Free Vibration Analysis Of Beam And Plate Structures Of Fiber-reinforced Functionally Graded Materials

Functionally Graded Materials(FGM)are materials that consist of two or more materials with a spatial gradi ent distribution that can be designed for harsh working environments and complex working conditions due to their structure.Compared with traditional homogeneous materials,fiber-reinforced materials have obvious anisotropy,and their complex mechanical pr operties have become the focus of scientific research.The research object of this paper is the structure of fiber-reinforced functional gradient material with FGM as the matrix material and fiber as the reinforcement,to study the free vibration and buckl ing characteristics of fiber-reinforced FGM beams in thermal environment and the f ree vibration of fiber-reinforced FGM plates.The specific research work in this paper is as follows.First,the background and importance of FGM and fiber-reinforced composites are presented.Then,the development and research status of FGM and fiber-reinforced composites are described.Finally,the background and application of the differential quadrature method(DQM)used in the numerical solution of this paper are introduced.Second,the free vibration characteristics of fiber-reinforced FGM beams under thermal environment are investigated.The physical parameters of the fiber-reinforced FGM material are given by the mixed-rate model,and the exponential model FGM is selected as the base material,and the fibers are laid along the beam axis and uniformly distributed in the beam cross-section.Based on the classical beam theory system,the free vibration control differen tial equations of fiber-reinforced FGM beams are established by applying Hamilton’s principle,taking into account the temperature-dependent characteristics of each material property parameter and the thermal axial force caused by thermal expansion in the thermal environment.The free vibration control differential equation of the fiber-reinforced FGM beam is made dimensionless by introducing dimensionless parameters,and the dimensionless equation is transformed into a system of eigenvalue equations and th e dimensionless natural frequency is obtained by using DQM.The validity and correctness of the method have been verified by degenerating the model into FGM beams against the exact solutions of the existing literature.The effects of temperature,temperature ri se and beam aspect ratio on the dimensionless natural frequencies of fiber-reinforced FGM beams with different fiber contents under different boundary conditions are given.Finally,the influence of each influencing factor on the dimensionless natural frequency of FGM beams is discussed based on the numer ical results.Then,the free vibration problem of fiber-reinforced FGM plates is investigated,which must take into account the anisotropy of the material because its model is affected by the fiber lay angle,unlike the beam model.First,the formula for t he physical parameters of fiber-reinforced plates and the effect of the fiber lay angle on the physical parameters of the material are given.Then,based on the classical plate theory,the Hamilton principle is used to derive the control differential equat ion for the free vibration of the fiber-reinforced FGM plate.The control diff erential equation is dimensionless and then the dimensionless natural frequency is solved using DQM.The model is degenerated into a homogeneous plate and a general FGM plate for data comparison with existing literature to verify the validity of the soluti on method.Finally,the effects of fiber volume fraction,aspect ratio,ceramic-to-metal elastic modulus ratio,and density ratio o f the FGM matrix and fiber lay angle on the nat ural frequency are calculated and analyzed under six boundary conditions.Finally,the results of the study of the free vibration and of fiber-reinforced FGM structures are summarized,and new ideas for the fu rther work are proposed.