An extension to Adhikari iterative method: A novel approach for obtaining complex eigensolutions in linear non-classically damped systems

Abstract

This paper introduces an extended version of the Adhikari iterative method, adjusted for decoupling non-classically linear damped systems and refining the determination of complex eigenvalues. By integrating a self-adjoint theorem and leveraging spectral localization, the extension employs the complex eigenvectors from the Adhikari method to enhance the stability and accuracy of complex eigenvalue determination. This novel approach demonstrates a marked improvement in precision and stability. The study comprehensively assesses various dynamic characteristics, including damped and undamped eigenvalues, damping ratios, damping loss factors, and Frequency Response Function (FRF). Additionally, a novel methodology for computing FRF responses is proposed, involving the identification of eigensolutions within decoupled dynamical systems. The extension's effectiveness is assessed using the exact results from the state-space method as a benchmark, applying to three distinct non-classically damped models from previous research. The results are compared with those obtained using the original Adhikari method. The findings significantly reduce errors, affirming the extension's proficiency in approximating complex eigensolutions. These outcomes mark a notable advancement in the field, facilitating further research for developing more robust techniques for analysing complex dynamical systems.