Date of Award

Summer 2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Mechanical Engineering

Committee Director

Gene Hou

Committee Member

Miltos Kotinis

Committee Member

Duc T. Nguyen

Call Number for Print

Special Collections; LD4331.E56 D375 2013

Abstract

This thesis intends to prove that singularity functions can be used to perform static and vibration analyses and their sensitivity analysis of stepped beams subjected to various support constraints. Specifically, this thesis develops formulations using singularity functions for static and vibration analyses of a simply-supported, a roller­ supported, and a spring-supported stepped beam. The Static and Vibration Sensitivity Analysis formulations are derived for the simply-supported beam to show the feasibility of this approach. The techniques presented in this thesis can be extended to various other supports constraints such as a middle support, and spring support or any other variation of particular interest.

While research has been done on methods to perform sensitivity analysis, the area of using singularity functions for this purpose has not been much explored. This method using singularity functions provides a convenient alternative for analyzing the static and vibration sensitivity of stepped beams.

Both, the static and vibration analyses and their respective sensitivity analysis are observed in this thesis. The static and vibration analyses are performed on three variations of a stepped beam based on how they are constrained by their supports: a simply-supported stepped beam, a middle roller-supported stepped beam, and a linear spring-supported stepped beam. For these instances, external forces and lumped masses are considered. The static and vibration sensitivity analyses are performed in depth on the simply-supported stepped beam observed on the previous analysis to demonstrate the effectiveness of this approach. Jointly, the static and vibration analyses and their sensitivity analysis presented in this thesis, set up the foundation for furthering extended analysis of stepped beams constrained by other various supports.

Singularity functions are used to set up the formulas for the moment, curve, deflection, and design sensitivity of the analytical expression of the deflection of the stepped beams. These singularity function formulas are ran in Matlab to obtain the numerical results, and to be plotted. The numerical results are validated by comparing them to that of the Finite Element Method (FEM) in MD NASTRAN, and the sensitivity of the deflection results are validated with the Finite Difference method (i.e., Central Difference method).

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DOI

10.25777/kmkb-rh39

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