<p>In structural dynamic topology optimization, the dynamic compliance has widely been used as an objective function in a minimization procedure for vibration mitigation. However, it is really not a positive-definite response measurement under a harmonic load excitation, and then, has to be artificially defined as an absolute value of the structural response. Furthermore, when the excitation frequency exceeds the first natural frequency of the initial structural design, the optimization program may fail to converge to a clear material layout without primary load transfer paths. Recently, the time-averaged power input to the structure is proposed as the objective function to reduce the structural vibration. For comparison purpose, the physical meanings of these two design objectives are elaborated and their collaborative relationship is revealed in this study. Furthermore, the dynamic topology optimizations for minimizing these two distinctive responses of a continuum structure are performed, respectively, to reveal their effects upon the final material layout. Besides, the fundamental natural frequency constraint is introduced in the optimal design process for avoidance of a substantial loss of the integral structural stiffness when the excitation frequency is higher than the first natural frequency of the initial configuration. Through two typical numerical examples considering various situations of the excitation frequency and fundamental frequency constraint, the influences of the two objective functions upon the final topology are investigated in detail. Based on the comprehensive comparisons of optimization results, the rationality and applicability of the two objective functions are discussed extensively.</p>