A. K. Abramian
V. L. Andreyev
D. A. Indejtchev
Acad. of Sci. of Russia, St. Petersburg
Inst. for Problems of Mech. Eng., Bolshoy 61 V.O., St. Petersburg 199178, Russia
It has been found that by the type of a system operator and type of inclusions the discrete spectrum may lie above the cutoff frequency of the continuous spectrum as well as below it. It is shown that the standing modes located in the inclusions region are caused by the trapping modes effect. Necessary and sufficient conditions for low-and high-frequency trapping modes were found. The discrete spectrum shifts to the continuous spectrum axis and initiation of high-frequency trapping modes is accompanied by a phenomenon of traveling waves damping. Special attention is paid at the advance of vibration through hydroelastic systems. Despite this, the problem of the effect of symmetry of a structure on the initiation of high-frequency trapping modes is studied. Some natural frequencies of finite structures are equal to discrete frequencies of the similar infinite structures. A peculiarity of the emergence of these frequencies of the finite structures is that the frequencies are multiples of two (in case of one-dimensional structures).