Harmonics are created by non-linear devices connected to the power system. Power system harmonics are multiples of the fundamental power system frequency and these harmonic frequencies can create distorted voltages and currents. Distortion of voltages and currents can affect the power system adversely causing power quality problems. Therefore, estimation of harmonics is of high importance for e...

One may produce the qth harmonic of a string of length π by applying the ‘correct touch’ at the node π/q during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their ‘touch’ is a damper of magnitude b concentrated at π/q. The ‘correct touch’ is that b for which the modes, that do not vanish at π/q, are maximally damped. We here examine the as...

odically occur in a facility’s electrical system can cause equipment malfunction, data distortion, transformer and motor insulation failure, overheating of neutral buses, nusiance tripping of circuit breakers, and solid-state component breakdown. The cost of power quality problems can be enormous. Equipment replacement can cost tens of thousands of dollars. Downtime, however, can run in the mil...

We investigate the effect of small spatiotemporal modulations in subwavelength-dimensioned phononic crystals with large band gaps, on frequency spectrum for elastic waves polarized plane periodicity. When radius cylinders periodically placed inside a matrix highly-contrasting properties is time-varying, we find that due to appearance harmonics throughout spectrum, notion gap destroyed general, ...