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In this study random vibration of a cantilever tapered beam under distributed stationary stochastic excitation with Gaussian probability density function is investigated. early free vibration analysis is performed to obtain the mode shapes of beam in form of Bessel functions, then the response is described in summation of mode shapes, and auto correlation of response is shaped by considering the mode shapes of tapered beam, also spectral density matrix of excitation is derived with cooperation of mode shapes and two dummy variables. in next step by means of frequency response and taking Fourier integral of autocorrelation of response, spectral density of displacement is computed and by using spectral density of displacement, variance of random displacements for various positions along the beam are achieved. Finally elasticity equation is applied to derive random strain and stress of beam. Comparing the variance of random stress with yield stress of beam leads to obtain probability of beam failure.

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Seismic pounding between adjacent buildings is an undesirable phenomenon. Depending on the characteristics of the colliding buildings, pounding might cause severe structural damage in some cases, and even collapse is possible in some extreme situations. In order to mitigate the risk of seismic pounding between new buildings, current seismic design codes prescribe a minimum separation distance between adjacent structures. The value of the minimum separation distance is assumed equal to the peak relative displacement computed at the most likely pounding location and corresponding to a site-specific seismic intensity. Examining the collision possibility of adjacent structures as a result of earthquake is the basis of formulating regulations for determining minimum dimensions of separation distances. This distance can be calculated in different ways. In previous studies, double difference combination has been generally used to determine this distance and their only difference is in determining correlation coefficient of seismic response in two adjacent systems. This coefficient which depends on period and damping of the two systems has been obtained in previous works with the assumption of a linear behavior of structures. In the nonlinear range, the same correlation coefficient obtained from the linear mode is used by making structure behavior equivalent to linear mode and introducing values of effective damping and period. Modified values of period and damping depend on the requirement of system ductility under the applied record, which has been obtained for a specific behavioral model and from numerous numerical studies. In this study, the correlation coefficient of the two systems was presented using random vibration equations for the systems by Bouc - Wen different hysteresis behavior model. Moreover, the proposed relation could be applied for different input stimulation with specific spectral density and is more comprehensive than previous relations. Ductility demand of the system corresponding to the input spectral density was determined by random vibration relations and the probability distribution of relative displacement between the two systems which was obtained from the presented relations was compared with the existing ones. This study evaluates the accuracy of two different criteria to calculate the separation necessary to prevent seismic pounding between nonlinear hysteretic structural systems. All of the criteria considered in this paper make use of the same basic equation of the Double Difference Combination rule, but they adopt different procedures to estimate the correlation between displacement responses of nonlinear hysteretic systems. Monte Carlo analysis used to verify the relations presented for two adjacent nonlinear systems under the applied record which were simulated by a specified spectral density in stationary and non-stationary forms. Results obtained through Monte Carlo simulations indicate that the relation presented in this study is completely satisfactory and none of the two criteria evaluated in this study is exact.

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In this article, Monte Carlo simulation method is used in conjunction with finite elements (FEs) for probabilistic free vibration and stability analysis of pipes conveying fluid. For fluid-structure interaction, Euler-Bernoulli beam model is used for analyzing pipe structure and plug flow model for representing internal fluid flow in the pipe. By considering structural parameters of system as random fields, the governing deterministic partial differential equation (PDE) of continuous system is transformed into a stochastic PDE. The continuous random fields are discretized by mid-point and local average discretization methods; then, by Monte Carlo simulations in each iteration loop, every distributed-parameter PDE having stochastic lumped-parameters is transformed into a deterministic distributed-parameter PDE. Each PDE is transformed into a system of deterministic ordinary differential equations (ODEs) by using FEs. Accordingly, all of the deterministic and stochastic parameters of system are discretized. For free vibration analysis, the eigenvalue problem is solved for investigating the complex-valued eigenvalues and critical eigenfrequencies. Consequently, having complex eigenfrequencies and divergence points, the statistical responses of stochastic problem are obtained like expected values, standard deviations, probability density functions, and the probability of occurrence for divergence instabilities.

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The nonlinear vibration of sandwich viscoelastic plates under wide-band random excitation is investigated. The main attention is put on the influence of the one-to-one internal resonance, arisen from the close natural frequencies of the asymmetric modes of a near-square plate, on the response. The multi-modal response and the on-off intermittency phenomenon are especially considered. The mathematical modeling of the mid-layer is based on the moderate transverse shear strains and rotations, which have led to both geometrical and material nonlinearities. For the nonlinear constitutive equation of the mid layer, a single integral viscoelastic model is used. The displacement field in the thickness direction is also assumed to be linear for the in-plane components and quadratic for the out-of-plane components. Moreover, the Kirchhoff theory with the von-Karman nonlinearities are used for the outer layers. The solution is initiated by applying the perturbation method along with the Galerkin’s method to obtain integro-differential ordinary equations in time. These equations are then, solved using the Gaussian and non-Gaussian closure methods and the results are used to investigate the occurrence of the bifurcation with the aid of the Pseudo-arclength continuation method. Numerical results are presented for the multi-modal response and the minimum excitation intensity required for the nonlinear interaction between asymmetric modes.

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The satellites on the ground during construction and transportation, in launching stage and operation in space are under various types of dynamic loads, including high and low frequency vibrational loads, acoustics, shock, impact, etc., each of which can be an important source in the creation of stress on the satellite. The satellite components should be designed in such a way that can continue to operate while facing these situations. Electronic boards, in particular their solder joints, are critical components of satellites. Therefore, investigation of damage in design process of boards have great importance. Loading pattern on the satellite during its operation is usually random which considered as quasi-static load. Improvement of the design of the satellite against the weaknesses shown while facing different loads is essential, and given the fact that it is time consuming and costly to carry out laboratory tests, the use of analytical methods for checking the strength and lifetime of the structure can be very useful. In this research, random vibrations environment is equivalent to pseudo-static loads, and using the multilayer plate theory, the stresses in solder joints and failure of joints under this loading will be investigated. Also, the effect of parameters such as electronic board width and the boundary condition of the printed circuit board on the solder joints' stress will be considered in analytical solution.