Nonlinear vibrations in nuclei

On the Tfd Treatment of Collective Vibrations in Hot Nuclei

The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction and long-range particle-hole effective forces is reexamined. In contrast with earlier studies it is found that a wave function of a thermal phonon is depended not only on the Fermi-Dirac thermal occupat...

SU(3) Symmetry and Scissors Mode Vibrations in Nuclei

We show that a nearly perfect SU(3) symmetry emerges from an extended Projected Shell Model. Starting from a deformed potential we construct separate bases for neutron and proton collective rotational states by exact angular momentum projection. These rotational states are then coupled by diagonalizing a residual pairing plus quadrupole interaction. The states obtained exhibit a one-to-one corr...

Forced Vibrations for a Nonlinear Wave Equation

A Brief Introduction to Nonlinear Vibrations

Vibration phenomena that might be modelled well using linear vibration theory include small amplitude vibrations of long, slender objects like long bridges, aeroplane wings, and helicopter blades; small rocking motions of ships in calm waters; the simplest whirling motions of flexible shafts, and so on. However, interactions between bridges and foundations, between wings/blades and air, between...

Nonlinear vibrations of thin hyperelastic plates

Static deflection as well as free and forced nonlinear vibration of thin square plates made of hyperelastic materials are investigated. Two types of materials, namely rubber and soft biological tissues, are considered. The involved physical nonlinearities are described through the Neo-Hookean, Mooney-Rivlin, and Ogden hyperelastic laws; geometrical nonlinearities are modeled by the Novozhilov n...