Abstract
We discuss the propagation of Rayleigh waves at the boundary of a semi-infinite elastic lattice connected to a system of gyroscopic spinners. We present the derivation of the analytical solution of the equations governing the system when the lattice is subjected to a force acting on the boundary. We show that the analytical results are in excellent agreement with the outcomes of independent finite element simulations. In addition, we investigate the influence of the load direction, frequency and gyroscopic properties of the model on the dynamic behavior of the micro-structured medium. The main result is that the response of the forced discrete system is not symmetric with respect to the point of application of the force when the effect of the gyroscopic spinners is taken into account. Accordingly, the gyroscopic lattice represents an important example of a non-reciprocal medium. Hence, it can be used in practical applications to split the energy coming from an external source into different contributions, propagating in different directions.
Highlights
According to their original definition, Rayleigh waves are a class of elastic waves that propagate on the surface of an infinite homogenous isotropic solid, and they are confined within a superficial region whose thickness is comparable with their wavelength (Rayleigh, 1885)
We present for the first time the analytical derivation of the displacement field in a semi-infinite elastic lattice incorporating gyroscopic spinners, focusing the attention on Rayleigh waves
We investigate how the gyricity affects the behavior of Rayleigh waves traveling along the boundary and of the waves propagating into the bulk of the medium
Summary
According to their original definition, Rayleigh waves are a class of elastic waves that propagate on the surface of an infinite homogenous isotropic solid, and they are confined within a superficial region whose thickness is comparable with their wavelength (Rayleigh, 1885) These waves are well known by seismologists, since they are usually detected after the occurrence of an earthquake. They are observed in other common urban activities, such as construction and demolition works and vehicular traffic, in addition to industrial processes and technologies, like mining exploration, nondestructive testing and design of electronic instruments. Trapped modes associated with Rayleigh-Bloch waves in systems incorporating periodic gratings or periodic arrays of resonators were analyzed by Porter and Evans (1999), Porter and Evans (2005), Linton and McIver (2002) and Directional Control of Rayleigh Waves
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