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In this work, we have characterized the frame bundle F M admitting metallic structures on almost quadratic ϕ -manifolds ϕ 2 = p ϕ + q I − q η ⊗ ζ , where p is an arbitrary constant and q is a nonzero constant. The complete lifts of an almost quadratic ϕ -structure to the metallic structure on F M are constructed. We also prove the existence of a metallic structure on F M with the aid of the J ˜ tensor field, which we define. Results for the 2-Form and its derivative are then obtained. Additionally, we derive the expressions of the Nijenhuis tensor of a tensor field J ˜ on F M . Finally, we construct an example of it to finish. [ABSTRACT FROM AUTHOR]