This study reports on a joint experimental and analytical study of premixed laminar flames impinging onto a plate at controlled temperature, with special emphasis on the study of periodically oscillating flames. Six types of flame structures were found, based on parametric variations of nozzle-to-plate distance (H), jet velocity (U), and equivalence ratio (phi). They were classified as conical, envelope, disc, cool central core, ring, and side-lifted flames. Of these, the disc, cool central core, and envelope flames were found to oscillate periodically, with frequency and sound pressure levels increasing with Re and decreasing with nozzle-to-plate distance. The unsteady behavior of these flames was modeled using the formulation derived by Durox et al. [D. Durox, T. Schuller, S. Candel, Proc. Combust. Inst. 29 (2002) 69-75] for the cool central core flames where the convergent burner acts as a Helmholtz resonator, driven by an external pressure fluctuation dependent on a velocity fluctuation at the burner mouth after a convective time delay tau. Based on this model, the present work shows that tau = Re[2j tanh(-1) (2 delta omega + (1+N) j omega(2) - j omega(2)(0)/2 delta omega + (1-N) j omega(2) j omega(2)(0))] + 2 pi K / omega, i.e., there is a relation between oscillation frequency (omega), burner acoustic characteristics (omega(0), delta), and time delay tau, not explicitly dependent on N, the flame-flow normalized interaction coefficient [D. Durox, T. Schuller, S. Candel, Proc. Combust. Inst. 29 (2002) 69-75], because partial derivative tau/partial derivative N = 0. Based on flame motion and noise analysis, K was found to physically represent the integer number of perturbations on flame surface or number of coherent structures on impinging jet. Additionally, assuming that tau = beta H/U, where H is the nozzle-to-plate distance and U is the mean jet velocity, it is shown that beta(Disc) = 1-8, beta(CCC) = 1.03, and beta(Env) = 1.0. A physical analysis of the proportionality constant beta showed that for the disc flames, tau corresponds to the ratio between H and the velocity of the coherent structures. In the case of envelope and cool central core flames, tau corresponds to the ratio between H and the mean jet velocity. The predicted frequency fits the experimental data, supporting the validity of the mathematical modeling, empirical formulation, and assumptions made. (c) 2006 The Combustion Institute. Published by Elsevier Inc. All rights reserved.