Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, More >

Chia-Cheng Tsai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 151-162, 2008, DOI:10.3970/cmes.2008.027.151

Abstract In this paper we develop analytical particular solutions for the polyharmonic and the products of Helmholtz-type partial differential operators with Chebyshev polynomials at right-hand side. Our solutions can be written explicitly in terms of either monomial or Chebyshev bases. By using these formulas, we can obtain the approximate particular solution when the right-hand side has been represented by a truncated series of Chebyshev polynomials. These formulas are further implemented to solve inhomogeneous partial differential equations (PDEs) in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). Numerical experiments, which include More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 137-150, 2008, DOI:10.3970/cmes.2008.027.137

Abstract For the inverse vibration problem, a Lie-group shooting method is proposed to simultaneously estimate the time-dependent damping and stiffness functions by using two sets of displacement as inputs. First, we transform these two ODEs into two parabolic type PDEs. Second, we formulate the inverse vibration problem as a multi-dimensional two-point boundary value problem with unknown coefficients, allowing us to develop the Lie-group shooting method. For the semi-discretizations of PDEs we thus obtain two coupled sets of linear algebraic equations, from which the estimation of damping and stiffness coefficients can be written out explicitly. The present More >

Mira Mitra¹, S. Gopalakrishnan²

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 125-136, 2008, DOI:10.3970/cmes.2008.027.125

Abstract In this paper, the wave characteristics, namely, the spectrum and dispersion relations of multi-wall carbon nanotubes (MWNTs) are studied. The MWNTs are modeled as multiple thin shells coupled through van der Waals force. Each wall of the MWNT has three displacements, i.e, axial, circumferential and radial with variation along the axial and circumferential directions. The wave characteristics are obtained by transforming the governing differential wave equations to frequency domain via Fourier transform. This transformation is first done in time using fast Fourier transform (FFT) and then in one spatial dimension using Fourier series. These transformed equations More >

K. Jayabal, A. Arockiarajan, S.M. Sivakumar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 111-124, 2008, DOI:10.3970/cmes.2008.027.111

Abstract A three dimensional micromechanically motivated model is proposed here based on firm thermodynamics principles to capture the nonlinear dissipative effects in the polycrystal ferroelectrics. The constraint imposed by the surrounding grains on a subgrain at its boundary during domain switching is modeled by a suitable modification of the switching threshold in a subgrain. The effect of this modification in the dissipation threshold is studied in the polycrystal behavior after due correlation of the subgrain behavior with the single crystal experimental results found in literature. Taking into consideration, all the domain switching possibilities, the volume fractions More >

B Radhika¹, S S P,a¹, C S Manohar^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 79-110, 2008, DOI:10.3970/cmes.2008.027.079

Abstract Reliability of nonlinear vibrating systems under stochastic excitations is investigated using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis tests, and the next stage involves More >

Sanjay Mittal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 63-78, 2008, DOI:10.3970/cmes.2008.027.063

Abstract Flow past a circular cylinder looses stability at a Reynolds number,Re~47. It has been shown, in the past, that the linear stability analysis (LSA) of the steady state solution can predict not only the critical Re, but also the non-dimensional frequency, St, of the associated instability. For larger Re the non-linear effects become important and the LSA of the steady-state flow does not predict the correct St. It is shown that, in general, the LSA applied to the time-averaged flow can result in useful information regarding its stability. This idea is applied to the Re = 100 flow past More >

Vadiraja D. N.¹, A. D. Sahasrabudhe²

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 49-62, 2008, DOI:10.3970/cmes.2008.027.049

Abstract Rotating beams are flexible structures, which are often idealized as cantilever beams. Structural modelling of rotating thin-walled composite beam with embedded MFC actuators and sensors using higher shear deformation theory (HSDT) is presented. A non-Cartesian deformation variable (which represents arc length stretch) is used along with two Cartesian deformation variables. The governing system of equations is derived from Hamilton's principle and solution is obtained by extended Galerkin's method. Optimal control problem is solved using LQG control algorithm. Vibration characteristics and optimal control for a box beam configuration are discussed in numerical examples. Gyroscopic coupling between More >

T. Kar, M.L. Munjal¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 37-48, 2008, DOI:10.3970/cmes.2008.027.037

Abstract In the present work, a wedge structure made of absorbing panels has been analyzed by making use of the matrizant analysis with the help of the Boundary-Condition-Transfer (BCT) algorithm. The rectangular panel wedge, as it is called in this manuscript, is simple in geometry. The theoretical model, based on the plane wave acoustical coupling between multiple interacting ducts of variable cross sectional area, is applied to predict the pressure reflection coefficient of the present wedge configuration. Bulk reaction and hence wave propagation in the wedge material has been assumed in the proposed model. An asymptotic More >

Jyoti Ranjan Majhi, Ranjan Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 25-36, 2008, DOI:10.3970/cmes.2008.027.025

Abstract The flapping equation for a rotating rigid helicopter blade is typically derived by considering 1) small flap angle, 2) small induced angle of attack and 3) linear aerodynamics. However, the use of nonlinear aerodynamics can make the assumptions of small angles suspect. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived in this paper with nonlinear aerodynamics . Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are More >