Asset Details
Do you wish to reserve the book?
Closed-form eigensolutions and exact complex mode superposition method for non-proportionally rate-independent damped systems
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Closed-form eigensolutions and exact complex mode superposition method for non-proportionally rate-independent damped systems
Do you wish to request the book?
Closed-form eigensolutions and exact complex mode superposition method for non-proportionally rate-independent damped systems
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Closed-form eigensolutions and exact complex mode superposition method for non-proportionally rate-independent damped systems
2025
Overview
PurposeThe main objectives of this paper are to develop a novel perturbation method (PM) to solve the complex-orthogonal eigenvalue problem and further propose an exact complex mode superposition method (CMSM) for the non-proportionally rate-independent damped systems.Design/methodology/approachA novel PM is developed to solve the eigenvalue problem. The PM reduced the N-order generalized complex eigenvalue problem into a set of n algebraic equations by the perturbation theory. The convergence and accuracy of the PM are demonstrated by several numerical examples. Further, an exact CMSM is presented. The influences of the imaginary part response of the modal coordinate and the off-diagonal elements of the damping matrix as well as the modal truncation on the solution by CMSM are discussed to illustrate the effectiveness of the developed CMSM.FindingsThe eigenvalues obtained by PM would converge to the exact ones with the increase of the modal numbers. For seismic response, the influence of the imaginary part solutions of the modal coordinate would increase with the increase of the coupling factor. The contribution of higher modes to acceleration response is greater than that to the displacement. The cumulative mode contribution coefficient of acceleration is developed to estimate the numbers of the complex modes for the acceleration seismic response by the CMSM.Originality/value1. An eigenvalue perturbation method for a rate-independent damped system is proposed. 2. PM is carried out by the real mode and accomplishes the reduction of the matrix. 3. CMSM is established for rate-independent damped systems. 4. CMSM considers the effect of imaginary part solutions of the modal coordinate. 5. Modal truncation index is developed to estimate the complex mode number for CMSM.
Publisher
Emerald Publishing Limited,Emerald Group Publishing Limited
