Modal Analysis and Testing for Structural Integrity and Design

TITLE:  Modal Analysis and Testing for Structural Integrity and Design WORK DONE BY:  K. LAKSHMI NARAYANA GUIDED BY:   Dr.C. Jebaraj AIM & SCOPE OF THIS WORK:       Structural integrity and design validation of any vibrating structure is important in terms of safety and cost. Modal testing and modal analysis are the tools which can be used to handle the above requirement of vibrating structures. This thesis describes these tools, the procedure as to how to use these tools and case studies of the effectiveness of these tools.       The cracks/damage in vibrating structures are due to their limited fatigue strength or due to the defect in manufacturing processes. These cracks open for a part of the cycle and close when the vibration reverses its direction. These cracks will grow over time, as the load reversal continues, and may reach a point where they pose a threat to the integrity of the structure itself or even cause damage to the life of people. Efforts have been made to identify the crack location in simple beam like structures in the initial chapters of the thesis.       The crack in a structure will affect the modal parameters both locally and globally. Studies have been carried out to identify the crack location using those modal parameters that get changed locally and globally. It is observed that the crack can be located exactly by monitoring changes that occur in the modal parameters locally such as variation in torsion mode and strain mode. This procedure has limitations in terms of extracting these locally varying modal parameters. A new technique is presented to identify the presence of a crack and its location using the changes that occur in a few of its lowest natural frequencies, one of the modal parameters that changes globally. An analytical expression is derived to calculate the variation in frequencies due to the presence of the crack. The study was carried out both analytically and experimentally and the results are presented in the thesis. From the observations made from this study a method is suggested to identify the location of the crack and the procedure is illustrated with a case study.       The analysis of a vibrating structure is not straight-forward. Designers determine the modal parameters of a mechanical structure either by experimental or by numerical methods. Results of both investigations are expected to correlate closely but in reality they do not. Experimental measurements on prototype give information only about the structure being tested. Finite element models allow to predict the dynamic behavior of the structure under various loading and boundary conditions. However the reliability of the finite element model is not guaranteed because of the approximations involved in modeling for both field variables and geometry. Model updation techniques verify and correct these finite element models by means of experimental data. The result of a model updating analysis is a finite element model that is more reliable for further predictions. These are discussed in the latter part of the thesis.       Model updation involves 1) Model matching of the experimental and numerical results by various procedures so as to have one to one comparison. 2) Correlation of the results by a set of techniques to study and decide whether a correction of the numerical (FEM) model is needed or not. 3) Selection of updating parameters by conducting a sensitivity analysis in case of bad correlation and 4) Computing new values of updating parameters and incorporating it into the FE model and computing the FE results. The procedure is repeated till the correlation is good.       Model updation procedure is applied to a beam like structure to identify the crack location, to a plate like structure to find equivalent length and to a plate with an added unknown mass to find the location of mass and the mass itself. Model updation procedure is also demonstrated to trouble shoot a sub assembly and to design validate a large assembly. RESULTS:

Mode shapes of uncracked and cracked free-free plate(Modes1 to 5)	Mode shapes of uncracked and cracked free-free plate(Modes6 to 10)

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