Vibration and flutter analyses of cantilever trapezoidal honeycomb sandwich plates

Abstract

In this article, free flexural vibration and supersonic flutter analyses are studied for cantilevered trapezoidal plates composed of two homogeneous isotropic face sheets and an orthotropic honeycomb core. The plate is modeled based on the first-order shear deformation theory, and aerodynamic pressure of external flow with desired flow angle is estimated via the piston theory. For this goal, first applying the Hamilton's principle, the set of governing equations and boundary conditions are derived. Then, using a transformation of coordinates, the governing equations and boundary conditions are converted from the original coordinates into new computational ones. Finally, the differential quadrature method is employed and natural frequencies, corresponding mode shapes, and critical speed are numerically achieved. Accuracy of the proposed solution is confirmed by the finite element simulations and published experimental results. After the validation, effect of various parameters on the vibration and flutter characteristics of the plate are investigated. It is concluded that geometry of hexagonal cells in the honeycomb core has a weak effect on the natural frequencies and critical speed of the sandwich plate, whereas thickness of the honeycomb core has main influence on the natural frequencies and the critical speed. Besides, it is shown that the honeycomb core thickness has optimum values that lead to the most growth in the natural frequencies or critical speed. These optimum magnitudes can be taken into account by designers to increase the natural frequencies or expand flutter boundaries and make aircrafts safer in supersonic flights. It is also concluded that geometrical parameters of the hexagonal cells and thickness of the honeycomb core have no significant effect on the value of the critical flow angle.

Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins

“…In the relations above, the Young's modulus, shear modulus, density, and Poisson's ratio are defined in a homogenized form by means of the mechanical properties E h , G h , ρ h and v h of the honeycomb material [34]. Besides, φ 0 is the internal cells angle of the honeycomb structure; ϕ 0 = h 0 /l 0 and γ 0 = t 0 /l 0 stand for the internal aspect ratio and dimensionless cells thickness, respectively, in which h 0 , l 0 and t 0 are the geometrical parameters defining the hexagonal cells as represented in Figure 1.…”

Vibration analysis of cantilever FG-CNTRC trapezoidal plates

“…Substituting Eqs. (4), (5), (7) and (11) into Eq. (10), the set of governing equations can be derived as and external boundary conditions can be written as in which…”

“…On the other hand, trapezoidal plates are widely used in mechanical, civil and aeronautical engineering applications such as bridges, wings, tails and fins of aircrafts. However, due to the mathematical difficulties and complexities involved in formulation, mechanical analysis of CNTRC trapezoidal plates is poorly investigated in comparison with those of rectangular, skew and circular plates [2][3][4][5][6][7].…”

Hypersonic Aeroelastic Response of Elastic Boundary Panel Based on a Modified Fourier Series Method

“…Substituting equations (15) and (17) into equation (16) According to the modal orthogonality, after multiplying both ends of equation (18) by W i and integrating the new equation, the ith order equation can be obtained…”

“…In addition, the differential quadrature method (DQM) [18] and other methods have also been used for flutter analysis of plates. However, the structural models used in the flutter analysis of plates are usually plates with simple classical boundaries, and the study on elastic boundary plates focuses on free vibration instead of flutter.…”