Surprises of the transformer as a coupled oscillator system

We study a system of two RLC oscillators coupled through a variable mutual inductance. The system is interesting because it exhibits some peculiar features of coupled oscillators: (i) there are two natural frequencies; (ii) in general, the resonant frequencies do not coincide with the natural frequencies; (iii) the resonant frequencies of both oscillators differ; (iv) for certain choices of parameters, there is only one resonant frequency, instead of the two expected.

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.