“…Table 2 lists value of the first six frequencies and corresponding experimental ones, reported by Romero et al. [52]. Except for the fifth mode which has evident difference, an excellent agreement between the presented numerical solution and experimental tests can be observed.…”
Section: Homogenous Trapezoidal Platesupporting
confidence: 55%
“…A suitable adaptation between the suggested solution and experimental tests is seen, and the comparisons approve high accuracy of the proposed solution. Figure 6.Comparison between the presented solutions and experimental results [52]. …”
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.
“…Table 2 lists value of the first six frequencies and corresponding experimental ones, reported by Romero et al. [52]. Except for the fifth mode which has evident difference, an excellent agreement between the presented numerical solution and experimental tests can be observed.…”
Section: Homogenous Trapezoidal Platesupporting
confidence: 55%
“…A suitable adaptation between the suggested solution and experimental tests is seen, and the comparisons approve high accuracy of the proposed solution. Figure 6.Comparison between the presented solutions and experimental results [52]. …”
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.
“…Consequently, most studies on these structural elements use approximate analytical or numerical methods. In many cases, experimental and computational methods can be combined so that the data obtained by one of the methods can be used by the other one to verify the results [5]. In this work, the system was studied analytically and experimentally.…”
Digital Speckle Interferometry is a non invasive full-field coherent optical technique used in mechanical vibration measurement. In this research, it is used for tuning resonant frequencies of vibrating plates in order to investigate the dynamical behavior of perforated plates. The plate was excited to resonant vibration by a sinusoidal acoustic source. Fringe pattern produced during the timeaverage recording of the vibrating plate, for several resonant frequencies were registered. Results of plates fixed at one edge having internal holes and attached masses are presented. Experimental natural frequencies and modal shapes are compared to those obtained by an analytical approximate solution based on the Rayleigh-Ritz method with the use of orthogonal polynomials as coordinate function. A high degree of correlation between computational analysis and experimental results was observed, proving the potentiality of the optical technique as experimental validation of the numerical simulations.
“…This table shows that no specified trend can be detected for effect of skew angle on value of natural frequencies of the plate which can be explained by confrontation between effects of α and β. [49] 153.0000 594.0000 717.0000 1571.000 1970.000 2320.000 Dimensionless natural frequencies Fig. 8.…”
In this paper, a numerical solution is presented for free vibration analysis of cantilever functionally graded carbon nanotubereinforced trapezoidal plates. The plate is modeled based on the first-order shear deformation theory, effective mechanical properties are estimated according to extended rule of mixture, and the set of governing equations and boundary conditions are derived using Hamilton's principle. Generalized differential quadrature method is employed, and natural frequencies and corresponding mode shapes are derived numerically. Convergence and accuracy of the solution are confirmed, and effect of various parameters on the natural frequencies is investigated including geometrical characteristics, volume fraction and distribution of carbon nanotubes. Because of similarity of the studied model with the wing, tail and fin of aircrafts and missiles, results of this paper can be useful in design and analysis of aeronautic vehicles in the near future. It is worth mentioning that results of this paper may serve as benchmarks for future studies.
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