This study examines local oscillatory shear dynamics of spherical polymer grafted nanoparticles (PGNs) composed of a rigid nanoparticle core of fixed radius, (Formula presented.) nm, and coronas of varying number of grafted polymer arms, (Formula presented.). The grafted polymer arms are end-functionalized such that the interacting PGNs form labile bonds when their coronas overlap. The effect of PGN structure on local dynamics is examined by imposing controlled oscillatory displacement on simple systems constructed using three identical interacting PGNs with bonded interactions under mechanical equilibrium. The displacement-induced bond evolution between PGNs in this system is captured employing a master equation for determining probability of finding n bonds between PGNs as a function of oscillation frequency ((Formula presented.)). A multi-component model combined with master equation approach is employed for modeling the effect of varying number of grafted arms ((Formula presented.) and 1200) and strain amplitude ((Formula presented.)) on the local shear response of the PGN system. The resulting shear response is analyzed using both linear and non-linear rheological measures obtained using the Chebyshev polynomial framework. The rheological measures thus obtained are found to vary strongly with the number of grafted arms and strain amplitude. © 2021 Wiley-VCH GmbH