Resonance and localized shear vibration of bi-material elastic resonator

The paper is dedicated to the problem of shear vibration of compound resonator, made from two different elastic materials, with rectangular cross section, when one side of the resonator is traction free, three other sides are clamped. The existence of two different types of vibration, namely localized and natural types are established. Possibility of coinciding of localized and natural frequencies from two different spectrums are shown, resulting in the internal resonance occurrence that does not exist in one phase material resonator, with ordinary boundary conditions.