Engineering Commons^™

Using Complex Orthogonal Decomposition To Extract Dispersion Relationships For Mass Chain, Nicholas A. Valente, Rickey A. Caldwell

Across the Bridge: The Merrimack Undergraduate Research Journal

Complex orthogonal decomposition (COD) was used to determine the extracted dispersion relationship of a traveling wave in a mass chain. When COD extracts a wavenumber it will produce M values for each wavenumber, γi, and N values for each frequency, ωi; where M is the number of masses and N is the number of time samples. In this work, least squares and a simple mean of the M-γi’s and N-ωi’s extracted values were used to determine each γi and ωi, respectively. An analytical dispersion relationship for the mass-chain is derived in addition to an approximate dispersion relationship. The approximate derivation …