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The full set of conditions for synchronous harmonic oscillations in multiple LC circuits are established. These are for discrete lossless linear systems in source-free response. An Electric Networks literature review indicates that even the very basic condition for synchronous harmonic free oscillations is rarely presented, which is: initial conditions as an eingenvector for the initial charges and no currents (for t = 0). It is demonstrated herein that there are more conditions: three in total; in addition, simulation results are presented to illustrate all these possibilities, in which synchronous harmonic oscillation can actually be experienced. It is also noted here, that reactance or LC networks are correct models in Physics (pulsed power systems, metamaterials and metal-dielectric composites) and for Engineering devices (electrotherapy, ignition and radio). IEEE

A novel design procedure for tuned mass dampers in isolated structures is presented. The proposed optimization method is specifically developed to control base displacements or to solve the large isolator displacement problem in this type of structures under earthquakes. Therefore, it is based on a displacement transmissibility function, T, a particular case of the general transmissibility concept, which comes from Vibration Isolation. Three contributions are: 1) application of new seismic displacement narrowbandness, 2) simpler relative transmissibility function, and 3) compound design of isolation plus tuned mass damper. A standard isolated model is used to show that the base displacement can be controlled at levels in the proximity of the ground motion (T ≈ 1), which results in a positive comparison with previous isolation plus tuned mass damper solutions; this is one of the main co...

As a large base displacement level is the main drawback of the generally very successful seismic isolation technique, latest optimization procedures for the subsystem at base are focused on the control of that displacement. One family of procedures is based on the existence of one predominant frequency in earthquake excitation, which is evident only if the spectral analysis is performed considering displacement as the input, rather than the common ground acceleration. Nevertheless, recent results, besides corroborating the existence of one predominant period, have produced an improvement in the computation of this single spectral parameter. In this paper, this more reliable seismic predominant frequency is employed in previously successful methodologies to control isolator displacement. The hypothesis is that an enhanced model of the input will result in an improved structural response, ...