Modeling the Vibrations of Deformable Elements of Apparatus Structures under Vibration Disturbing Loads

The problem of mitigating vibrations of radioelectronic devices is an urgent problem in mechanical engineering of aircraft industry. The purpose of the study is to investigate the vibrations of platelike elements with attached masses under the influence of vibration loads. All deformable elements are viscoelastic. The viscoelastic properties obey the hereditary Boltzmann–Volterra integral relation. Linear vibrations of the considered mechanical system are investigated. For reduction of impulse perturbations of a radioelectronic unit with attached masses, a method and an algorithm for solving the problem are developed. The method of complex amplitudes, the methods of mathematical physics equations, the Gauss method, the Mueller method, and the Godunov orthogonal run method were used in developing a method for solving the problem. An algorithm for determining the resonance frequency and amplitude of displacements of the considered mechanical system was proposed. Application of the proposed mathematical model taking into account viscous properties of the elements allows achieving an up to 25% reduction in the total impulse loads of the radioelectronic devices. It is established that the use of rubber shock absorbers reduces the amplitudes of vibrations of the equipment up to 30%. It is also established that the use of dissipative and inhomogeneous design allows maximal reduction (up to 40–50%) of resonant amplitudes of radioelectronic devices in low-frequency ranges.