Control of natural vibration frequencies of shallow shells using wire-type actuators

Shallow shells are widely used in the aeronautical and aerospace industries, where the problem of controlled variation in the natural frequencies of the structure remains relevant nowadays. In this context, the use of mechanical actuators based on shape memory alloy wires offers considerable promise due to their compact design and ability to develop significant forces. In this work, the possibility of using such devices to control the natural frequencies of a segment of a shallow cylindrical shell is investigated numerically. The strains developed in the shell are found from the nonlinear relations taking into account the hypotheses of the Reissner-Mindlin theory. These relations are then linearized with respect to a state with a small deviation from the initial equilibrium caused by a decrease in the wire length. In order to reduce the computational cost, the shape memory effect is not simulated directly. Instead, an equivalent wire deformation of a certain value is prescribed. A mathematical formulation of the dynamic problem is based on the variational principle of virtual displacements, which takes into account the prestress state. The position of wires with respect to the circumferential coordinate and their initial deformation (shortening) are determined separately for each frequency (mode shape) of vibration by solving the optimization problem with constraints. The values of the objective function are determined using the capabilities of the ANSYS Mechanical APDL software, in which the natural frequencies of the examined structure are calculated by the finite element method. The reliability of the results is confirmed by comparing them with the data presented in the literature for a circular cylindrical shell subjected to internal pressure. A series of calculations showed that wire shortening leads not only to a change in the natural frequencies of vibrations up and down, but also has a qualitative effect on the corresponding mode shapes and their sequential order in the spectrum. It was also found that an increase in the convexity of the shell (its elevation relative to the plane) reduces the efficiency of the wire actuators.