The Research On Vibration And Acoustic Characteristics Of Functionally Graded Plates And Shells

Functionally graded materials(FGMs) are composed of two or more materials through continuously changing its fractions along dimension. FGMs have the advantages of high temperature resistance, good toughness, high strength and so on, so they have been widely used in aerospace, energy, machinery, defense and other fields. The mechanical behavior of functionally graded material structures is an important direction in mechanics research fields. The vibration and acoustic characteristics of functionally graded plates and shells in air are studied in this thesis.First, the free vibration characteristics of an functionally graded rectangular plate with simply supported boundary conditions are studied. Based on the classical thin plate theory and by ignoring the influence of the shear deformation, the natural frequency is obtained by assuming the modal function. On the basis of the above study, the power flow characteristics of FG rectangular plate under harmonic excitation are analyzed. The flexural displacement is solved by modal superposition method, then the power flow vector and flow maps are obtained by visualization method.Second, the models of baffled and unbaffled FG rectangular plates are set up and the acoustic characteristics are analyzed. According to the Rayleigh integral formula, the far field sound pressure of a baffled FG rectangular plate is obtained, then the radiated sound power is solved by impedance matrix. Through the Green function, the sound pressure and radiated sound power of an unbaffled FG rectangular plate are obtained. The influence of baffle on acoustic characteristics are discussed by comparing the results.Finally, the free vibration characteristics of a functionally graded cylindrical shell with simply supported ends are obtained. Based on the classical thin shell theory and ignored the influence of the shear deformation, the natural frequency is obtained by assuming modal function. Considering the influence of internal pressure, the free vibration characteristics of a FG cylindrical shell are discussed, and an analytical method for predicting elastic buckling pressure is presented based on the relationship between the natural frequency and internal pressure.