Free Vibration Analysis Of Rotating Functionally Graded Rectangular Plates

Rotating structures are widely used in modern machinery and daily appliances,such as gas turbines,steam turbines,water turbines and various booster pumps,as well as electric fans and so on.Therefor’e,the study of the vibration characteristics of the rotating rectangular plate system is of great significance.To get fiurther optimal design of the rotating rectangular plate,the new type of the functionally graded materials with excellent properties such as preventing the delaminating and slowing down the heat stress are app lied in structural design of rotating rectangular plate,which makes the complex rotating rectangular plate systems with more application scope.In th,is paper,the free vibration problem of a functionally graded rectangular plate fixed on a rotating rigid hub is studied.Specific research work includes:(1)For the vibration of functionally graded rectangular plates with uniform rotation speed,based on the constitutive equation of functionally graded materials and considering the influence of rotational inertia,the motion system is described in inertial coordinate system and rotational coordinate system.The lateral vibration equation and boundary conditions are derived by using Hamilton variational principle.By introducing dimensionless meth,od,the motion equation and boundary conditions are discretized by differential quadrature method,and the complex characteristic equation of the system is obtained(2)When the functional gradient index is zero,the free vibration of a rotating elastic rectangular plate is analyzed.Firstly,the eigenvalue of the system is calculated without considering the setting angle,which is the natural frequency of the free vibration of the rotating rectangular plate.The numerical results are compared with the existing values to verify the feasibility of the method.Then the effect of the dimensionless angular velocity,radius-length ratio,aspect ratio,thickness ratio,and the setting angle on the first three order natural frequencies is analyzed.(3)Considering the influence of functionally graded materials,the free vibration characteristics of the rotating functionally graded rectangular plates are analyzed and discussed.Firstly,the influence of the functional gradient index on the first three order natural frequencies is analyzed in other certain parameters condition.Furthermore,the variation rules and characteristics of the first three orders of natural frequencies with the gradient index are analyzed respectively,under the influence of different angular velocity,radius-length ratio,aspect ratio,thickness ratio and setting angle.