The　problem　treated　in　this　paper　is　the　optimal　electromechanical　setting　of　energy　harvesters　working　with　vibrations　of　random　nature.　We　consider　a　simple　system　composed　of　two　parts;　one　electrical　circuit　with　a　mechanical　single-degree-of-freedom　system,　coupled　to　a　piezoelectric　element.　The　electric　circuit　is　modeled　as　a　simple　one,　composed　of　a　resistance　and　a　capacity　only,　while　a　linear　viscoelastic　model　is　used　for　the　mechanical　element.　The　only　joint　electro　and　mechanical　element　is　the　piezoelectric　device,　which　is　controlled　by　both　the　mechanical　velocity　and　the　electrical　tension.　This　scheme　is　treated　as　dimensionless　using　the　random　vibration　theory　since　the　base　excitation　is　considered　as　a　stationary　white　noise　Gaussian　process.　To　consider　the　non-uniform　frequency　content,　that　characterizes　many　real　vibration　phenomena,　the　input　is　properly　colored　using　simple　linear　filters.　System　response　statistics　is　evaluated　by　covariance　approach,　producing　both　covariance　matrix　of　system　parameters　and　mean　value　of　electric　power　under　different　filters　and　systems　configurations.　The　optimal　ratio　between　the　periods　of　the　mechanical　and　electric　systems　is　thus　defined　maximizing　the　mean　power　value.　This　ratio　is　obtained　numerically　for　some　test　cases　in　a　graphic　representation　to　evaluate　the　sensitivity　response　to　selected　parameters.　©　2019　The　Author(s).