Experimental reconstruction of the vibration field in a cylindrical shell

Abstract

The problem of reconstruction of a vibration field in an unmeasured region of a thin cylindrical shell is considered. The forced vibrating shell of finite dimension is divided into two parts: the first part (the measurement region) is accessible for measuring any vibration characteristics while the second part (the reconstruction region) is considered as ‘‘inaccessible.’’ The problem is solved using the general approach–see the presentation by Yu. I. Bobrovnitskii at this Special Session. The vibration field of the shell was modeled by a finite sum of normal waves, amplitudes of which were determined by equating the modeling values to the data. The SVD technique was used in the inverse procedure for parameter identification. Most attention was paid to finding an appropriate method for choosing the best model of the shell which minimized the reconstruction error. For the measurement error 0.08 of the experiment conducted, the reconstruction error varied from 0.2 to 0.7 as the measurement region diminished from 0.7 to 0.3.