Politeknik Dergisi 2147-9429 Gazi Üniversitesi 10.2339/politeknik.1622599 Structural Dynamics Yapı Dinamiği A Dynamic Instability Study of Shallow Shell Panels with Simply Supported Edges Basitçe Desteklenen Kenarlara Sahip Sığ Kabuk Panellerin Dinamik Kararsızlık Çalışması https://orcid.org/0000-0001-8617-2134 Pany Chıtaranjan VSSC 04 21 2026 29 4 1 8 01 18 2025 05 11 2025 Copyright © 1998, Politeknik Dergisi 1998 Politeknik Dergisi

An efficient, general finite element (FE) of triangular shape is employed in investigating the panels (flat and shallow shell curved panels) dynamic instability subjected to supersonic air flow. The all edges of panel are simply-supported (SSSS). The fluid that's on the plate's bottom is not in motion. Linearized piston theory is used to determine aerodynamic loads. Hamilton's principle is used to generate the dynamic instability motion equations, which characterize panels instability during their interaction with the supersonic the airflow. The eigenvalues of Lagrange's motion equation are obtained by conventional methods. Here, aerodynamic damping is excluded. In panels, the basis of thin, very small deformation shells is considered. Critical dynamic pressure was determined. The FE code is corroborated by examining outcomes of a flat square panel (radius of curvature R of shallow shell tends to ∞) with the literature data. In addition, the proposed shallow-shell FE is applied to cylindrical curved plates with SSSS boundary conditions to demonstrate the limited dynamic instability results, corresponding to different curvature parameters available in the literature for different FE formulations. Results and data from the literature compare fairly. It is clear that the dynamic instability limit of the panels grows with an increase in the curvature parameter (in the lower range) of the panels with SSSS edge constraint. It was figured out that in-plane edge constraints had an impact on dynamic instability limits.

Süpersonik hava akışına maruz kalan panellerin (düz ve sığ eğri kabuk paneller) dinamik kararsızlığının araştırılmasında üçgen şekilli, etkin ve genel bir sonlu eleman (SE) kullanılmıştır. Panelin tüm kenarları basit mesnetlidir (SSSS). Panel altındaki akışkan hareket halinde değildir. Aerodinamik yüklerin belirlenmesinde lineerleştirilmiş piston teorisi kullanılmıştır. Süpersonik hava akışıyla etkileşim sırasında panellerin kararsızlık davranışını tanımlayan dinamik kararsızlık hareket denklemleri, Hamilton prensibi kullanılarak türetilmiştir. Lagrange hareket denkleminin özdeğerleri geleneksel yöntemlerle elde edilmiştir. Bu çalışmada aerodinamik sönümleme dikkate alınmamıştır. Paneller için ince, çok küçük şekil değiştiren kabuklar esas alınmıştır. Kritik dinamik basınç belirlenmiştir. SE kodu, düz kare panelin (sığ kabuğun eğrilik yarıçapı R sonsuza yaklaştığında) sonuçları ile literatürdeki veriler karşılaştırılarak doğrulanmıştır. Ayrıca, önerilen sığ kabuk SE yöntemi, SSSS sınır şartlarına sahip silindirik eğrilikli plakalara uygulanmış ve farklı SE formülasyonları için literatürde mevcut olan çeşitli eğrilik parametrelerine karşılık gelen sınırlı dinamik kararsızlık sonuçları ortaya konmuştur. Elde edilen sonuçlar, literatürle oldukça uyumludur. SSSS kenar kısıtına sahip panellerde, eğrilik parametresinin (düşük aralıkta) artmasıyla birlikte dinamik kararsızlık sınırının da arttığı açıkça görülmüştür. Ayrıca, panel kenarlarındaki düzlem içi sınır şartlarının dinamik kararsızlık sınırları üzerinde etkili olduğu belirlenmiştir.

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