• Structural Engineering and Mechanics
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• 제60권1호
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• pp.1-19
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• 2016

In this study, the supersonic panel flutter of doubly curved composite sandwich panels with variable thickness is considered under aerothermoelastic loading. Considering different radii of curvatures of the face sheets in this paper, the thickness of the core is a function of plane coordinates (x,y), which is unique. For the first time in the current model, the continuity conditions of the transverse shear stress, transverse normal stress and transverse normal stress gradient at the layer interfaces, as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of the sandwich panel are satisfied. The formulation is based on an enhanced higher order sandwich panel theory and the vertical displacement component of the face sheets is assumed as a quadratic one, while a cubic pattern is used for the in-plane displacement components of the face sheets and the all displacement components of the core. The formulation is based on the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear approximation, the one-dimensional Fourier equation of the heat conduction along the thickness direction, and the first-order piston theory. The equations of motion and boundary conditions are derived using the Hamilton principle and the results are validated by the latest results published in the literature.

• Advances in aircraft and spacecraft science
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• 제8권4호
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.566-571
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• 2007

In this study, it is investigated the thermal post-buckling characteristics of step-formed FG panel under the heat and supersonic flow. Material properties are assumed to be temperature dependent as well as continuously varying in the thickness direction of the panel according to a simple power law distribution in terms of the volume fraction of the constituent. First-order shear deformation theory(FSDT) of plate is applied to model the panel, and the von Karman strain-displacement relations are adopted to consider the geometric nonlinearity due to large deformation. Also, the first-order piston theory is used to model the supersonic aerodynamic load acting on a panel. Numerical results are summarized to reveal the thermal post-buckling behaviors of FG panels with various volume fractions, temperature conditions and aerodynamic pressures in detail.

• Advances in aircraft and spacecraft science
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• 제4권4호
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• pp.449-465
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• 2017

The aim of the present work is to present a computational study of the non-linear aero-elastic behavior of a multi-layered Thermal Protection System (TPS). The severity of atmospheric re-entry conditions is due to the combination of high temperatures, high pressures and high velocities, and thus the aero-elastic behavior of flexible structures can be difficult to assess. In order to validate the specific computational model and the overall strategy for structural and aerodynamics analyses of flexible structures, the simplified TPS sample tested in the 8' High Temperature Tunnel (HTT) at NASA LaRC has been selected as a baseline for the validation of the present work. The von $K{\acute{a}}rm{\acute{a}}n^{\prime}s$ three dimensional large deflection theory for the structure and a hybrid Raleigh-Ritz-Galerkin approach, combined with the first order Piston Theory to describe the aerodynamic flow, have been used to derive the equations of motion. The paper shows that a good description of the physical behavior of the fabric is possible with the proposed approach. The model is further applied to investigate structural and aero-elastic influence of the number of the layers and the stitching pattern.

• Structural Engineering and Mechanics
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• 제84권4호
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• pp.437-452
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• 2022

For the first time, the higher-order shear and normal deformable plate theory (HOSNDPT) is used for the vibration and flutter analyses of the multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates under supersonic airflow. For modeling the supersonic airflow, the linear piston theory is adopted. In HOSNDPT, Legendre polynomials are used to approximate the components of the displacement field in the thickness direction. So, all stress and strain components are encountered. Either uniform or three kinds of non-uniform distribution of graphene platelets (GPLs) into polymer matrix are considered. The Young modulus of the FG-GPLRC plate is estimated by the modified Halpin-Tsai model, while the Poisson ratio and mass density are determined by the rule of mixtures. The Hamilton's principle is used to obtain the governing equations of motion and the associated boundary conditions of the plate. For solving the plate's equations of motion, the Galerkin approach is applied. A comparison for the natural frequencies obtained based on the present investigation and those of three-dimensional elasticity theory shows a very good agreement. The flutter boundaries for FG-GPLRC plates based on HOSNDPT are described and the effects of GPL distribution patterns, the geometrical parameters and the weight fraction of GPLs on the flutter frequencies and flutter aerodynamic pressure of the plate are studied in detail. The obtained results show that by increasing 0.5% of GPLs into polymer matrix, the flutter aerodynamic pressure increases approximately 117%, 145%, 166% and 196% for FG-O, FG-A, UD and FG-X distribution patterns, respectively.

• Wind and Structures
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• 제29권6호
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• pp.457-469
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• 2019

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al₂O₃ that increase in volume fraction of ceramic (Al₂O₃) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

• Composites Research
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• 제13권5호
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• pp.50-59
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• 2000

본 논문에서는 복합재료 패널 플러터를 억제할 수 있는 두 가지 방법에 대해서 연구하였다. 첫번째, 능동제어 방법에서는 선형 제어 이론을 바탕으로 제어기를 설계하였으며 제어입력이 작동기에 가해진다. 여기서 작동기로는 PZT를 사용하였다. 두 번째, 인덕터와 저항으로 구성되어진 션트회로를 사용하여 시스템의 감쇠를 증가시킴으로써 패널 플러터를 억제할 수 있는 새로운 방법인 수동감쇠기법에 대한 연구가 수행되었다. 이 수동감쇠기법은 능동적 제어보다 강건(robust)하며 커다란 전원 공급이 필요하지 않고 제어기나 감지 시스템과 같이 복잡한 주변 기기가 필요 없이도 실제 패널 플러터 억제에 쉽게 응용할 수 있는 장점을 가지고 있다. 최대의 작동력/감쇠 효과를 얻기 위해서 유전자 알고리듬을 사용하여 압전 세라믹의 형상과 위치를 결정하였다. 해밀턴 원리를 사용해서 지배 방정식을 유도하였으며, 기하학적 대변형을 고려하기 위해 von-Karman의 비선형 변형률-변위 관계식을 사용하였으며 공기력 이론으로는 준 정상 피스톤 1차 이론을 사용하였다. 4절점 4각형 평판 요소를 이용하여 이산화된 유한 요소 방정식을 유도하였다. 효율적인 플러터 억제를 위해 패널 플러터에 중요한 영향을 미치는 플러터 모드를 이용한 모드축약기법을 사용하였으며, 이를 통해 비선형 연계 모달 방정식이 얻어지게 된다. 능동적 제어 방법과 수동 감쇠 기법에 의해 수행되어진 플러터 억제 결과들을 Newmark 비선형 시분할 적분법을 통해 시간 영역에서 살펴 보았다.