  We prove some inequalities of Payne-P\'olya-Weinberger-Yang type for
eigenvalues of fourth-order elliptic operators in weighted divergence form on
complete Riemannian manifolds which generalizes the corresponding result for
the clamped plate problem. We also prove estimates for lower order eigenvalues
that contain some of the estimates from the literature. As an application of
our results, we obtain eigenvalues estimates for the bi-drifted Cheng-Yau
operator.
