In the new advanced drive schemes, identification and modeling of the load complex characteristics can play an important role to predict the dynamic performance of the proposed control strategy. The novelty of this paper consists in the classification of the different types of the nonlinear loads which the electrical drive systems may encounter. In this study, nonlinear components of mechanical loads are divided into two groups. The first type includes nonlinear phenomenon caused by the nature of load which is predictable and identifiable. Another type of loads nonlinear characteristic happens due to the occurrence of a mechanical fault in motor, coupling or load parts. Generally, this type of non-intended nonlinear effect is not predictable and often occurs in the installation and operation stage of the drive system utilization. In this paper, the performance of an induction servo drive system has been simulated under the influence of different types of non-linear industrial loads.

Stiffness plays an important role in the earthquake rupture dynamics. At the main slip zone, the response of the system following a solicitation is both a function of stiffness and the heterogeneity of the surroundings. This work studies the effect of heterogeneity of Earth crust, particularly the effect of spatial dependence of stiffness during the nucleation phase of an earthquake. Based on Burridge Knopoff's 1D model, we have redesigned the dynamics of an earthquake, taking into account the spatial variation of stiffness. Given the complexity of the differential system obtained, a digital approach was used to trace solutions to the problem. We represented the variation curves of temperature, energy and displacement as well as the speed obtained when the rigidity is constant (CS) and when the stiffness is nonlinear (NLS). Then a comparative study was conducted between the two cases. The result show that by considering the space-dependent of stiffness, the stick-slip movements occurred and a succession of oscillations with decreasing amplitude in time, separate to the case where it was considering to be constant. The non-linearity of the stiffness reveals that each oscillation is separated from the next by a coseismic phase. For non-linearities of order one and in the presence or absence of a fluid, the spatial dependence of stiffness suggests the existence of a seismic motion with decreasing amplitude, which always precedes by a steady state when the stiffness is nonlinear, which is not the case when the stiffness is constant; moreover, the amplitude of the movement decreases with the increase in the pore-fluid ratio. For nonlinearities of order three and in the presence of a fluid, the introduction of heterogeneity into the motion reduced the charging time before any seismic activity. Besides, it reveals existence of a transient phase that appears before steady state during nucleation phase. When going from TP to SH law and also to VW law, a quantitative difference is observed, which is not the case for a qualitative difference on these different laws. This work shows that before observing a steady state during nucleation, there are a multitude of micro seismic activity characterized by oscillations with time decreasing amplitudes.

General solution of the time-dependent strain energy release rate for delamination cracks in multilayered functionally graded load-bearing beam structures which exhibit non-linear creep is derived. The Material is functionally graded along the length of layers. The Ramberg-Osgood stress-strain relation is used by assuming that the Material in each layer behaves differently in tension and compression. The second term in the Ramberg-Osgood relation includes time dependence to treat the non-linear creep. The solution derived holds for multilayered functionally graded beams with arbitrary number of layers which have different width and Material properties. The solution is applied for a delamination in a multilayered beam with a built-in end. An analysis is performed also by considering the balance of the energy in the multilayered beam configuration for the sake of verification. The effect of time is also studied. It is found that the strain energy release rate grows with the time. The results obtained here are useful for understanding the time-dependent delamination in multilayered functionally graded structural components subjected to non-linear creep.

Delamination fracture of a two-dimensional functionally graded multilayered four-point bending beam that exhibits non-linear behaviour of the Material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under consideration has an arbitrary number of layers. Each layer has individual thickness and Material properties. A delamination crack is located arbitrary between layers. The Material is two-dimensional functionally graded in the cross-section of each layer. The beam mechanical behaviour is described by a power-law stress-strain relation. The fracture is analyzed also by applying the J-integral approach in order to verify the solution derived for the strain energy release rate. The effects of crack location, Material gradient and non-linear behaviour of Material on the delamination fracture are evaluated. It is found that the Material non-linearity leads to increase of the strain energy release rate. Therefore, the Material non-linearity should be taken into account in fracture mechanics based safety design of two-dimensional functionally graded multilayered structural members. It is found also that the delamination behaviour can be effectively regulated by using appropriate Material gradients in the design stage of functionally graded multilayered structural members and components.

Analytical and Adomian decomposition methods have been developed to determine the large defection of a functionally graded cantilever beam under inclined end loading by fully accounting for geometric nonlinearities, and by incorporating the physical properties of functionally graded Materials, and have also been solved. The large defection problem will also be solved by using an FEA solver. Results obtained only due to end loading are validated using a developed analytical solution. The Adomian decomposition method yields polynomial expressions for the beam configuration. The equilibrium equation of a functionally graded cantilever beam actuated through self-balanced moments has been derived and solved using the Adomian decomposition method and the FEA solver for which no closed form solution can be obtained. Some of the limitations and recipes to obviate these are included. The Adomian decomposition method will be useful toward the design of functionally graded compliant mechanisms driven by smart actuators.