Coupling of flexural and longitudinal wave motion in a finite periodic structure with asymmetrically arranged transverse beams

A companion paper [J. Acoust. Soc. Am. 118, 3010–3020 2005] has examined the phenomena of flexural-longitudinal wave coupling in a practically undamped and semi-infinite periodic waveguide with structural side-branches. The effect of structural damping on wave coupling in such a waveguide is examined in the first part of the present paper, and the damping-dependent decrease in wave coupling is revealed for a structure with multiresonant side-branches. In the second part, the simplifying semi-infinite assumption is relaxed and general expressions for the junction responses of finite and multicoupled periodic systems are derived as a generalization of the governing expressions for finite, mono-coupled periodic systems [Ohlrich, J. Sound Vib. 107, 411–434 (1986)]. The present derivation of the general frequency response of a finite system utilizes the eigenvectors of displacement responses and wave forces that are associated with the characteristic wave-types, which can exist in a multicoupled periodic system [Mead, J. Sound Vib. 40, 19–39 (1975)]. The third part of the paper considers a finite specific test-structure with eight periodic elements and with structural terminations at the extreme ends. Audio-frequency vibration responses of this tri-coupled periodic structure are predicted numerically over a broad range of frequencies and a very good agreement is found with the measurement results obtained from an experiment with a nominally identical, periodic test-structure which is freely suspended.