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Abstract In this work, nonlinear electromagnetic vibration energy harvesting from cantilever beam under base harmonic oscillation is investigated and the effects of electromagnetic parameters on behavior of system is considered. For modeling assumed mode method is used, and beam is modeled in according to Timoshenko theory, which includes shear deformation and rotary inertia. In energy harvesting, the frequency response of the system is very important because it shows the best areas for energy harvesting and it is a good criterion for designing energy harvesters, hence a semi analytical method is used to find simply the amplitude of oscillation in terms of excitation frequency. In this method, at first equations of motion are solved with complex averaging method and obtained equations are solved with continuation method. For validation, comparison between results obtained from numerical and semi analytical method is given. Also comparison between linear and nonlinear system, and stability of periodic response and their bifurcations are given. In addition, in order to the effect of number of mode shapes and convergence of solution, frequency response of one, two, three modes and four modes cases are compared with together.

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In this paper, the effect of ductile damage on the behavior of a dented pipe subjected to internal pressure is investigated by experimental and numerical methods. In the numerical investigation, the plastic behavior of pipes under indentation is studied using continuum damage mechanics theory and the elastic-plastic finite element analysis. Finite element calculations are carried out using the damage plasticity model proposed by Xue and Wierzbicki (X-W). The proposed damage plasticity model incorporates effects of four parameters that play important role in predicting the fracture initiation, namely the damage rule, the softening effect, the hydrostatic pressure and the Lode angle. The target dent depth is considered as an indication of the load bearing capacity of the pipe under indentation process by a rigid spherical indenter. To validate numerical calculations, a series of experimental tests are conducted on the API XB steel pipe with atmospheric pressure. After verification, numerical calculations for different ranges of internal pressures, wall thicknesses and indenter diameters with and without damage effect are carried out for aluminum 2024-T351 pipe and results are compared. It is shown that damage plays an important role on the load bearing capacity of an indented pipe. Results of the present study confirm the credibility of the proposed model in predicting the ductile fracture under multi-axial state of stress loadings.