Eliminating the modal truncation problem encountered in frequency responses of viscoelastic systems

• We consider the modal truncation problem encountered in viscoelastic systems.
• Frequency response is obtained by means of the mode superposition method.
• Projection technique is used to eliminate the modal truncation problem.
• Three examples are provided to illustrate the effectiveness of the derived results.

Increasing the number of degrees of freedom used in finite element analysis for mechanical and structural systems with viscoelastic damping, the need to consider the modal truncation problem of viscoelastic systems is more than ever before. The higher modes may be unnecessary to obtain in dynamic analysis for engineering applications. For viscoelastic systems, the modal truncation problem may be more frequently encountered since the nonviscous modes are difficult or even impossible to be found accurately even if a small-scaled problem is considered for some eigensolution methods. This study aims at eliminating the influence of the higher modes on the frequency responses of viscoelastically damped systems. A method is presented by making the equilibrium equations of motion into a subspace equation spanned in terms of the columns of a projection basis obtained by considering the use of the contribution of the lower modes and the first two terms of the Neumann expansion of the contribution of the unavailable modes. Finally, three example studies are provided to illustrate the effectiveness of the derived results. It is shown that the proposed method can reduce the modal truncation error significantly.