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In recent years,the need for low power electronic circuits like sensors and wireless systems, has been considered by many researchers.Excessive weight, limited lifetime of the batteries and also having problem in replacing them, are the main reasons for harvesting energy from ambient vibrations. Among the various sources of environmental energy, mechanical vibrations, has gained popularity due to the availability. Among the different methods of ambient vibration energy harvesting, piezoelectric method, is one of the good ways to harvest energy due to the favorable effects of electromechanical coupling. The most common means of harvesting energy from vibrations, is a unimorph or bimorph cantilevered beam. In the present paper, electrical energy harvesting from Euler-Bernoulli trapezoidal cantilevered unimorph beam with base excitation using distributed parameter method has been considered. First, equations of motion analytically obtained and then using Assumed modes method(for rectangular beam), system’s natural frequencies is calculated and output voltage, current and power diagrams are presented. For verifying results, presented voltage, current and power diagrams for trapezoidal configuration close to rectangular configuration that it’s results are published in references, will be compared. Then, functional parameters for trapezoidal energy harvester, with resistance value changes for energy consumer has been analyzed.

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In this paper the effect of artificial noise on the performance of nonlinear system identification method in reconstructing the response of a cantilever beam model having a local nonlinearity is investigated. For this purpose, the weak form equation governing the transverse vibration of a linear beam having a strongly nonlinear spring at the end is discretized by using Rayleigh-Ritz approach. Then, the derived equations are solved via Rung-Kutta method and the simulated response of the beam to impulse force is obtained. By contaminating the simulated response to artificial measurement noise, nonparametric nonlinear system identification is applied to reconstruct the response. Accordingly, intrinsic mode functions of the response are obtained by using advanced empirical mode decomposition, and nonlinear interaction model including intrinsic modal oscillators is constructed. Primary results show that the presence of noise in the response highly affects the sifting process which results in extraction of spurious intrinsic mode functions. In order to eradicate the effect of noise on this process, noise signals are used as masking signals in the advanced empirical mode decomposition method and intrinsic mode functions corresponding to the noise are extracted. Based on this approach, the dynamic of the noise in the response is identified and noise reduced signals are reconstructed by the intrinsic modal oscillators with appropriate accuracy.

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A variety of numerical methods were developed for the wave propagation analysis in the field of structural health monitoring. In this framework, meshless methods are suitable procedure for the analysis of problems such as damage initiation and its propagation or the fracture of materials. In this study, Hermit-type radial point interpolation method (HRPIM) is investigated for the numerical modeling of flexural wave propagation and damage quantification in Euler-Bernoulli beams using MATLAB. This method employs radial basis function (RBF) and its derivatives for interpolation which leads to Hermitian formulation. The evaluation of performance and capability of HRPIM is based on the comparison between the captured HRPIM ang benchmark signals using the root mean square error (RMSE) and reflection ratio from damage. The algorithm of damage quantification is the analytical solution which relates the reflection ratio to the damage extent. In this study, Gausian-type RBF is utilized and the number of field nodes, the size of support domain, shape parameters of RBF, the number of polynomials in the interpolation formula, the arrangement of background cells and the number of Gaussian points in damage length are the effective parameters on results. Based on the evaluation, the acceptable values and range of theses parameters are presented for correct modeling.

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In this paper nonlinear modal interactions and stability of a Rayleigh beam carrying a mass-spring-damper system are investigated. For this purpose, the dimensionless equations governing the vibration of the system are analyzed based on multiple scales method. By considering viscoelastic Kelvin-Voigt damping in the beam, complex mode shapes and time-dependent resonance frequencies are extracted. Using the traditional form of the multiple scales method results in physical contradiction in the time response of the concentrated mass which should be resolved. After free vibration analysis, the forced response of the system under harmonic force with frequency close to the first natural frequency and occurrence of one-to-three internal resonance is studied. The parameters of the one degree of freedom system are considered in a way that the modal interaction occurs via internal resonance mechanism. In this condition, frequency response of the system and its stability are investigated and it is shown that the unstability associated with the jump and Hopf bifurcation occurs in the vibration amplitude. Plots of the time response, phase and Poincare show that periodic, quasi-periodic and chaotic vibration may take place in the system. In order to verify the present paper’s results, the natural frequencies of the system are compared to those of the previous studies; in addition to this comparison, the frequency response based on numerical integration validates the results of the present paper.