A new physically realisable internal 1:1 resonance in the coupled pendulum–slosh system

The problem of dynamic coupling between a rectangular container undergoing planar pendular oscillations and its interior potential fluid sloshing is studied. Neumann boundary-value for the motion inside deduced from Bateman–Luke variational principle. governing integro-differential equation suspended container, single rigid pivoting rod, Euler–Lagrange forced pendulum. rigid-body partial differential equations are linearised, characteristic natural resonant frequencies coupled dynamical system presented. It found that internal 1:1 resonances exist an experimentally realistic setup, which has important physical implications. In addition, new instability in linearised whereby occurs when rod length shorter than critical length, explicit formula given.