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Abstract. The aim of this work is to investigate the nonlinear forced vibration of beams containing an arbitrary number of cracks and to perform a multi-crack identification procedure based on the obtained signals.Cracks are assumed to be open and modelled trough rotational springs linking two adjacent sub-beams. Forced vibration analysis is performed by a developed time differential quadrature method. The obtained nonlinear vibration responses are analyzed by Huang Hilbert Transform. The instantaneous frequency is used as damage vibration responses are analyzed by Huang Hilbert Transform. The instantaneous frequency is used as damage index tool for cracks detection.