On the basis of introducing the complex modulus model of viscoelastic materials and considering the elastic boundary of the cylindrical shell

the finite element program was developed to solve the nonlinear calculation problem of vibration frequency and damping for the composite cylindrical shell in view of the frequency dependence. A composite shell element with 4 nodes and 24 degrees of freedom was created to simulate the mechanical behavior of the cylindrical shell with partially covered viscoelastic damping layer

and the stiffness and mass matrices of the element were derived. A circumference variable stiffness elastic constraint model with 6 spring groups was proposed to simulate the elastic boundaries at the bottom of the cylindrical shell. The dynamic finite element equations of the composite cylindrical shell were determined

and the iterative calculation process of solving its vibration frequency and damping by eigenvector increment method was described. A case study for the cylindrical shell with ZN-1 free damping layer was performed and the results showed that the maximum error between the calculation results of the proposed algorithm and the experiment values was 369%. In addition

the frequency dependence of the viscoelastic material had an effect on the natural frequency of the composite structure of less than 001%

but the maximum effect on the modal loss factor was 10947%.