Gravitational resonances on f(R)-brane

In this paper, we investigate various f ( R )-brane models and compare their gravitational resonance structures with the corresponding general relativity (GR)-branes. Starting from some known GR-brane solutions, we derive thick f ( R )-brane solutions such that the metric, scalar field, and scalar potential coincide with those of the corresponding GR-branes.We find that for the branes generated by a single or several canonical scalar fields, there is no obvious distinction between the GR-branes and the corresponding f ( R )-branes in terms of gravitational resonance structure. Then we discuss the branes generated by a K-field. In this case, there could exist huge differences between GR-branes and f ( R )-branes.