Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

•A framework is proposed for the identification of a single nonlinear mode.•A nonlinear mode can be characterized with linear frequency and a single nonlinear cubic coefficient.•The phase resonance can be measured in forced regime using a phase-locked loop.•The phase-locked loop is a robust technique for measuring nonlinear forced responses and backbone curves.•The proposed methodology is applied to a circular plate, a chinese gong and piezoelectric beam.