ABSTRACTThis paper addresses the problem of predicting the behaviors of a compositematerial, which consists of a matrix and a spherical inclusion coated by a multilayeredinterphase, under thermal and/or mechanical loading variations and basedon the micromechanics principles. The multi-layered interphase, which in generalincludes different properties for each layer, is modeled by applying the multiinclusionmodel. The considered damage mode, which is represented by theprogressive debonding of the particle from the interphase, is assumed to becontrolled by a critical energy criterion and the Weibull’s distribution function. Theeffects of the interphase parameters such as its thickness and the properties of eachlayer on the effective thermomechanical properties and the vibration characteristicsof composites with multi-layered interphases are presented and discussed. Thenatural frequencies give information about the resonance avoidance whereas modeshapes give information about observability and controllability of different structures.Therefore, the natural frequencies and mode shapes as vibration characteristics areinvestigated based on Euler and Timoshenko theories.