Journal of Aerospace Engineering

The present paper is the last part of a three-part survey paper, in which I give a review of several research directions in the area of mathematical analysis of flutter phenomenon. Flutter is known as a structural dynamical instability, which occurs in a solid elastic structure interacting with a flow of gas or fluid and consists of violent vibrations of the structure with rapidly increasing amplitudes. The focus of this paper is a collection of models of fluid-structure interaction, for which precise mathematical formulations are available. My main interest is in the analytical results on such models: the results that can be used to explain flutter and its qualitative and even quantitative treatments. This study does not pretend to be a comprehensive review of an enormous engineering literature on analytical, computational, and experimental aspects of the flutter problem. I present a brief exposition of the results obtained in several selected papers or groups of papers. In this paper, I concentrate on the most well-known cases of flutter, i.e., flutter in aeroelasticity. Namely, I discuss aircraft flutter in historical retrospective and outline some future directions of flutter analysis. The last two sections of the paper are devoted to the precise analytical results obtained in my several recent works on a specific aircraft wing model in a subsonic, inviscid, incompressible airflow. I also mention that in the previous papers (Parts I and II of the survey), I discuss such topics as: (1) bending–torsion vibrations of coupled beams; (2) flutter in transmission lines; (3) flutter in rotating blades; (4) flutter in hard disk drives; (5) flutter in suspension bridges; and (6) flutter of blood vessel walls.

The free vibration of beams whose flexural motions in both principal planes are coupled with torsion is investigated by using the dynamic stiffness method. First, the governing differential equations of motion in free vibration are derived using Hamilton’s principle. The dynamic stiffness matrix is then developed from the solution of these differential equations when the oscillatory motion of the beam is harmonic. Finally, the resulting dynamic stiffness matrix is applied with particular reference to the Wittrick–Williams algorithm to carry out the free vibration analysis of a few illustrative examples. The numerical results are discussed and this is followed by some concluding remarks.

A formulation based on the linearized shallow shell theory has been developed by Delale and Erdogan to determine the stress intensity factors of a shell with a through-the-thickness crack. The drawback in the formulation is that the crack-face closure at the compressive edges when a cracked shell is subjected to a bending load is not taken into account, which results in the penetration of material at the crack faces. The present research is aimed to improve the formulation by including the effect of the crack-face closure on the stress intensity factors. Simulation of the closure is achieved by a line contact at the compressive edges of the crack faces. The unknown contact force is then computed by solving a mixed-boundary value problem iteratively to ensure that either the normal displacement of the crack face at the compressive edges equals zero or the contact pressure equals zero along the crack length. The results have shown that the crack-face closure significantly influences the magnitude of the stress intensity factors and tends to reduce the maximum stress intensity factor. The magnitude of the reduction varies with the curvatures of the shell and the ratio of the two curvatures as well.

Extremely high-suction pressures generated beneath the conical vortex flow in the roof-corner region have a devastating effect on the building roofs in high-wind events. The application of quasi-steady theory near the roof corners of low-rise buildings deserves careful investigation for the appropriate assessment of the design wind loads. A synchronized incident wind and pressure data acquisition system was set up on the full-scale experimental building at Texas Tech Univ. Experiments were conducted systematically to simultaneously collect the incident wind and roof-corner pressure data under the influence of cornering winds. By using a conditional sampling technique, a bivariate quasi-steady model was established to incorporate the influence of both horizontal and vertical wind directional variations on the roof-corner pressures. Comparison between the measured pressures and the model-predicted pressures has shown that the quasi-steady theory in the suggested form is applicable in the roof-corner separated flow region where vortices are present. This conclusion further justifies the application and codification of quasi-steady approach for wind load assessment of low-rise buildings and other structures.

An experimental and modeling system for the modeling of multilayer composite fabrics used in a gas turbine engine containment system is developed. Specifically, Kevlar 49 $(17\times 17)$ and Zylon AS $(35\times 35)$ fabrics are used in the study. The experimental setup is first used to obtain the material properties of these fabrics. Later, one or more layers of these fabrics is tightly wrapped around a steel cylinder that simulates an engine containment housing. A steel penerator (or a blunt nose) is used in a static test by slowly pushing against the fabric. The resulting load-deflection data are used to compute a variety of parameters, including the energy absorption capacity. The material behavior obtained from the experimental study is then used as the constitutive model in a finite element simulation of the static test. The objective is to develop a procedure for understanding the relative strengths and weaknesses of different fabrics and to aid in the development of finite element modeling of actual fan blade-out events.

An analytical model is presented to predict the nonlinear response of a double-wall sandwich cylindrical shell system subjected to random excitation. Nonlinear spring-dashpot models are integrated into the system to characterize the behavior of the soft core. Donnell’s thin shell theory is used to develop the governing nonlinear equations of motion. A Monte Carlo simulation of stationary random processes, multimode Galerkin-type approach, and numerical integration procedures are used to develop linear and nonlinear response solutions of simply supported cylindrical shells. Numerical results include time domain response histories, root-mean-square values and response spectral densities. Parametric studies are performed to investigate the effects of nonlinearity, shell thickness, core stiffness, and thickness.

The solar radiation absorbed in massive building components is stored and later emitted as long-wave thermal radiation into the interior space. Heat storage capacity is directly related to the mass of the building envelope surrounding this space and particularly that of high-mass, homogeneous earthen or cementitious material. A thermal storage cycle is created by the time-lag effect if sufficient mass is available. A similar strategy applied to the lunar and/or Martian regolith would provide a surface structure with micrometeorite and radiation protection, thermal insulation, and natural supplemental heat energy that would significantly reduce the energy requirements met by mechanical equipment. HEAT2 is an energy simulation program that solves heat transfer problems using the partial differential heat conduction equation in two dimensions with the method of explicit finite differences. HEAT2 simulation data suggests that, although thermal mass is most suitable for climates where desired indoor temperatures fall within a large daily external temperature gradient, the heat storage cycle is least effective at the annual extremes occurring in midwinter and in midsummer. A more moderate climate will allow the heat storage cycle to modulate between positive and negative heat flows which are then shifted to align with peak load conditions, reducing energy demand. Also, diurnal and seasonal temperature gradients can initiate a sequence of phase transitions in the soil’s moisture content affecting the overall conductivity. This study will present a more accurate explanation of the heat transfer processes occurring in soils of varying compositions when thermal properties are altered by transient climatic conditions.