Showing papers by "Earl H. Dowell published in 2018"

Detecting multi-pulse chaotic dynamics of high-dimensional non-autonomous nonlinear system for circular mesh antenna

Abstract: This paper investigates the global bifurcations and multi-pulse jumping chaotic dynamics of circular mesh antenna. An equivalent continuum circular cylindrical shell is employed to represent the circular mesh antenna. Based on the four-dimension non-autonomous nonlinear governing equations of motion for the equivalent continuum circular cylindrical shell derived by Zhang et al. (2016, 2017), the improved extended Melnikov theory of the non-autonomous nonlinear system is utilized to conduct a theoretical analysis of the multi-pulse jumping chaotic motions for the equivalent continuum circular cylindrical shell. The thermal excitation and damping coefficient are considered as the controlling parameters to analyze their effect on the nonlinear vibrations and bifurcations of the equivalent continuum circular cylindrical shell. Numerical simulations are also introduced to further verify the existence of the multi-pulse jumping chaotic motions for the equivalent continuum circular cylindrical shell. The results obtained from the numerical simulations are compared to those obtained from the Melnikov theoretical prediction.

Nonlinear Response of an Inextensible, Cantilevered Beam Subjected to a Nonconservative Follower Force

Abstract: The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers consider a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and the agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear postcritical limit cycle oscillations (LCO) are studied including a concentration on the force which enforces the inextensibility constraint.

Analysis on global and chaotic dynamics of nonlinear wave equations for truss core sandwich plate

Abstract: This paper presents the study on the chaotic wave and chaotic dynamics of the nonlinear wave equations for a simply supported truss core sandwich plate combined with the transverse and in-plane excitations. Based on the governing equation of motion for the simply supported sandwich plate with truss core, the reductive perturbation method is used to simplify the partial differential equation. According to the exact solution of the unperturbed equation, two different kinds of the topological structures are derived, which one structure is the resonant torus and another structure is the heteroclinic orbit. The characteristic of the singular points in the neighborhood of the resonant torus for the nonlinear wave equation is investigated. It is found that there exists the homoclinic orbit on the unperturbed slow manifold. The saddle-focus type of the singular point appears when the homoclinic orbit is broken under the perturbation. Additionally, the saddle-focus type of the singular point occurs when the resonant torus on the fast manifold is broken under the perturbation. It is known that the dynamic characteristics are well consistent on the fast and slow manifolds under the condition of the perturbation. The Melnikov method, which is called the first measure, is applied to study the persistence of the heteroclinic orbit in the perturbed equation. The geometric analysis, which is named the second measure, is used to guarantee that the heteroclinic orbit on the fast manifold comes back to the stable manifold of the saddle on the slow manifold under the perturbation. The theoretical analysis suggests that there is the chaos for the Smale horseshoe sense in the truss core sandwich plate. Numerical simulations are performed to further verify the existence of the chaotic wave and chaotic motions in the nonlinear wave equation. The damping coefficient is considered as the controlling parameter to study the effect on the propagation property of the nonlinear wave in the sandwich plate with truss core. The numerical results confirm the validity of the theoretical study.

A study of the natural modes of vibration and aeroelastic stability of a plate with a piezoelectric material

Abstract: The natural modes as well as the aeroelastic stability of a plate with attached piezoelectric material in response to a change in electric potential are studied. A finite element model is developed based on the classical lamented plate theory. The piezoelectric stiffening effect is obtained using the concept of a change in geometric stiffness. Three piezoelectric configurations are considered in the present work: (1) with the piezoelectric actuators covering the whole plate, (2) with the piezoelectric actuators covering a portion of the plate near the clamped support, and (3) with the piezoelectric actuators covering a portion of the plate near the free end. In all the three cases, the piezoelectric sheets cover the plate on both sides. The second configuration is effective in stiffening the plate, while the first and third configurations are effective in buckling the plate. We also find the piezoelectric force has a significant effect on wing natural modes and aeroelastic stability. An increase in negative applied voltage can increase the aeroelastic stability, while increasing the positive voltage can decrease the plate stability. The piezoelectric effect on the plate torsional modes is more significant than its effect on its bending modes. The selection of the piezoelectric material configuration as well as the applied voltage is important for stiffening or weakening a plate.

Computational Study of Aeroelastic Limit Cycles due to Localized Structural Nonlinearities

Abstract: Aeroelastic systems including all-moving control surfaces and aircraft wings with stores may experience limit cycling caused by nonlinear structural and/or aerodynamic mechanisms. These systems are...

Bending-torsional instability of a viscoelastic cantilevered pipe conveying pulsating fluid with an inclined terminal nozzle

Abstract: In the present study, dynamic stability of a viscoelastic cantilevered pipe conveying fluid which fluctuates harmonically about a mean flow velocity is considered; while the fluid flow is exhausted through an inclined end nozzle. The Euler-Bernoulli beam theory is used to model the pipe and fluid flow effects are modelled as a distributed load along the pipe which contains the inertia, Coriolis, centrifugal and induced pulsating fluid flow forces. Moreover, the end nozzle is modelled as a follower force which couples bending vibrations with torsional ones. The extended Hamilton's principle and the Galerkin method are used to derive the bending-torsional equations of motion. The coupled equations of motion are solved using Runge-Kutta algorithm with adaptive time step and the instability boundary is determined using the Floquet theory. Numerical results present effects of some parameters such as fluid flow fluctuation, bending-to-torsional rigidity ratio, nozzle inclination angle, nozzle mass and viscoelastic material on the stability margin of the system and some conclusions are drawn.

Catastrophe-Theory-Based Modeling of Airfoil-Stall Boundary at Low Reynolds Numbers

Abstract: Airfoil stall at low Reynolds numbers is a complex nonlinear dynamic phenomenon, which is characterized by catastrophe and hysteresis. It is difficult but important to mathematically describe the s...

The sound field of a rotating dipole in a plug flow.

Abstract: An analytical far field solution for a rotating point dipole source in a plug flow is derived. The shear layer of the jet is modelled as an infinitely thin cylindrical vortex sheet and the far field integral is calculated by the stationary phase method. Four numerical tests are performed to validate the derived solution as well as to assess the effects of sound refraction from the shear layer. First, the calculated results using the derived formulations are compared with the known solution for a rotating dipole in a uniform flow to validate the present model in this fundamental test case. After that, the effects of sound refraction for different rotating dipole sources in the plug flow are assessed. Then the refraction effects on different frequency components of the signal at the observer position, as well as the effects of the motion of the source and of the type of source are considered. Finally, the effect of different sound speeds and densities outside and inside the plug flow is investigated. The solution obtained may be of particular interest for propeller and rotor noise measurements in open jet anechoic wind tunnels.

Iterative techniques for analyzing nonlinear vibrating dynamical systems in the frequency domain

Abstract: The nonlinear response of prototypical structures experiencing harmonic excitation is studied using novel techniques called iterative harmonic analysis (IHA) and iterative modal analysis (IMA). First, a simple damped oscillator with a cubic hardening stiffness nonlinearity is studied, and IHA is used in this single-degree-of-freedom system. In this first section, a high-order harmonic balance is applied, and IHA is employed in order to find the amplitude coefficients for different harmonics and their codependence. Additionally, a set of nested sums are identified that describe the harmonic coupling explicitly. Secondly, a pinned–pinned nonlinear beam of rectangular cross-section is studied, and IMA is applied to find the amplitude coefficients for different modes and their codependence. The nonlinearity is introduced through the membrane effect, where axial strain due to transverse deflection becomes a significant contributor to the system behavior. Typical frequency-domain methods cannot be easily applied to these systems as the solutions of the differential equations lead to intricate coupling between coefficients of the solution, and no analytical expression exists for those coefficients. Based upon these examples, other nonlinear systems may also be considered in future work using either a modal-based or finite element model. Finally, the advantages of the new method (reduced computational cost) as well as the limitations (effectively the same as those of an nth-order harmonic balance) are emphasized.

Progress Toward Efficient Compression Algorithms for Application in Flight Simulation Environments

Abstract: Modern computational fluid dynamic simulations of flows about naval vessels produce an enormous amount of flow-field data. The computations are performed in order to model details of the erratic un...

Measuring the Aero-Refueling Hose Model’s Sectional-Bending-Stiffness in the RMCFLM Experimental System

Abstract: By modeling an aero-refueling hose as a flexible pipe, an experimental research is performed on measuring the sectional bending stiffness of a flexible pipe withstanding a internal-pressurized fluid. A Revised Midpoint-Concentrate-Force-Loading Methodology (RMCFLM) with its valid range is developed to measure the sectional bending stiffness of a flexible pipe. The total system measurement error would be controlled within 7%. Three test specimens of a silica gel pipe, a polyvinyl chloride pipe and a rubber hose with fabric insert are conducted to measure their sectional-bending-stiffness in variable internal-pressurized fluid. The sectional-bending-stiffness increases with an incremental fluid pressure in a flexible pipe. Furthermore, the equivalent elastic modulus of a pipe is smaller and a incremental rate of the sectional-bending-stiffness is larger.