The initial value problem for a lumped parameter model arising from design of magneto–electromechanical device with a current-carrying conductor is analyzed. The differential equation is nonlinear because it includes the magnetic force term. The analysis for the dynamic pull-in occurring in the system is presented. The pull-in threshold is given analytically in terms of model parameters. Sufficient conditions for the existence of periodic solutions are proved analytically and verified numerically. The results can be useful for understanding and design of one-degree-of-freedom models of magnetically actuated beams.

A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are $L^2 $ error estimates for the error between the extended fully discrete finite element solutions and the exact solution.

To evaluate novel turbine designs, the wind energy sector extensively depends on computational fluid dynamics (CFD). To use CFD in the design optimization process, where lower-fidelity approaches such as blade element momentum (BEM) are more popular, new tools to increase the accuracy must be developed as the latest wind turbines are larger and the aerodynamics and structural dynamics become more complex. In the present study, a new concurrent aerodynamic shape optimization approach towards multidisciplinary design optimization (MDO) that uses a Reynolds-averaged Navier–Stokes solver in conjunction with a numerical optimization methodology is introduced. A multidisciplinary design optimization tool called DAFoam is used for the NREL phase VI turbine as a baseline geometry. Aerodynamic design optimizations in terms of five different schemes, namely, cross-sectional shape, pitch angle, twist, chord length, and dihedral optimization are conducted. Pointwise, a commercial mesh generator is used to create the numerical meshes. As the adjoint approach is strongly reliant on the mesh quality, up to 17.8 million mesh cells were employed during the mesh convergence and result validation processes, whereas 2.65 million mesh cells were used throughout the design optimization due to the computational cost. The Sparse Nonlinear OPTimizer (SNOPT) is used for the optimization process in the adjoint solver. The torque in the tangential direction is the optimization’s merit function and excellent results are achieved, which shows the promising prospect of applying this approach for transient MDO. This work represents the first attempt to implement DAFoam for wind turbine aerodynamic design optimization.