Earl H. Dowell

Panel flutter - A review of the aeroelastic stability of plates and shells

Panel flutter theory applied to aeroelastic stability of flat unloaded plates and cylindrical shells

Acoustoelasticity: General theory, acoustic natural modes and forced response to sinusoidal excitation, including comparisons with experiment

A comprehensive theoretical model has been developed for interior sound fields which are created by flexible wall motion resulting from exterior sound fields. Full coupling between the wall and interior acoustic cavity is permitted. An efficient computational method is used to determine acoustic natural frequencies of multiply connected cavities. Simplified formulae are developed for interior sound levels in terms of cavity, wall and external acoustic field parameters. Comparisons of theory and experiment show generally good agreement.

Proper Orthogonal Decomposition Technique for Transonic Unsteady Aerodynamic Flows

A new method for constructing reduced-order models (ROM) of unsteady small-disturbance flows is presented. The reduced-order models are constructed using basis vectors determined from the proper orthogonal decomposition (POD) of an ensemble of small-disturbance frequency-domain solutions. Each of the individual frequency-domain solutions is computed using an efficient time-linearized flow solver. We show that reduced-order models can be constructed using just a handful of POD basis vectors, producing low-order but highly accurate models of the unsteady flow over a wide range of frequencies. We apply the POD/ROM technique to compute the unsteady aerodynamic and aeroelastic behavior of an isolated transonic airfoil and to a two-dimensional cascade of airfoils

Localization of vibrations by structural irregularity

An investigation of the localization phenomenon is presented for disrodered structural systems consisting of weakly coupled component systems. Emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system from the modes of the individual subsystems. The principal feature of this perturbation method is that it not only considers the variations of the parameters as perturbations, but it also treats the small coupling between subsystems as a perturbation. Such a perturbation analysis is cost effective as compared to a global eigenvalue analysis of the entire system, and proves to be very accurate. Moreover, it provides physical insight into the localization phenomenon, and allows one to formulate a criterion that predicts the occurrence of strongly localized modes. Results are obtained for a chain of single-degree-of-freedom coupled oscillators, but these can be readilt generalized to deal with chains of multi-degree-of-freedom component systems.

Nonlinear Inviscid Aerodynamic Effects on Transonic Divergence, Flutter and Limit Cycle Oscillations

By the use of a state-of-the-art computational e uid dynamic (CFD) method to model nonlinear steady and unsteady transonice owsin conjunction with a linearstructural model,an investigationismadeinto how nonlinear aerodynamics can effect the divergence, e utter, and limit-cycle oscillation (LCO) characteristics of a transonic airfoil cone guration. A single-degree-of-freedom (DOF) model is studied for divergence, and one- and two-DOF models are studied for e utter and LCO. A harmonicbalancemethod in conjunction with the CFD solver is used to determine the aerodynamics for e nite amplitude unsteady excitations of a prescribed frequency. A procedure for determining the LCO solution is also presented. For the cone guration investigated, nonlinear aerodynamic effects are found to produce a favorable transonic divergence trend and unstable and stable LCO solutions, respectively, for the one- and two-DOF e utter models. Nomenclature a = nondimensional location of airfoil elastic axis, e=b b, c = semichord and chord, respectively cl, cm = coefe cients of lift and moment about elastic axis, respectively e = location of airfoil elastic axis, measured positive aft of airfoil midchord h, ® = airfoil plunge and pitch degrees of freedom I® = second moment of inertia of airfoil about elastic axis

On the aeroelastic instability of two-dimensional panels in uniform incompressible flow

Abstract A theoretical and experimental study is presented of the aeroelastic instability of a panel with various boundary conditions on its leading and trailing edges, exposed to air flow over its upper surface or on both sides. The flow is incompressible and two-dimensional (no span-wise deformation of the panel). The case of a panel clamped at its leading edge and free at its trailing edge is investigated both theoretically and experimentally. Agreement between theory and experiment is fair. The aerodynamic theory of steady non-circulatory flow is applied for panels fixed at both ends, and the quasi-steady and full unsteady aerodynamic lifting theories to a cantilevered panel (free at the trailing edge). The analogy with incompressible flow through a long slender tube is pointed out. Theory shows that a panel with both ends fixed loses its stability by divergence, while the instability of a cantilevered panel is of a flutter type. The latter is also confirmed experimentally.

Governing Equations for Vibrating Constrained-Layer Damping Sandwich Plates and Beams

A simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers. The natural boundary conditions related to this equation are determined and some typical numerical results obtained by this equation are given. The equation is valid within the linear theories of elasticity and viscoelasticity in the absence of any constraints on thicknesses, positions, symmetries, and densities of the layers.

Experimental and Theoretical Study on Aeroelastic Response of High-Aspect-Ratio Wings

An experimental high-aspect-ratio wing aeroelastic model with a slender body at the tip has been constructed, and the response due to flutter and limit-cycle oscillations (LCO) has been measured in a wind-tunnel test. A theoretical model has been developed and calculations made to correlate with the experimental data. Structural equations of motion based on nonlinear beam theory are combined with the ONERA aerodynamic stall model to study the effects of geometric structural nonlinearity and steady angle of attack on flutter and LCO of high-aspect-ratio wings. Static deformations in the vertical and torsional directions caused by a steady angle of attack and gravity are measured, and results from theory and experiment are compared. A dynamic perturbation analysis about a nonlinear static equilibrium is used to determine the small perturbation flutter boundary, which is compared to the experimentally determined flutter velocity and oscillation frequency. Time simulation is used to compute the LCO response. The results between the theory and experiment are in good agreement for static aeroelastic response, the onset of flutter, and dynamic LCO amplitude and frequency.

Three-Dimensional Transonic Aeroelasticity Using Proper Orthogonal Decomposition-Based Reduced-Order Models

The proper orthogonal decomposition (POD) based reduced order modeling (ROM) technique for modeling unsteady frequency domain aerodynamics is developed for a large scale computational model of an inviscid flow transonic wing configuration. Using the methodology, it is shown that a computational fluid dynamic (CFD) model with over a three quarters of a million degrees of freedom can be reduced to a system with just a few dozen degrees of freedom, while still retaining the accuracy of the unsteady aerodynamics of the full system representation. Furthermore, POD vectors generated from unsteady flow solution snapshots based on one set of structural mode shapes can be used for different structural mode shapes so long as solution snapshots at the endpoints of the frequency range of interest are included in the overall snapshot ensemble. Thus, the snapshot computation aspect of the method, which is the most computationally expensive part of the procedure, does not have to be fully repeated as different structural configurations are considered.

Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system

Abstract For aeroelasticity of plates and shells, the equations of motion are well established. Results obtained by numerical time integration have been compared to those obtained by topological theories of dynamics and also from experiment. All of these suggest that chaotic self-excited oscillations may occur for this deterministic system.