Document Type : Research Paper

Authors

• Iman Shojaei ¹
• Hossein Rahami ²

¹ Department of Biomedical Engineering, University of Kentucky, Lexington, KY 40506, USA.

² School of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran.

Abstract

Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kronecker products and matrix manipulations. Specifically, the eigensolution of the corresponding regular mechanical system was inserted in the algorithm to further accelerate the solution. The developed method allowed reduction in computational complexity (i.e., $\mathrm{O}(n^2)$) when compared to earlier methods. The application of the method was indicated using a simple example.

Keywords

• Global near-regular systems
• Vibration analysis, Eigensolution
• Kronecker products
• Matrix operations