Development of computational schemes of group targeted connections for some elastic systems

Introduction. For some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel, methods of creating additional connections were developed, the introduction of each of which purposefully increases the value of only one natural frequency to a given value, while not changing any of the other natural frequencies and not one of the natural modes (forms of natural oscillations). If it is necessary to increase the values of several natural frequencies in a targeted manner, then this requirement can be implemented by creating an appropriate number of separate targeted connections. The computational scheme of each of the individual targeted connections should include racks installed at the nodes of mass application and directed along the trajectory of their movement. In some cases, individual targeted connections can be independently installed on the original (initial) system. In most cases, on the basis of individual targeted connections, a computational scheme of a united group targeted connection is developed, which increases all the intended frequencies to the set values, without changing any of the other natural frequencies and not one of the natural modes. Calculation examples are presented.Materials and methods. Methods of targeted control of the frequency spectrum of natural oscillations of elastic systems are used in the paper. These methods, which are based on the introduction of additional connections, were proposed and developed in the works of L.S. Lyakhovich. For verification purposes, the finite element method (FEM) and the corresponding software are also used.Results. A method of forming a matrix of additional stiffness, which corresponds to a group targeted connection is proposed. The requirements for those targeted connections, on the basis of which a group targeted connection is formed, are formulated. An algorithm for the development of a group targeted connection is proposed with allowance for the formulated requirements. Verification of the proposed algorithm for the development of a group targeted connection is done with the use of SCAD and Lira Software products.Conclusions. The results of the work can be used by research and design organizations, as well as in higher education institutions in the preparation of special courses for construction specialties (areas of training).

natural frequency, natural mode, targeted connection, group targeted connection, additional stiffness coefficients, targeted frequency spectrum control, building systems, elastic systems