Identification of Stiffness Reductions Using Partial Natural Frequency Data
TheaSokheang
2019
In vibration-based damage detection in structures, often changes in the
dynamic properties such as natural frequencies, modeshapes, and derivatives of
modeshapes are used to identify the damaged elements. If only a partial list of
natural frequencies is known, optimization methods may need to be used to
identify the damage. In this research, the algorithm proposed by Podlevskyi & Yaroshko (2013) is used to determine
the stiffness distribution in shear building models. The lateral load resisting
elements are presented as a single equivalent spring, and masses are lumped at
floor levels. The proposed method calculates stiffness values directly, i.e., without optimization, from the known partial list of natural frequency data and mass
distribution. It is shown that if the number of stories with reduced
stiffness is smaller than the number of known natural frequencies, the stories
with reduced stiffnesses can be identified. Numerical studies on building
models with two stories and four stories are used to illustrate the solution
method. Effect of error or noise in given natural frequencies on stiffness
estimates and, conversely, sensitivity of natural frequencies to changes in
stiffness are studied using 7-, 15-, 30-, and 50-story numerical models. From
the studies, it is learnt that as the number of stories increases, the natural
frequencies become less sensitive to stiffness changes. Additionally, eight
laboratory experiments were conducted on a five-story aluminum structural
model. Ten slender columns were used in each story of the specimen. Damage was
simulated by removing columns in one, two, or three stories. The method can
locate and quantify the damage in cases presented in the experimental studies. It
is also applied to a 1/3 scaled 18-story steel moment frame building tested on
an earthquake simulator (Suita et al., 2015) to identify the reduction in the
stiffness due to fractures of beam flanges. Only the first two natural
frequencies are used to determine the reductions in the stiffness since the
third mode of the tower is torsional and no reasonable planar spring-mass model
can be developed to present all of the translational modes. The method produced possible cases of the
softening when the damage was assumed to occur at a single story.