This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests. Young's modulus vector of Fourier components of the forcing signal nth modal variable first modal response amplitude taken at drive frequency second modal response amplitude taken at third harmonic of drive frequency vector of Fourier components of the voltage signal sent to the shaker amplifier resonant component of the nth modal variable response amplitude of u n axial coordinate lateral coordinate linear modal damping ratio phase Poisson's ratio mass density nth mode shape function shorthand for ϕ n ( x i ) , ϕ n ( x L ) linear natural angular frequency of nth mode resonant response frequency of nth modal variable 
Periodic responses of a structure with 3:1 internal resonance