Çeşitli Kenar Sınır Koşullarına Sahip İnce İzotropik Düz Plakaların ve Eğri Plakaların Panel Çarpıntı Sayısal Çalışması

Öz

Bu makale de, etkili, yüksek hassasiyetli üçgen sığ kabuk sonlu elemanlar kullanılarak, farklı kenar sınır koşullarına sahip düz plakaların ve eğri plakaların süpersonik panel çarpıntsı sayısal olarak incelenmiştir. Plakanın alt tarafındaki akışkanın durağan olduğu varsayılmıştır. Lineer piston teorisi, plakanın üst yüzeyine uygulanabilir. Aerodinamik yükleri değerlendirmek için doğrusallaştırılmış piston teorisi kullanılmıştır. Karmaşık bir özdeğer probleminin çözümü Hamilton ilkesine göre formüle edilir. Lagrange'ın hareket denklemi, özdeğerleri bulmak için standart yöntemler kullanılarak elde edilir. Mevcut sonlu eleman analizi, aerodinamik sönümlemeyi yok sayar. Geliştirilen sonlu elemanlar paneller için ince ve küçük deforme olmuş kabuklar teorisi dikkate alınır. Geliştirilen sonlu elemanlar kodunu doğrulamak için basitçe desteklenen kenarlı (S-S-S-S) kare ve dikdörtgen düz panellerin, dört sabit kenarlı kare plakanın (C-C-C-C) ve uzunluk yan kelepçeli kare plaka (C-S-C-S) sonuçları yayınlanmış veilerle karşılaştırılmıştır. Literatür verilerinin sınırlı olduğu kare ve dikdörtgen düz panel için diğer kenar sınır koşullarının (S-C-S-C, C-S-C-S ve C-C-C-C) flutter sonuçları değerlendirilmiştir. Çapraz akış yönündeki (S-C-S-C) sabit koşulun, kritik flutter basınç parametreleri ve flutter frekansları üzerinde önemli bir etkiye sahip olduğu bulunmuştur. Ayrıca, yukarıda bahsedilen etkiyi incelemek için, mevcut sonlu eleman (FE), çarpıntı sonuçlarını bulmak için S-C-S-C (çapraz akış yönünde kısıtlı ve süpersonik akışa maruz kalan), S-S-S-S sınır koşullarına sahip kavisli plakalara genişletildi.

Anahtar Kelimeler

• Panel çarpıntısı
• Sonlu eleman
• Kenar sınır koşulları
• Süpersonik akış
• Piston teorisi

Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions

Öz

In this article, supersonic panel flutter analysis of flat plates and curved plates with different edge boundary conditions are studied, using efficient, high precision triangular shallow shell finite elements. The fluid on the underside of the plate was is assumed to be stationary. The linear piston theory can be applied to the top surface of the plate. The linear piston theory was used to evaluate the aerodynamic loads. The solution of a complex eigenvalue problem was formulated according to Hamilton’s principle. Lagrange’s equation of motion was obtained using standard methods for finding eigenvalues. Current finite element analysis ignores aerodynamic damping. For panels, the theory of thin and small deformed shells was taken into account. To validate the developed finite element code, the results of a square and rectangular flat-panels with simply supported edges (S-S-S-S), a square plate with four fixed edges (C-C-C-C), and a square plate with the length side clamps (C-S-C-S) were compared with the published data. The flutter results of other edge boundary conditions (S-C-S-C, C-S-C-S, and C-C-C-C) for square and rectangular flat panels are evaluated for which literature data is limited. It has been found that the fixed condition in the cross-flow direction (S-C-S-C) has a significant effect on the critical flutter pressure parameters and flutter frequencies. Further, to study the aforementioned effect, the current finite element (FE) has been extended to curved plates with S-C-S-C(constrained in the cross-flow direction and exposed to supersonic flow), SS-S-S boundary conditions to find flutter results.

Anahtar Kelimeler

• Panel flutter
• Finite element
• Edge boundary conditions
• Supersonic flow
• Piston theory

Kaynakça

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