Engineering Commons^™

Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …

The Modeling Of Structural-Acoustic Interaction Using Coupled Fe/Be Method And Control Of Interior Acoustic Pressure Using Piezoelectric Actuators, Yucheng Shi

Mechanical & Aerospace Engineering Theses & Dissertations

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural--acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the …

Finite Element Nonlinear Random Response Of Composite Panels Of Arbitrary Shape To Acoustic And Thermal Loads Applied Simultaneously, Roger R. Chen

Mechanical & Aerospace Engineering Theses & Dissertations

The nonlinear random response of composite plates to the simultaneously applied, combined acoustic/thermal loads are investigated in this dissertation. A finite element formulation for the nonlinear random response is developed. The three-node Mindlin plate element with improved transverse shear is extended and employed. The extension includes the development of the thermal geometric matrix, the mass matrix, the first- order and second-order nonlinear stiffness matrices, and the thermal and mechanical load vectors. An innovative solution procedure has been created which is believed to be the first attempt to analyze nonlinear random response of complex composite panels subjected to simultaneous acoustic and …

Finite Element Frequency Domain Solution Of Nonlinear Panel Flutter With Temperature Effects And Fatigue Life Analysis, David Yongxiang Xue

Mechanical & Aerospace Engineering Theses & Dissertations

A frequency domain solution method for nonlinear panel flutter with thermal effects using a consistent finite element formulation has been developed. The von Karman nonlinear strain-displacement relation is used to account for large deflections, the quasi-steady first-order piston theory is employed for aerodynamic loading and the quasi-steady thermal stress theory is applied for the thermal stresses with a given change of the temperature distribution, ΔΤ (x, y, z). The equation of motion under a combined thermal-aerodynamic loading can be mathematically separated into two equations and then solved in sequence: (1) thermal-aerodynamic postbuckling and (2) limit-cycle oscillation. The Newton-Raphson iteration technique …

A Finite Element Formulation For The Large Deflection Random Response Of Thermally Buckled Structures, James Eugene Locke

Mechanical & Aerospace Engineering Theses & Dissertations

The effects of temperature and acoustic loading are included in a theoretical finite element large deflection formulation for thin, isotropic plate and beam type structures. Thermal loads are applied as steady-state temperature distributions, and acoustic loads are taken to be stationary and Gaussian with zero mean and uniform magnitude and phase over the surface of the structure. Material properties are considered to be independent of temperature. Also, inplane and rotary inertia terms are assumed to be neglegible, and all inplane edge conditions are taken to be immovable. For the random vibration analysis, cross correlation terms are included.

The nature of …