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This paper examines the solution of a damped beam equation whose damping characteristics are well-defined by the fractional derivative (FD). Homotopy Analysis Method (HAM) is applied for calculating the dynamic response (DR). Unit step and unit impulse functions are deliberated for this analysis. Acquired results are illustrated to show the movement of the beam under various sets of parameters with different orders of the FDs. Here FD is defined in the Caputo sense. Obtained results have been compared with the solutions achieved by Adomian decomposition method (ADM) to show the efficiency and effectiveness of the presented method.

In this article, free vibration of SingleWalled Carbon Nanotube (SWCNT) resting on exponentially varying Winkler elastic foundation is investigated by using Differential Quadrature Method (DQM). Euler-Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of edge conditions. Obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are illustrated to show the effects of nonuniform parameter, nonlocal parameter, aspect ratio,Winkler modulus parameter and edge conditions on the frequency parameters.

In this paper, Differential Quadrature Method (DQM) is applied to investigate free vibration of Single Walled Carbon Nanotubes (SWCNTs) with exponentially varying stiffness based on non-local Euler-Bernoulli beam theory. Application of DQ method in the governing differential equation converts the problem to a generalized eigenvalue problem and its solution gives frequency parameters. Convergence of the results show that DQM solutions converge fast. In this article, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

In this article, free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) is investigated by using the Differential Quadrature Method (DQM). Here width of the cross-section is assumed to vary exponentially along the length of the nano-ribbon. Euler–Bernoulli beam theory is considered in conjunction with the nonlocal elasticity theory of Eringen. Step by step procedure is included and MATLAB code has been developed to obtain the numerical results for different scaling parameters as well as for four types of boundary conditions. Convergence study is carried out to illustrate the efficiency of the method and obtained results are validated with known results in special cases showing good agreement. Further, numerical as well as graphical results are depicted to show the effects of the nonuniform parameter, nonlocal parameter, aspect ratio and edge conditions on the frequency parameters.

Abstract: In this paper, a regression based artificial neural network model for multi input single output (MISO) systems has been developed. The time devoted in training this model is considerably less in comparison with the traditional ANN model and the number of neurons in the hidden layer can be fixed by choosing a regression polynomial of desired degree. The proposed model has been used and simulated for an example problem of transverse vibrations of plates viz. vibration of circular and elliptic annular plates. There exist nine different boundary conditions for the present example problem which are all simulated using the model. The training and testing with unseen patterns show the efficacy and reliability of the proposed technique for the MISO systems. Comparison of the proposed model with the traditional ANN model shows the former to be better and much efficient. [Copyright &y& Elsevier]

This paper presents the use of two-dimensional boundary characteristic orthogonal polynomials as the shape functions in the Rayleigh-Ritz method to study the vibration of non-homogeneous plates with a curved boundary, and of elliptical plates in particular. The non-homogeneity considered here is a sort of generalized radial tapering that belongs to a special class such that the taper always extends to zero elasticity and zero density at the plate edges. The first five natural frequencies are reported here for various combinations of the degrees of non-homogeneity. Plots have been presented to show the effect of the aspect ratio on different modes of vibrations for various shapes of elliptic plates and degrees of non-homogeneity. The results for non-homogeneous elliptical plates are entirely new and are not available elsewhere. Comparison can only be made for homogeneous plates, and in this case the results have been found to be in exact agreement with the results of available literature. [ABSTRACT FROM AUTHOR]