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Full-field dynamic shearography and laser Doppler vibrometric scanning are used to investigate the local contact acoustic nonlinear generation of delamination-induced effects on the vibration of a harmonically excited composite plate containing an artificial defect. Nonlinear elastic behavior caused by the stress-dependent boundary conditions at the delamination interfaces of a circular defect is also simulated by a 3-D second-order, finite-difference, staggered-grid model (displacement-stress formulation). Both the experimental and simulated data reveal an asymmetric motion of the layer above the delamination, which acts as a membrane vibrating with enhanced displacement amplitude around a finite offset displacement. The spectrum of the membrane motion is enriched with clapping-induced harmonics of the excitation frequency. In case of a sufficiently thin and soft membrane, the simulations reveal clear modal behavior at sub-harmonic frequencies caused by inelastic clapping.