Structural topology design optimization under inertialloads is studied in the paper. Based on the sensitivity scheme of structuralcompliance, the non-monotonous feature of the objective function isdescribed. Due to the design-depedent effects of loads and elementstiffness, various material penalization models are investigated to showtheir influences on the optimization results and iteration processes.Subsequently, an improved RAMP model with variable parameter is proposed andvalidated. For the problem with inequality volume constraint underself-weight loading, the optimal solution is obtained in stable convergenceway for the first time, also to approach the theoretic solution associatedwith a void structure without material. Theoretical and numerical resultsshowed that the compliance sensitivity remains no longer to be negative dueto the the design-dependent effect of inertial loads. This means that theobjective function is non-monotonous. As a result, the inequality volumeconstraint is not always active at the optimum solution. In other words,less material may lead to a stiffer structure for an optimum materiallayout. Besides, it is shown that the integration of a proper RAMP modelwith the BESO method can improve greatly the result so that both BESO and MPmethods become consistent for self-weight design problem whereas previouslyexisting optimization results obtained by BESO and MP methods are quitedifferent.