When subject to external load such as shear or compression,disordered solids undergo elastic deformation first and then a plastic rearrangement due to mechanical failure.It is believed that the instability associated with the plastic deformation is induced by the vanishing of the energy barrier in the direction of the normal mode of vibration with the lowest frequency.In this work,we show that fold instability analysis can be employed to explain the instabilities of disordered solids under load,which gives correct exponents of critical scaling relations for the frequency of lowest mode and energy barrier height along the mode.More importantly,we consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres.By calculating distributions of various parameters in scaling relations derived by fold instability analysis,we find that these instabilities produce a contribution to the density of vibrational states that scales as ω3 at low frequencies ω,and a contribution to the distribution of energy barriers ΔH that scales as ΔH-1/3 at low barrier heights.Recently,the scaling of the density of vibrational states for disordered solids have attracted a lot of attention.Different exponents have been proposed.Our scaling agrees with a recent observation when the glass stability is taken into account.Our study also reveals the importance of anharmonicity in jammed packings of frictionless spheres.