The analysis approach of the casing with viscoelastic damping material treatment under arbitrary elastic supports was proposed for the requirement of the vibration control of aero engine casing. The casing was considered as a thin-wall cylindrical shell. Then the governing dynamic equation of casing treated with the constrained layer damping was established

in which the effects of shear stress due to viscoelastic damping material were considered. By introducing a series of boundary spring elements

the boundary load of the casing was transformed into the elastic potential energy of the spring

and the effective simulation of the arbitrary boundary support stiffness on the casing was realized. Results showed that the increasing boundary stiffness could improve the natural frequencies of the casing

while the sensitivity of the damping characteristics to the support stiffness was opposite to the natural frequencies. In addition

in the design process of engineering casing

the satisfactory structural dynamic characteristics can be obtained by strengthening the circumferential and normal stiffness of the supporting structure.