Bei der Berechnung winderregter Schwingungen von Leiterseilen wird haufig das Ritz-Verfahren angewendet oder auch mit finiten Elementen gerechnet, wobei wegen der hohen Frequenzen der beobachteten Schwingungen mehrere hundert oder tausend Terme zu berucksichtigen sind. Hier wird ein anderer Weg eingeschlagen: Dampfungs- und Windleistung werden fur das halbunendlich bzw. unendlich lange Seil berechnet, was infolge des sehr dichten Spektrums der Eigenfrequenzcn des endlichen Seiles zu guten Ergebnissen fuhrt. Die Schwingungsamplituden folgen dann aus einer Energiebilanz. Mit Hilfe der Methode der singularen Storungen werden sehr einfache Formeln fur die Biegewechseldehnungen im Seil angegeben.

Ein einfaches Rechenmodell zur Berechnung winderregter Schwingungen an Hochspannungsleitungen mit Dämpfern

Transmission line vibrations

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model. [DOI: 10.1115/1.4029526]

Nonlinear Dynamics of Stockbridge Dampers

Ultra-wideband piezoelectric energy harvester based on Stockbridge damper and its application in smart grid

The aim of the present paper is to describe the application of the generalized integral transform technique (GITT) for the theoretical analysis of wind-induced vibrations on overhead conductors. In the mathematical model adopted, the complicated helicoidal geometry of the conductor is simplified by treating it as a homogeneous taut string simple supported at both ends. Solving the governing partial differential equation through the GITT approach, one derives purely analytical or analytical–numerical solutions for the conductor transverse displacement as a function of both position and time. In order to highlight the potential and flexibility of the GITT approach to account for realistic features of the phenomenon, three particular cases of practical interest are analyzed in detail, for which benchmark results are provided: (i) the damped-free vibrations of the conductor; (ii) the harmonic-forced vibrations of the conductor without and with Stockbridge dampers; and (iii) the forced vibrations of the conductor under a non-linear wind excitation. The current results may be combined with previous analytical predictions to compute the conductor amplitudes and bending strains at critical locations. Although this work is focused on a taut string model for the conductor, the approach described herein may be easily extendable to the beam model. Copyright © 2008 John Wiley & Sons, Ltd.

K. Hartmann

Papers

Dynamics of stockbridge dampers