Identification of the mass distribution of a vibrating system through an output-only modal identification technique

The paper presents an output-only technique for the identification of the mass distribution of a vibrating system. The methodology exploits the orthogonality of the natural modes of vibration and is applied to a spring-mass system with n masses. A system of n algebraic equations is built using: (a) a number of n - 1 inner products between the natural modes; (b) the total mass (known) as the sum of the lumped masses. The solution of the system provides the mass distribution in terms of lumped masses. The evaluation of the natural modes is performed through time domain decomposition (TDD). TDD consists in the proper orthogonal decomposition (POD, also known as Karhunen-Loe`ve decomposition, KLD) of the time-dependent displacement vector, suitably filtered to have one frequency (at once); this is equivalent to frequency domain decomposition (FDD). TDD (or FDD) provides a set of eigenvectors and eigenvalues. The former correspond to the natural modes; the latter equal the signal-energy of the corresponding modes. Modes with higher energy are considered for the algebraic equations system (a). Numerical results show a good agreement between identified mass distribution and (known) input values. The method can be extended to continuous structures in the discrete approach.