Dynamic Modeling and Structural Optimization of a Bistable Electromagnetic Vibration Energy Harvester

A novel bistable electromagnetic vibration energy harvester (BEMH) is constructed and optimized in this study, based on a nonlinear system consisting mainly of a flexible membrane and a magnetic spring. A large-amplitude transverse vibration equation of the system is established with the general nonlinear geometry and magnetic force. Firstly, the mathematical model, considering the higher-order nonlinearities given by nonlinear Galerkin method, is applied to a membrane with a co-axial magnet mass and magnetic spring. Secondly, the steady vibration response of the membrane subjected to a harmonic base motion is obtained, and then the output power considering electromagnetic effect is analytically derived. On this basis, a parametric study in a broad frequency domain has been achieved for the BEMH with different radius ratios and membrane thicknesses. It is demonstrated that model predictions are both in close agreement with results from the finite element simulation and experiment data. Finally, the proposed efficient solution method is used to obtain an optimizing strategy for the design of multi-stable energy harvesters with the similar flexible structure.

Nonlinear Generalized Beam Theory for open thin-walled members

In the framework of the Generalized Beam Theory (GBT) a new cross-section analysis is proposed, specifically suited for nonlinear elastic thin-walled beams (TWB). The approach is developed according to the nonlinear Galerkin method (NGM), which calls for the evaluation of nonlinear (passive) trial functions, to be used in conjunction with linear (active) trial functions, in describing the displacement field. The set of (quadratic) trial functions is determined here by requiring that the classic Vlasov’s kinematic hypotheses of the linear theory (i.e. (a) transverse inextensibility and (b) unshearability) are satisfied also in the nonlinear sense. The linear field is described by the so-called conventional displacements, by neglecting non-conventional displacements, which violate Vlasov’s hypotheses. The nonlinear trial functions thus generated are innovative deformation fields, which describe extensional and shear displacements in a different way from that of the non-conventional fields of the linear theory. In particular, they consist of non-constant tangential and out-of-plane displacements of the cross-section profile, able to ensure inextensibility and unshearability of all the plate elements, by balancing the second-order strains induced by the conventional displacements. Since nonlinear trial functions do not increase the number of the unknowns, the GBT spirit, as a reduction method, is preserved. A very promising example is discussed, which shows that equilibrium paths can be determined by using few linear trial functions in conjunction with the corresponding nonlinear trial functions, supplying good results when compared with burdensome finite-element solutions.

A multilevel method of nonlinear Galerkin type for the Navier-Stokes equations

The basic idea of this new method resides in the fact that the major part of the relative information to the solution to calculate is contained in the small modes of a development of Fourier series; the raised modes of which the coefficients associated being small, being negligible to every instant, however, the effect of these modes on a long interval of time is not negligible. The nonlinear Galerkin method proposes economical treatment of these modes that permits, in spite of a simplified calculation, taking into account their interaction correctly with the other modes. After the introduction of this method, we elaborate an efficient strategy for its implementation.