Applications of eigenmode coupling to damage detection in beams
Structural health monitoring using vibration response measurements is a common form of non-destructive testing. Many structural health monitoring techniques rely on shifts in natural frequency to detect the presence of damage. This reliance on changes in natural frequency can lead to the incorrect diagnosis of structural health due to the influence on natural frequency of variables besides damage such as the elastic modulus and mass density. These inertial and elastic properties vary from component to component and under different test conditions. There is a need for a wide-area vibrations-based damage detection method that does not operate directly on individual natural frequencies. This thesis investigates the use of the coupling between modes of vibration to detect damage in an aluminum beam. Modal coupling is a phenomenon in which certain mode shapes take on characteristics of neighboring mode shapes due to the presence of damage. It is demonstrated that modal coupling can be identified using a finite element model of a healthy beam specimen in conjunction with the solution of a perturbed eigenvalue problem. Solution of the perturbed eigenvalue problem by Taylor series expansion yields the eigenvalues and eigenmodes of the damaged beam. Coefficients of the Taylor series expansion terms are shown to predict which pairs of modes will couple, as well as providing a measure of coupling strength. Experimental verification of theoretical results is performed using roving impact testing and a three-dimensional laser vibrometer system. Several experimental iterations demonstrate that the effects of natural boundary conditions on modal coupling are significant. A roving impact test using a single small tri-axial accelerometer is conducted to estimate the healthy mode shapes of the beam when mass-loading is minimized. Coupling between the first longitudinal and seventh transverse bending modes of the beam is predicted by the solution to the perturbed eigenvalue problem for a notch placed at the beam's midpoint. Coupling between this pair of modes is measured using the laser vibrometer by exciting the beam with an actuator purely in the longitudinal direction and comparing modal deflections of the first longitudinal eigenmode for the healthy and notched beam specimens.
Krousgrill, Purdue University.
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