INFLUENCE OF THE SYMMETRY OF VIBRATIONS ON THE RESONANCE ON INHOMOGENEOUS WAVES IN ELASTIC HALF-LAYER

Abstract

A comparison of the resonance on inhomogeneous waves with symmetric and antisymmetric oscillations of a semiinfinite strip with free surfaces and a free edge is made. The field of wave in the semiinfinite strip is excited by the first normal wave propagating from infinity. It is shown that the resonance phenomenon on inhomogeneous waves in an elastic half-strip exists for both types of symmetry, the resonance frequency in both cases depends on the Poisson's coefficient. In this case, with symmetric oscillations, the frequency of resonance increases with increasing Poisson's coefficient, while with antisymmetric oscillations, it decreases. At symmetric oscillations, a resonance exists for the entire range of possible changes in the Poisson's coefficient. With antisymmetric oscillations, resonance is observed starting with the Poisson coefficient . In symmetric oscillations, resonance in inhomogeneous waves exists in the frequency range in which only one normal wave is propagated. At the resonant frequency, all waves with complex wave numbers have a maximum of amplitudes. The wave is determined with the first complex-wave number. As the frequency of a normal wave grows, its contribution to the formation of its own form at the resonance decreases. At the resonance frequency at symmetric oscillations, there are no normal waves in a wave field with a purely imaginary wave number. With antisymmetric fluctuations, the situation is substantially different. The resonance manifests itself in the frequency range in which two normal waves propagate. In this case, the first normal distribution wave is dominant, that is, it transmits the maximum of the energy of the reflected field. As in the symmetric case, the resonance on inhomogeneous waves is due to a significant excitation of a normal wave with the first complex wave number. Unlike symmetric oscillations, the amplitudes of nonhomogeneous waves of higher orders at the resonant frequency do not reach their maximum values. Beginning with the resonance frequency, two inhomogeneous waves with a purely imaginary wave number appear in the reflected field. The amplitudes of these waves significantly exceed the amplitude of the incident wave and vary in size. As the frequency increases, the difference between the wave numbers of the data of the heterogeneous waves increases and, accordingly, the difference between their amplitudes increases. Thus, the resonance on inhomogeneous waves with antisymmetric oscillations is due not only to an inhomogeneous wave with a complex wave number but also to heterogeneous waves with a purely imaginary wave number.