektrik Silindirin Çin Feneri Tipi Stabilite Kaybının Legendre Serileri ile Çözümü

Öz

Bu çalışmada, her iki ucundan düzgün yayılı eksenel basınç kuvveti etkisindeki piezoelektrik silindirin Çin feneri tipi stabilite kaybı problemleri lineer olmayan elektroelastisite teorisinin üç boyutlu kesin denklemleri yardımıyla eksenel simetrik durum için modellenmiştir. Bu problemlerin çözümü, detayları [1]’de verilen işlemler yardımıyla, lineer kısmi türevli diferansiyel denklem sistemini içeren seri sınır değer problemlerinin çözümüne indirgenir. Analitik çözüm için Legendre polinomları ile sınır koşullarının sağlatılmasında “pencere fonksiyonlar”ından yararlanılmıştır. Kritik parametrelerin belirlenmesinde, “başlangıç eğinti kriteri” kullanılmıştır [1-4]. MATLAB yardımıyla belirlenen sayısal sonuçlar, problem parametrelerinin stabilite kaybına sebep olan kritik basınç kuvvetine etkilerini göstermektedir. Bu çalışmanın literatürde verilen sayısal sonuçların değerlendirilmesinde önemli bir veri olacağı öngörülmektedir.

Anahtar Kelimeler

• Piezoelektrik
• silindir
• stabilite kaybı
• Legendre polinomu
• analitik çözüm

Destekleyen Kurum

Yıldız Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Proje Numarası

FBA-2024-6604

Etik Beyan

Bu çalışma etik kurul onayı gerektirmemektedir.

Teşekkür

Bu çalışma Yıldız Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından FBA-2024-6604 nolu proje kapsamında desteklenmiştir.

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