This article seeks to perform a combination of methodologies to fully model and evaluate the rudimentary performance of a thermoacoustic engine integrated with a piezoelectric energy harvester (TAP). First, the root locus method was employed to determine the critical design operating values of the thermoacoustic engine. Later, a lumped parameter model was developed as a matlab Simulink program to calculate the transient temperature and pressure responses of the thermoacoustic engine. In addition, a two-element reduced model (executed on matlab) and finite element analysis tools were used to simulate and assess the performance of aluminum-piezo (lead zirconate titanate (PZT-5H) and lead manganese niobate-lead titanate (PMN-PT)) disks that are to be integrated with the thermoacoustic engine. Last but most importantly, the piezo-diaphragm and thermoacoustic engine were coupled using the electrical analogy technique through which the onset conditions and resonance frequency of the integrated TAP system were determined. We take a traveling wave thermoacoustic engine and a commercially available piezoelectric disk as a test case for the analysis. It is concluded that the outcomes from the multiple methods are in good agreement with the experimental results.