The dynamic combustion process generates high amplitude pressure oscillations due to the thermo-acoustic instabilities, which are excited within the gas turbine. The combustion instabilities have a significant destructive impact on the life of the liner material due to the high cyclic vibration amplitudes at elevated temperatures. This paper presents a methodology developed for mechanical integrity analysis relevant to gas turbine combustors and the results of an investigation of combustion-acoustics-vibration interaction by means of structural dynamics. In this investigation, the combustion dynamics was found to be very sensitive to the thermal power of the system and the air-fuel ratio of the mixture that feed into the combustor. The unstable combustion caused a dominant pressure peak at a characteristic frequency, which is the first acoustic eigenfrequency of the system. Besides, the higher-harmonics of this peak were generated over a wide frequency-band. The frequencies of the higher-harmonics were observed to be close to the structural eigenfrequencies of the system. The structural integrity of both the intact and damaged test specimens mounted to the combustor were monitored by vibration-based and thermal-based techniques during the combustion operation. The flexibility method was found to be accurate to detect, localize and identify the damage. Furthermore, a temperature increase was observed around the damage due to the hot gas leakage from the combustor that can induce detrimental thermal stresses to consume the lifetime.