基于轮廓积分的黏弹性结构复特征值求解OA

To achieve high-accuracy,high robustness,and efficient computation of complex eigenvalues for viscoelastic damping structures with strong frequency dependence,a system control equation that can accurately characterize the frequency dependent complex stiffness characteristics of viscoelastic materials was established based on dynamic finite element theory.The block contour integration method was introduced into the solution process of the Nonlinear Eigenvalue Problem(NLEVP),and a closed integration contour was constructed on the complex plane.The original problem was transformed into a set of standard linear equation systems,and the sub-eigenspace in the target area was extracted through the trapezoidal integration formula.The results show that for the Kelvin-Voigt model,the maximum relative errors in the real and imaginary parts of the first ten eigenvalues are 0.18%and 7.71%,respectively.For the Maxwell model,all relative errors in both real and imaginary parts remain below 1%.The mode shapes agree closely with COMSOL Multiphysics simulations.The method captures all eigenpairs within the target area simultaneously,avoids convergence issues of traditional iterative methods effectively,and provides an effective numerical tool for accurate vibration analysis and high-performance damping design of complex engineering structures.