Isospectral Vibrating Systems
This book presents an isospectral approach for several important mechanical vibrating systems. Discrete and continuous isospectral systems are discussed using a simple multi-degree of freedom spring-mass system followed by illustration of isospectral beams and their solution through evolutionary computing. Next, it addresses axially loaded Euler-Bernoulli beams and aims to find isospectral counterparts of these systems. The practical application of these isospectral systems for vibration testing and for finding new closed form solutions is discussed. A considerable part of the book is devoted to isospectral rotating beams and their non-rotating analogs including Rayleigh beams. Aimed at researchers and graduate students in mechanical; aerospace; civil; automotive; ocean engineering especially mechanical vibrations, this monograph:
Discusses isospectral vibrating systems to aid vibration testing and computational analysis
Explores isospectral analogs between rotating and non-rotating structures
Provides simpler isospectral beams for vibration testing and for 3D printing
Uses firefly optimization method and electromagnetism inspired optimization method to find isospectral systems
Shows the use of isospectral systems to find new closed form solutions using an indirect approach
Chapter 1. Introduction: Spring-Mass Systems. 2. Discrete Models of Beams. 3. Beams with Tip-Force Discrete Models. 4. Gravity Loaded Beams-Discrete Models. 5. Rotating-Discrete Models. 6. Isospectral Beams-Electromagnetism Optimization. 7. Isospectral Beams-Closed Form Solutions. 8. Isospectral Systems for Testing. 9. Beams with Shared Eigenpairs. 10. Isospectral Rayleigh Beams. References. Index.