The　power　spectral　density　curves　of　the　random　vibration　response　of　a　plate　specimen　with　different　spectral　width　coefficients　were　obtained　by　selecting　different　frequency　ranges,　and　the　probability　distributions　of　the　stress　amplitudes　were　obtained　by　applying　Monte　Carlo　method　and　rainflow　counting　method.　Each　probability　distribution　was　divided　into　three　segments　by　the　corresponding　zero-order　spectral　moment　value,　and　each　segment　was　fitted　using　either　a　Rayleigh　function　or　an　exponential　function.　Finally,　a　probability　density　function　of　stress　amplitude　was　proposed　by　combining　two　Rayleigh　functions　and　an　exponential　function.　The　proposed　probability　density　function　can　be　used　to　obtain　the　stress　amplitude　probability　distribution　for　the　power　spectral　density　curves　of　structural　random　vibration　response　with　any　bandwidth,　and　the　accuracy　of　the　proposed　function　was　verified　based　on　the　response　data　of　a　specimen　of　7075-T651　aluminum　alloy　material　under　the　action　of　six　typical　power　spectral　curves.