Symbolic computations for random fields using second order perturbation method
نویسنده
چکیده
The main idea is to show the application of symbolic computations in analysis of engineering systems with random parameters. The general computational methodology is based on the stochastic second order perturbation method and its implementation in the mathematical package MAPLE 6. The entire approach is displayed on the example of simple single degree of freedom dynamical system with random spring stiffness. The results of symbolic computations are derived numerically in the form of probabilistic moments of the structural response computed for the whole analysis time domain. The general methodology can be applied to all these engineering problems where the response can be derived symbolically in deterministic case, while input parameters of the system are random variables, fields or processes characterized by the probability density function (PDF) of any type.
منابع مشابه
A NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.
متن کاملA Generalized Version of the Perturbation-based Stochastic Finite Difference Method for Elastic Beams
The main idea of this paper is to demonstrate a stochastic computational technique consisting of the generalized stochastic perturbation method using the Taylor expansions of random variables and the classical Finite Difference Method based on regular grids. As it is documented by computational illustrations, it is possible to determine, using this approach, also higher probabilistic moments fo...
متن کاملNonresonant Excitation of the Forced Duffing Equation
We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...
متن کاملA generalized stochastic perturbation technique for plasticity problems
The main aim of this paper is to present an algorithm and the solution to the nonlinear plasticity problems with random parameters. This methodology is based on the finite element method covering physical and geometrical nonlinearities and, on the other hand, on the generalized nth order stochastic perturbation method. The perturbation approach resulting from theTaylor series expansion with unc...
متن کاملA HOMOTOPY PERTURBATION ALGORITHM AND TAYLOR SERIES EXPANSION METHOD TO SOLVE A SYSTEM OF SECOND KIND FREDHOLM INTEGRAL EQUATIONS
In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.
متن کامل