Abstract
The problem of oscillations of an inhomogeneous beam made of a functionally gradient material in the framework of various deformation models - the Euler-Bernoulli model and the Timoshenko model in the presence of attenuation, which is described within the framework of the concept of complex modules for a standard viscoelastic body, is considered. The left end of the beam is pinched, and at the right end there is a concentrated moment oscillating with a certain frequency. The solution is built in two ways. In the first of them, on the basis of asymptotic analysis, a solution was constructed in the low-frequency domain, and a complete coincidence of solutions for the models under consideration in the low-frequency domain (up to the first resonance) for any laws of inhomogeneity was shown. In the second case, the influence of rheological factors on the amplitude-frequency characteristics of an inhomogeneous viscoelastic beam in the frequency range up to the third resonance was analyzed using the targeting method. A comparative analysis of the frequency response of two models for different laws of heterogeneity is carried out. Frequency response for various laws of inhomogeneity are presented, the movement of resonant frequencies depending on the dimensionless relaxation time is studied.
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