Non-linear panel flutter for temperature-dependent functionally graded material panels

Abstract

The non-linear flutter and thermal buckling of an FGM panel under the combined effect of elevated temperature conditions and aerodynamic loading is investigated using a finite element model based on the thin plate theory and von Karman strain-displacement relations to account for moderately large deflection. The aerodynamic pressure is modeled using the quasi-steady first order piston theory. The governing non-linear equations are obtained using the principal of virtual work adopting an approach based on the thermal strain being a cumulative physical quantity to account for temperature dependent material properties. This system of non-linear equations is solved by Newton-Raphson numerical technique. It is found that the temperature increase has an adverse effect on the FGM panel flutter characteristics through decreasing the critical dynamic pressure. Decreasing the volume fraction enhances flutter characteristics but this is limited by structural integrity aspect. The presence of aerodynamic flow results in postponing the buckling temperature and in suppressing the post buckling deflection while the temperature increase gives way for higher limit cycle amplitude.

Thermo-acoustic random response of temperature-dependent functionally graded material panels

“…The FGM panel adopted in this study is a mixture of nickel and silicon nitride (Si 3 N 4 ). The properties of the constituent materials are assumed to be temperature-dependent according to the following relation [16]: where, the coefficients P o , P 1 , P 2 and P 3 for young's modulus E, the Poisson ratio ν and the thermal expansion coefficient α of nickel and silicon nitride are given in Table 1 [23].…”

“…At T = 8 • C, the panel shows a decreased stiffness with such temperature rise through having higher deflection random vibration with rms = 0.0038, which is almost double the room temperature value. At T = 16 and 24 • C, which exceed the critical buckling temperature rise of the nickel panel [16], it is found that the thermal post-buckling deflections dominated the response and the panel shows a small-deflection random vibration about the buckling equilibrium position. Figure 3 depicts the central-line vibration mode shape for a nickel panel during certain period of time, while being at T = 8 • C and SPL = 90 dB.…”

“…To account for the temperature-dependence of material properties, the thermal strain was modeled as an integral quantity of thermal expansion coefficient with respect to temperature. Ibrahim et al [17] extended the formulation presented in [16] by including the shear deformation effect to make it capable of handling thick FGM panels. Sohn and Kim [18] studied the static and dynamic stabilities of FGM panels under supersonic airflows and elevated temperatures environment, while assuming temperature-independent material properties.…”

“…The influence of thermal environment on the critical flutter dynamic pressure of a flat FGM panel was studied by Prakash and Ganapathi [15]. Ibrahim et al [16] developed a frequency-domain solution to predict the flutter limit-cycle oscillation amplitudes of FGM panels under combined aerodynamic and thermal loads. To account for the temperature-dependence of material properties, the thermal strain was modeled as an integral quantity of thermal expansion coefficient with respect to temperature.…”

Thermoacoustic Random Response of Shape Memory Alloy Hybrid Composite Plates

“…They adopted an incremental finite element technique to capture the effect of the temperature dependence of material properties on the panel response. Ibrahim et al [8] presented a finite element solution for the thermal buckling and nonlinear flutter performance of thin functionally graded material panels under combined aerodynamic and thermal loads. To account for the temperature dependence of material properties, the thermal strain was modeled as an integral quantity of thermal expansion coefficient with respect to temperature.…”