Identification of Boundary Conditions Parameters of Two-Opening Beams with Damaged Support

In modern societies, the importance of financial and temporal resources is evident and has received attention in
recent decades, and it is predicted that such importance increases with time. Structural health monitoring and crack
detection are two topics in the field of civil engineering, which two areas have a key role and is considered almost
new knowledge in civil engineering. In this project, we will try to use basic structural dynamics relations and
strength of materials to achieve a better understanding of structural damage. In fact, this project offers a practical
method that uses natural frequency to help identify the rate of damage to the support, which can help structural
improvement. In this method, the only requirement is to obtain frequency from the structure and there is no need for
structural control and permanent presence of manpower. As you will see, dynamic parameters have a strong role in
this regard. What makes structural health and crack detection in particular both interesting and hard is significant
uncertainty of structural damage. In fact, much uncertainty is involved in formation of structural damage and its
detection and repair, which makes it a hard task with a high computational cost. Despite all these problems, due to
importance of structural health monitoring and attempt to make most of available resources, many researches have
been done in this regard and certainly the costs of knowledge of structural damage is much less than the material and
non-material damages of incidents in communities.
Although we studied a sample model of structure, given this discussion is newly emerged, this elementary model
will be needed in future for much more complicated models that are closer to real structures. Besides the above said,
we saw in this project that despite study of damage to supports is very important in overall stability of structure and
seems a difficult problem, a good knowledge of damage can be obtained using simple and reliable relations. The
structure studied in this project that had three damaged supports can provide a better model, compared to previous
ones, which were mostly in form of console or single-opening beams. However, addition of openings and use of
characteristic coefficients matrix equation to obtain shape function will be very hard and requires that we look for a
simpler alternative method in this section. The other points of this project include direct study of level of damage.
What has been sought so far rather in the area of damage detection includes an interpretation of the level of damage
through variations of frequency or study of trend of variations of mode shape. In this project, having obtained the
frequency of damaged structure using the said method, we obtained level of stiffness reduction.
As for direct solution, which is aimed to find proper shape function, acceptable results were obtained. But the
trend of results shows that error of this method increases as difference of stiffness of supports increases. It can be
inferred that, given Rayleigh’s opinion, difference of stiffness cause the main mode to take distance from the first
mode and such difference results in error. In fact, if stiffness of supports is symmetric, the main mode of the
structure, which unveils the main structure of the shape function, gets closer to the first mode, which makes the
initial assumption for shape function more acceptable.
In the second part, which is derivation of frequency function with the aid of Rayleigh method, as is the case with
direct solution method, the effect of factors of the main mode of structure changes the error level of the results. In
this part, by addition of test mass at points on the main mode. In direct solution, we obtained the shape function in
absence of test mass, which causes error to increase with test mass.