Recursive formulae and performance comparisons for first mode dynamics of periodic structures

• Published in: Smart materials and structures 2017-05, Vol.26 (5), p.55028
• Main Authors: Hobeck, Jared D, Inman, Daniel J
• Format: Article
• Language: English
• Subjects: energy harvesting; fan folded; metastructure; orthogonal spiral; recursive model; zigzag
• ISSN: 0964-1726; 1361-665X
• DOI: 10.1088/1361-665X/aa672b

Periodic structures are growing in popularity especially in the energy harvesting and metastructures communities. Common types of these unique structures are referred to in the literature as zigzag, orthogonal spiral, fan-folded, and longitudinal zigzag structures. Many of these studies on periodic structures have two competing goals in common: (a) minimizing natural frequency, and (b) minimizing mass or volume. These goals suggest that no single design is best for all applications; therefore, there is a need for design optimization and comparison tools which first require efficient easy-to-implement models. All available structural dynamics models for these types of structures do provide exact analytical solutions; however, they are complex requiring tedious implementation and providing more information than necessary for practical applications making them computationally inefficient. This paper presents experimentally validated recursive models that are able to very accurately and efficiently predict the dynamics of the four most common types of periodic structures. The proposed modeling technique employs a combination of static deflection formulae and Rayleigh's Quotient to estimate the first mode shape and natural frequency of periodic structures having any number of beams. Also included in this paper are the results of an extensive experimental validation study which show excellent agreement between model prediction and measurement. Lastly, the proposed models are used to evaluate the performance of each type of structure. Results of this performance evaluation reveal key advantages and disadvantages associated with each type of structure.