This　research　focuses　on　the　lightweight　topology　optimization　method　for　structures　under　the　premise　of　meeting　the　requirements　of　stability　and　vibration　characteristics.　A　new　topology　optimization　model　with　the　constraints　of　natural　frequencies　and　critical　buckling　loads　and　the　objective　of　minimizing　the　structural　volume　is　established　and　solved　based　on　the　independent　continuous　mapping　method.　The　eigenvalue　equations　and　composite　exponential　filter　functions　are　applied　to　convert　the　optimization　formulation　into　a　continuous,　solvable　mathematical　programming　model.　In　the　process　of　topology　optimization,　suitable　initial　values　of　the　filter　functions　are　chosen　to　avoid　local　modes,　and　the　dynamic　frequency　gap　constraints　are　added　in　the　optimal　model　to　prevent　mode　switches.　Furthermore,　for　the　optimal　structures　with　grey　elements　obtained　by　the　continuous　optimization　model,　the　bisection-inverse　iteration　is　applied　to　search　the　optimal　discrete　structures.　Finally,　a　detailed　scheme　is　given　for　the　buckling　and　frequency　topology　optimization　problem.　Numerical　examples　illustrate　that　the　modelling　method　of　minimizing　the　economic　index　with　given　performance　requirements　is　practical　and　feasible　for　multi-performance　topology　optimization　problems.