LAUSR

We perform an experimental and theoretical study to investigate the interaction between an external harmonic excitation and a self-excited oscillatory mode ( $f_{n0}$ ) of a prototypical thermoacoustic system, a horizontal Rijke tube. Such an interaction can lead to forced synchronization through the routes of phase locking or suppression. We characterize the transition in the synchronization behaviour of the forcing and the response signals of the acoustic pressure while the forcing parameters, i.e. amplitude ( $A_{f}$ ) and frequency ( $f_{f}$ ) of forcing are independently varied. Further, suppression is categorized into synchronous quenching and asynchronous quenching depending upon the value of frequency detuning ( $|\,f_{n0}-f_{f}|$ ). When the applied forcing frequency is close to the natural frequency of the system, the suppression in the amplitude of the self-excited oscillation is known as synchronous quenching. However, this suppression is associated with resonant amplification of the forcing signal, leading to an overall increase in the response amplitude of oscillations. On the other hand, an almost 80 % reduction in the root mean square value of the response oscillation is observed when the system is forced for a sufficiently large value of the frequency detuning (only for $f_{f}