An online algebraic estimation technique for natural and forcing frequencies for a class of uncertain and lumped-parameter vibrating mechanical systems with n degrees of freedom is described. In general, realistic vibrating systems can be affected by unknown exogenous excitation forces with multiple and independent frequency harmonic components. Hence, natural frequencies as well as excitation force frequencies can be simultaneously computed from an algebraic approach into a small interval of

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... me during online operation of the mechanical system. Measurements of an available output signal, associated with some specific degree of freedom, are only required for frequency estimation in time-domain. Information on mass, stiffness and damping matrices are not necessary for multifrequency estimation algorithms. Some analytical, numerical and experimental results on a cantilever Euler–Bernoulli beam are described to show and validate the acceptable estimation of multiple frequencies in forced multiple degrees of freedom vibrating systems.