Dynamics of Structural-Inhomogeneous Laminate and Shell Mechanical Systems with Point Constraints and Focused Masses. Part 2. Statement of the Problem of Forced Oscillations, Methods of Solution, Computational Algorithm and Numerical Results

摘要

A vibrational formulation, a technique, and an algorithm are proposed for assessing the resonance state of a package of rectangular plates and shells having point bonds and concentrated masses with different rheological properties of deformable elements under the influence of harmonic influences. The viscoelastic properties of elements are described using the linear Boltzmann-Volterra theory. An algebraic system of equations with complex coefficients is obtained, which is solved by the Gauss method. Various problems on steady-state forced vibrations for structurally inhomogeneous mechanical systems consisting of a package of plate and shell systems with concentrated masses and shock absorbers installed in it were solved. A number of new mechanical effects have been discovered associated with a decrease in the maximum resonance amplitudes of the mechanical system as a whole. The concept of “global resonance amplitude” is introduced to study the behavior of the resonance amplitudes of a mechanical system. An analysis of the numerical results showed that the interaction of resonant amplitudes is observed only in structurally inhomogeneous systems (in this case, with elastic and viscoelastic elements) and with a noticeable approximation of the natural frequencies.