The goal of this research is to compute the mode shapes and in some cases the natural frequencies of a lightly damped freely vibrating nonuniform beam using sensed outputs, via accelerometers. The methods applied are reduced-ordered mass weighted proper decomposition (RMPOD), state variable modal decomposition (SVMD) and smooth orthogonal decomposition (SOD). A permutation of input impulse magnitudes, input locations, signal length, and acceleration, velocity, displacement ensembles were used in the RMPOD decomposition to gain some experience regarding the effects of input parameters and signal types on modal estimations. An analytical approximation to the modal solution of the Euler-Bernoulli beam equation is developed for nonuniform beams. In the case of RMPOD the theory is pushed into the experimental realm. For SVMD and SOD the science is also extended into the experimental realm and is additionally applied to nonuniform beams. The results of this thesis are as follows: the analytical approximation accurately predicted the mode shapes of the nonuniform beam and can accurately predict frequencies if the correct material properties are used in the computations. RMPOD extracted accurate approximations to the first three linear normal modes (LNMs) of the thin lightly damped nonuniform beam. SVMD and SOD extracted both the natural frequencies and mode shapes for the first four modes of the thin lightly damped nonuniform beam.
Read
