Free Vibration Of Composite Sandwich Beams With Auxetic Core And Rotating FGM Timoshenko Beams On Elastic Foundations

It is great significance to make efficient and accurate analysis to the free vibration of rotating beams and sandwich beams,which have wide application in many field of engineering,like aircraft,civil engineering,mechanism etc.Differential Transform Method is a solution method with high computation accuracy and fast convergence based on Taylor serious.Using transformation rules,the differential and boundary conditon equations change into a set of algebraic equations.This thesis extends accurate method to the free vibration of sandwich beams with auxetic core and rotating beams,sets up an exact algorith for them.The main contents are as follows:Free vibration of the composite sandwich beams with auxetic core on elastic foundation is investigated based on sandwich beams principle and DTM.Firstly,the motion governing differential equations of the transverse free vibration of the composite sandwich beams with auxetic core on elastic foundation were derived by using Hamilton principle.Secondly,differential transformation method was used to transform the differential equation and the boundary condition.Finally,the effects of boundary conditions,high of auxetic core,Poisson’s ratio and elastic foundation modulus on the free vibration frequency of composite sandwich beams with auxetic core were considered.As the results show that DTM presents high accuracy and fast convergence for solving the nature frequency problem.Natural frequencies of the composite sandwich beams with auxetic core increase with the growth of the elastic foundation modulus.Under a certain elastic foundation modulus and high of auxetic core,the natural frequencies decrease along with the growth of the Poisson’s ratio.Under a certain elastic foundation modulus,the fundamental frequency increase with the growth of the high of auxetic core and under a certain high of auxetic core,the fundamental frequency decrease with the growth of the negative Poisson’s ratio.Free vibration of a rotating FGM beam on elastic foundation was investigated based on Timoshenko beam theory and DTM.The effects of different boundary conditions,rotating speed,elastic modulus and gradient index on the free vibration frequency of functionally graded material Timoshenko beam were considered.As the results show that the dimensionless natural frequencies of functionally graded material Timoshenko beam increase with the growth of the dimensionless rotating speed and the dimensionless elastic foundation modulus.Under a certain dimensionless rotating speed and dimensionless elastic foundation modulus,the dimensionless natural frequencies decrease along with the growth of the functionally graded material gradient index.