Mechanical Engineering Commons^™

Development Of Vibration And Sensitivity Analysis Capability Using The Theory Of Structural Variations, Ting-Yu Rong

Mechanical & Aerospace Engineering Theses & Dissertations

In the author's previous work entitled "General Theorems of Topological Variations of Elastic Structures and the Method of Topological Variation," 1985, some interesting properties of skeletal structures have been discovered. These properties have been described as five theorems and synthesized as a theory, called the theory of structural variations (TSV). Based upon this theory, an innovative analysis tool, called the structural variation method (SVM), has been derived for static analysis of skeletal structures (one-dimensional finite element systems).

The objective of this dissertation research is to extend TSV and SVM from one-dimensional finite element systems to multi-dimensional ones and from statics …

A New Adjoint Variable Method For The Sensitivity Analysis Of Dynamic Responses, Krishnamoorthy Ramesh

Mechanical & Aerospace Engineering Theses & Dissertations

A new adjoint variable method has been formulated for finding the sensitivity derivatives of dynamic system responses. Though the method can be based on any step-by-step time marching scheme, the Wilson Theta Method has been chosen as the basis of the new formulation . Wilson Theta Method is an implicit numerical integration scheme for finding the dynamic system responses. The new formulation uses the differential form of equations of motion as given by the Wilson Theta Method in its formulation of the adjoint equation. The conventional methods used for finding the sensitivity derivatives, namely, the direct differentiation technique, the central …

An Analysis Of The Response Of A Buckled Beam With Fixed Ends To An Harmonic Base Excitation Using The Finite Element Method, Peter John O'Donoghue

Mechanical & Aerospace Engineering Theses & Dissertations

A finite element formulation is developed to analyze the large deflection vibration of a buckled isotropic beam. The beam is buckled mechanically by an applied end displacement, and the dynamic loading is derived from the forced periodic base motion. The principle of virtual work is used to derive the system equations of motion. A Newton-Raphson iteration routine modified for the case of an applied end displacement is used with the incremental equations of motion to determine static deflection. The 0l time numerical integration algorithm is applied to the system of equations of motion in physical coordinates to determine dynamic response …

Effects Of Radiative Interactions In Molecular Gases Under Local And Nonlocal Thermodynamic Equilibrium Conditions, Manoj Kumar Jha

Mechanical & Aerospace Engineering Theses & Dissertations

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions.

The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are …

A Fracture Mechanics Analysis Of A 38 Inch Diameter Hot Pressed Beryllium Telescope Mirror, Phillip L. Brown

Mechanical & Aerospace Engineering Theses & Dissertations

A 38 inch diameter hot pressed beryllium telescope mirror was analyzed for structural integrity using finite-element modeling and a fracture mechanics analysis program, ZIP3D, developed for three-dimensional (3-0) solid and cracked bodies. The calculation of stress and mixed-mode fracture mechanics parameters for the mirror critical stress area was the objective of the mirror analysis.

Finite-element modeling for ZIP3D solution was performed in two stages. The first stage modeling modeled the mirror configuration on a global basis for calculation of accurate nodal displacements. The second stage modeling reduced the modeled mirror configuration to a set of localized models for calculation of …

Development Of A Model Updating Technique For Controls-Structures Integrated Design Optimization, Angela Georges

Mechanical & Aerospace Engineering Theses & Dissertations

A model updating technique is developed with the intent of providing an efficient means of improving the accuracy of the modelling of the vibrational qualities of a large, flexible structure as it undergoes an integrated controls-structures design optimization. The proposed technique utilizes eigenvalue/eigenvector sensitivity information, two different model reduction methods which assign weights of importance to the vibrational modes of the structure, and modal switching based upon the modal weights determined by the model reduction methods. Issues associated with the numerical implementation of the proposed technique, such as discontinuities induced by modal switching, are also addressed.

The proposed model updating …

Modal Analysis Of Gyroscopically Coupled Sound-Structure Interaction Problems, Vijay B. Bokil

Mechanical & Aerospace Engineering Theses & Dissertations

In many practical situations we encounter sound-structure interaction between the fluid in a cavity and the flexible wall on the boundary. The aircraft cabin interacting with its fuselage and double-leaf partition walls interacting with the enclosed cavity are some of the typical examples. The vibratory behavior of the structure and the acoustical pressure inside the cavity are affected by this interaction.

In most of the cases, the governing differential equations for the coupled system can be shown to involve gyroscopic coupling. A special method has been applied to decouple the equations in terms of pairs of generalized coordinates and the …

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 …

Dynamic Test/Analysis Correlation Using Reduced Analytical Models, Paul E. Mcgowan

Mechanical & Aerospace Engineering Theses & Dissertations

Test/analysis correlation is an important aspect of the verification of analysis models which are used to predict on-orbit response characteristics of large space structures. This thesis summarizes the study of using reduced analysis models for performing dynamic test/analysis correlation. The reduced test-analysis model (TAM) has the same number of degrees-of-freedom (DOF) as the number of test measurements. This allows the direct comparison of modal parameters between ground vibration test results and finite element model (FEM) analysis results. The TAM can also be used for pre-test analysis and to aid in the post-test mathematical model updating process.

Herein, four methods for …

Simulation And Measurement Of The Radiant Field Produced By Quartz Heating Systems, Travis Lee Turner

Mechanical & Aerospace Engineering Theses & Dissertations

A method is developed for predicting the radiant heat flux distribution produced by tungsten-filament tubular quartz heating systems with reflectors. The method is an application of Monte Carlo simulation, which takes the form of a ray tracing or random walk scheme. The method is applied to four systems of increasing complexity including; a single unreflected lamp, a single lamp with a flat reflector, a single lamp with a parabolic reflector, and up to six lamps in a six-lamp contoured reflector heating unit. The general methodology of the Monte Carlo method is discussed and applied to the simulation of thermal radiation. …

Finite Element Analysis Of Thermal Post-Buckling And Vibrations Of Thermally Buckled Composite Plates, Charles Clifton Gray

Mechanical & Aerospace Engineering Theses & Dissertations

The development of supersonic and hypersonic flight vehicles such as the High Speed Civil Transport and the National Aero-Space Plane has created an increased need for analysis of structures at very high temperatures. Bisplinghoff and Pian, Yang and Han, and Dokmeci and Boley have conducted experimental and analytical studies to determine the effect of elevated temperatures on the vibration characteristics of isotropic plates, Chen and Chen, and Meyers and Hyer have clone studies on thermal buckling and post-buckling of composite plates, respectively.

The thermal loads which will be imposed on the new high speed aircraft will be too great for …

Automating Tolerance Synthesis: A Framework And Tools, Stephen C.-Y. Lu, Robert G. Wilhelm

Department of Mechanical and Materials Engineering: Faculty Publications

This paper describes CASCADE-T—a new approach to tolerance synthesis that uses a complete representation of the conditional tolerance relations that exist between features of a part under design. Conditional tolerances are automatically determined from functional requirements and shape information. Tolerance primitives based on the virtual boundary requirements approach to tolerance representation are composed to form more complex tolerance relationships. Artificial intelligence techniques, including a constraint network, frame-based system, and dependency tracking are used to support flexible and detailed computation for tolerance analysis and synthesis.

The Effectiveness Of Viscoelastic Damping Treatments On A Flexible Manipulator Subjected To Torsional Loads, Leah L. Remias

Mechanical & Aerospace Engineering Theses & Dissertations

The advent of new technology has led to an increasing number of missions in space. The space shuttle Remote Manipulator System (RMS) is a lightweight flexible manipulator currently used in NASA space missions. The future role of the RMS and similar flexible manipulators may include in-space construction and assembly tasks. Because these tasks require precise motion and short settling time of the end-point oscillations, effective vibration control schemes are being investigated.

Passive damping techniques have shown to provide a considerable amount of damping in controlling flexural vibrations. In this research passive damping via constrained viscoelastic damping treatments is explored as …

Nondestructive Detection Of An Undeserable Metallic Phase, T1, During Processing Of Alumnum-L Thumalloys, Otto Buck, David J. Bracci, David C. Jiles, Lisa J.H. Brasche, Jeffrey E. Shield, Leonard S. Chumbley

Department of Mechanical and Materials Engineering: Faculty Publications

A method is disclosed for detecting the T1 phase in aluminum-lithium alloys through simultaneous measurement of conductivity and hardness. In employing eddy current to measure conductivity, when the eddy current decreases with aging of the alloy, while the hardness of the material continues to increase, the presence of the T1 phase may be detected.

Finite Element Analysis Of Structures With Constrained Viscoelastic Layer Damping, Yung Chen

Mechanical & Aerospace Engineering Theses & Dissertations

It has been demonstrated that constrained viscoelastic layer damping treatments provide an effective means of passive control for structural vibration. These treatments dissipate vibrational energy by inducing shear strain in a thin layer of viscoelastic material. Our interest is in adding passive damping to a structure as an augmentation to active control. For such applications it is desirable to achieve high damping performance in a given frequency range with a minimum of added weight. Most damping treatments employ spatially continuous constraining layers over the entire viscoelastic layer. Plunkett and Lee have shown that the effectiveness of the damping treatment can …

Numerical Investigation Of A Non-Newtonian Material Through A Sudden Pipe Expansion, V. G. Masanja

Tanzania Journal of Engineering and Technology (TJET)

A numerical method for solving two dimensional elliptic boundary-value problems of fourth order is used for finding stationary solutions of the equations of motion for a laminar flow through a sudden pipe expansion of an incompressible non-Newtonian fluid with a constitutive equation of the Reiner-Rivlin (R-R) type. Results for the Newtonian fluid, which is a special case, are in excellent agreement with those by previous investigators and they demonstrate the reliability, superiority and accuracy of the method. Results for the non-Newtonian cases could be of value for fixing ideas about visco-elastic behaviour although the R-R fluid allows only inelasticity: this …

Eigensensitivity Analysis For Space Structures With Applications In Design Optimization, Sean Patrick Kenny

Mechanical & Aerospace Engineering Theses & Dissertations

Eigensensitivity analysis is concerned with the rates of changes of eigenvalues and eigenvectors with respect to design variables. Eigensolutions of space structures are found to display four distinct characteristics, three of which are related to various types of repeated eigenvalues. This study will address three cases of the real symmetric structural eigenvalue problem. The three cases that will be considered are: distinct eigenvalues, repeated eigenvalues with distinct first eigenvalue derivatives, and repeated eigenvalues with infinitely repeating eigenvalue derivatives. Analytic formulations for eigenvalue/ vector derivatives will be presented for each of the three cases. The directional differentiability of eigenvalues for the …

The Influence Of Payload Dynamics On Trajectory Tracking Performance Of Robot Manipulator, Atul G. Kelkar

Mechanical & Aerospace Engineering Theses & Dissertations

Future space mission plans call for extensive use of remote manipulator systems for tasks such as assembly of lunar vehicles or space station modules, servicing of satellites, etc. These tasks demand very high precision end-effector motion control. Methods for compensating manipulator dynamics to achieve better trajectory tracking performance have been investigated by many researchers. Still, it is not always clear whether the added complexity of dynamic compensation is warranted for a given system. As an aid in evaluating when dynamic compensation is required, this thesis presents a method for the determination of maximum endpoint tracking error due to uncompensated inertial …

A Systematic Procedure For The Analysis And Design Of Deployable Space Structures, Praveen Kumar

Mechanical & Aerospace Engineering Theses & Dissertations

An integrated graph theory and a symmetry-based approach have been developed for the type synthesis of deployable truss structures. Using this systematic approach, a bay of a deployable structure may be looked upon as being built around an axis or a plane of symmetry, including anti-symmetry. By providing a fictitious joint along this axis, the problem of structural design and analysis can be reduced to the study of one plane or face of the given structure. Each face is considered to be an assemblage of structural links connected by joints which form a closed kinematic chain. The conventional graph representation …

Comparison Of Digital Controllers Used In Magnetic Suspension And Balance Systems, William Allen Kilgore

Mechanical & Aerospace Engineering Theses & Dissertations

Dynamic systems that were once controlled by analog circuits are now controlled by digital computers. Presented is a comparison of the digital controllers presently used with magnetic suspension and balance systems. The overall response of the systems are compared using a computer simulation of the magnetic suspension and balance system and the digital controllers. The comparisons include responses to both simulated force and position inputs. A preferred digital controller is determined from the simulated responses.

The Effects Of Bending On The Strain Distributions In A Stiffener-Skin Interface Region, Osvaldo F. Lopez

Mechanical & Aerospace Engineering Theses & Dissertations

An analytical and experimental study to assess the effect of bending on the adhesive strain distributions in a stiffener-skin interface region is described. A one-dimensional beam analysis is derived using a variational approach. Parametric studies are conducted to assess the effects of stiffener, skin, and adhesive thickness and adhesive material nonlinearity on the adhesive layer extensional and shear strain distributions subjected to applied bending. Two experimental methods of measuring through-the-thickness extensional strains in an adhesive are investigated. One method involves measuring the changes in the resistance of a composite strain sensor subjected to applied tension and compression loads. The second …

Application Of Shape Sensitivity Analysis For Computation Of Transient Free-Surface Flows, Frank Nicolas Michel

Mechanical & Aerospace Engineering Theses & Dissertations

Shape sensitivity analysis is introduced into a numerical scheme simulating a transient free-surface flow and applied to the case of a fluid advancing through a bed of cylinders. For this incompressible Newtonian flow, viscous forces are dominant. A penalty function finite element formulation is used to solve the problem. Coordinates of nodes on the moving boundary are chosen as design variables and an analytical formulation of the gradient of the finite element algebraic system, with respect to these variables, is derived.

In a numerical example, the results obtained with and without sensitivity analysis are compared. The efficiency and accuracy of …

Explicit And Implicit Calculations Of Turbulent Cavity Flows With And Without Yaw Angle, Guan-Wei Yen

Mechanical & Aerospace Engineering Theses & Dissertations

Computations have been performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows have been generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference, (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30% faster, is found to produce better time accurate results. The Reynolds stresses have been modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses have been …

Investigating The Method Of Structural Topological Variations For Sensitivity Analysis And Design Optimization, Niki A. Mehta

Mechanical & Aerospace Engineering Theses & Dissertations

The method of structural topological variations is a newly developed technique for analysis of frame structures. It provides a novel method that completely avoids formulating and solving simultaneous equations, required in the finite element displacement method. The principal objective of this thesis is to investigate the method of topological variations as a possible design tool and study its applicability in the sensitivity analysis and in the process of design optimization.

A computer code was developed for this method to obtain its comparative performance against the finite element displacement method. For analysis of large structures involving frequent local modifications, the method …

Global/Local Stress Analysis Of Composite Structures, Jonathan B. Ransom

Mechanical & Aerospace Engineering Theses & Dissertations

A method for performing a global/local stress analysis is described and its capabilities are demonstrated. The method employs spline interpolation functions which satisfy the linear plate bending equation to determine displacements and rotations from a global model which are used as "boundary conditions" for the local model. Then, the local model is analyzed independent of the global model of the structure. This approach can be used to determine local, detailed stress states for specific structural regions using independent, refined local models which exploit information from less-refined global models. The method presented is not restricted to having a priori knowledge of …

A Reiner-Rivlin Fluid Flow Through Entrance Region Of A Circular Pipe, V. G. Masanja

Tanzania Journal of Engineering and Technology (TJET)

The flow of a Reiner-Rivlin fluid with two viscosity coefficients through the entrance region of a circular pipe has been studied numerically. In particular the growth of the entrance length as a function of the Reynolds number and the non-Newtonian parameters has been examined. Where comparison could be made, the results have been compared with existing experimental -and numerical data as well as the limited theoretical work available.

The Effects Of Nonlinearities On The Optimal Design Of Forced Vibrating Beams, Cheryl Celestine Jackson

Mechanical & Aerospace Engineering Theses & Dissertations

The optimal design of a beam under harmonic excitations is formulated and solved numerically for linear and nonlinear forced vibration theories. The beam has a nonuniform cross-sect ion, whose thickness can change during the optimization procedure. Based on the numerical results, for the given input frequency range, the linear vibration theory produces a more conservative design than the nonlinear vibration theory.

The analytical formulation for both theories is presented. For the linear case, a mean case is defined for the self-weight on a beam, and an alternating case is defined for input forcing frequencies which cause fatigue variations on a …

The Effect Of Elastic Boundary Conditions On The Dynamic Response Of Rectangular Plates, Terry K. Brewer

Mechanical & Aerospace Engineering Theses & Dissertations

Natural frequencies and forced steady-state harmonic response for the vibration of uniform rectangular plates with edges elastically restrained against rotation and transverse translation are addressed. A single mode Rayleigh-Ritz solution is derived using functions that describe the normal modes of vibration of a beam whose ends are elastically restrained. The finite element solution is obtained for comparison. MACSYMA symbolic manipulation system is implemented as an aid to the mathematical rigor of the Ritz approach and NASTRAN finite element code is used to model the mechanical system. Comparisons are made to published results and the solutions of this study are found …

Coupled Bending-Torsion Steady-State Response Of Pretwisted, Nonuniform Rotating Beams Using A Transfer-Matrix Method, Carl E. Gray Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations …

Eigenvalue And Eigenvector Design Sensitivity Analysis For Nonlinear Beam Vibrations, Jian-Zhong Yuan

Mechanical & Aerospace Engineering Theses & Dissertations

A beam with immovable ends under large amplitude oscillations is axially subjected to an amplitude-dependent stretching force which is induced by the geometrical nonlinearity. The design sensitivity analysis for such a beam is investigated in this study.

Two variational formulations based on different approximations of nonlinear stretching force are studied firstly. The analytical equations of design sensitivity analysis for these nonlinear eigenproblems are then derived. Finally, a computational scheme using finite element method is developed to calculate the design sensitivity derivatives of the eigenvalue and eigenvector numerically. Numerical examples associated with the nonlinear eigenvalue and eigenvector analysis, as well as …