Time domain aero-thermo-elastic instability of two-dimensional non-linear curved panels with the effect of in-plane load
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Time domain aero‑thermo‑elastic instability of two‑dimensional non‑linear curved panels with the effect of in‑plane load considered Hamid Moosazadeh1 · Mohammad M. Mohammadi2 Received: 24 February 2020 / Accepted: 23 August 2020 © Springer Nature Switzerland AG 2020
Abstract This study presents aero-thermo-elastic Instability of two-dimensional Non-linear Curved Panels. Aero-thermo-elasticity plays an important role in the design and optimization of supersonic aircrafts. Furthermore, the transient and nonlinear effects of the thermal and aerodynamic environment encompassing a curved surface cannot be ignored. Accordingly, a homogenous curved plate with a high length-to-width ratio and simply-supported boundary conditions is assumed. The effect of large deflection is included in the equations through von Kármán non-linear strain–displacement relations. The thermal load is assumed to be a steady-state temperature non-uniform distribution. Structural properties such as modulus of elasticity and thermal expansion coefficient are assumed to be temperature-dependent. The novelty is incorporating first- and third-order piston theory for the non-linear curved panel flutter analysis under the effects of inplane and thermal loads. Hamilton’s principle is used and partial differential equations are derived. The semi-analytical weighted residual method for the nonlinear curved panel is utilized. The fourth- and fifth-order Runge–Kutta iterative method are deployed to obtain the non-linear aero-thermo-mechanical deflections. Non-linear frequency analysis of cambered panel with the combined effects of aerodynamics, thermal and in-plane loads is investigated for the first time. The increase in panel curvature leads to a complicated behavior in the non-linear structural frequency variations. With increasing in-plane compressive load, complicated oscillating behavior is observed. More critical instability boundary for cambered panel is detected through the use of third-order piston theory. In addition, with an increase in panel curvature from 0 to 3, the panel displacement increases and for higher camber ratio, it decreases. Keywords Panel flutter · In-plane load · Thermal effects · First-order piston theory · Third-order piston theory · 2D panel · Time domain List of symbols h Panel thickness H Curvature height H/h Curvature changes w0 Out-of-plane displacement a Plate width 𝜂 Tension or compression force coefficient D Plate stiffness E Elastic modulus 𝜈 Poisson’s ratio
Rx Radii of curvature ΔPa Aerodynamic pressure Pd Unsteady aerodynamic force Ps Initial static aerodynamic force c∞ Speed of sound U∞ Free-stream steady velocity P∞ Atmospheric pressure 𝜌∞ Air density 𝛾 Isentropic gas constant M Mach number
* Hamid Moosazadeh, [email protected]; Mohammad M. Mohammadi, [email protected] | 1Department of Aerospace Engineering, Tarbiat Modares University, Tehran, Iran. 2Fuel Cell Technology Research Laboratory, Malek Ashtar University of Technology, Tehran, Iran. SN Applied Sciences
(2020)
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