Mode veering in coupled contiunous systems

The phenomenon of mode veering occurs in systems with a varying parameter. As the parameter varies, so do the natural frequencies. When two natural frequencies approach each other they often rapidly veer apart, instead of crossing. The veering is accompanied by rapid variations in the eigenvectors. This phenomenon is analysed in this paper with the focus being on coupled continuous systems. The uncoupled modes define the degrees of freedom, with a particular definition of uncoupled being defined. Conservative coupling is assumed to couple the uncoupled modes. The natural frequencies of the uncoupled system, defined as be- ing uncoupled when the other degrees of freedom are blocked, depend on the variable parameters and can cross at certain critical frequencies. The loci of these uncoupled-blocked natural frequencies form a skeleton about which veering occurs. The natural frequencies of the coupled system are seen to veer at these critical frequencies in the presence of arbitrarily small coupling, with the eigenvectors rotating and swapping from one branch to another. The separation of the branches around the critical frequencies is seen to depend on the coupling parameter. If the modes are damped veering still occurs unless the levels of damping associated with the two branches are sufficiently different. If there is instead strong coupling then there is usually a slow evolution of the eigenvalue loci rather than rapid veering. Examples are pre-sented, including coupled plate systems, to illustrate the results.