Acoustics

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Natural (archaeology)

Journal of Sound and Vibration

In this paper the relationship is studied between the bounding frequencies of the propagation zones of mono-coupled periodic systems and the natural frequencies of the individual elements of which the system is composed. It is also shown how these relate to the natural frequencies of finite mono-coupled periodic systems. The concept of the characteristic receptance of a free wave in the periodic system is developed, and the manner in which this receptance varies with frequency is studied. It is used to examine the attenuation and phasechange undergone by a free wave when it impinges on and is reflected from a non-dissipative boundary. This leads on to a simple physical explanation for the occurrence of natural frequencies of finite systems in either the attenuation zones or propagation zones of the infinite system. Distinction is drawn between systems whose elements are symmetric or unsymmetric, positive-definite or semi-definite.

Wave propagation and natural modes in periodic systems: I. Mono-coupled systems