A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams

This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

BAYESIAN PREDICTION FOR THE TWO-PARAMETER EXPONENTIAL DISTRIBUTION BASED ON TYPE Ⅱ DOUBLY CENSORING

The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.

Group Method Analysis of MHD Mixed Convective Flow Past on a Moving Curved Surface with Suction

The group-theorytic approach is applied for solving the problem of the unsteady MHD mixed convective flow past on a moving curved surface. The application of two-parameter groups reduces the number of independent variables by two, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effects of varying parameters governing the problem are studied. A comparison with previous work is presented.

Computational Methods in the Theory of Synthesis of Radio and Acoustic Radiating Systems

A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems, is presented in the paper. The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.

Group solution for an unsteady non-Newtonian Hiemenz flow with variable fluid properties and suction/injection

The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two- parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge-Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.

Average Life Prediction Based on Incomplete Data

The two-parameter exponential distribution can often be used to describe the lifetime of products for example, electronic components, engines and so on. This paper considers a prediction problem arising in the life test of key parts in high speed trains. Employing the Bayes method, a joint prior is used to describe the variability of the parameters but the form of the prior is not specified and only several moment conditions are assumed. Under the condition that the observed samples are randomly right censored, we define a statistic to predict a set of future samples which describes the average life of the second-round samples, firstly, under the condition that the censoring distribution is known and secondly, that it is unknown. For several different priors and life data sets, we demonstrate the coverage frequencies of the proposed prediction intervals as the sample size of the observed and the censoring proportion change. The numerical results show that the prediction intervals are efficient and applicable.

NON-SYMMETRICAL LARGE DEFORMATION OFA SHALLOW THIN CONICAL SHELL

In this paper, non-symmetrical large deformation problem of a shallow conical shell is studied by two-parameter perturbation method. The third-order approximate analytical solution of the deformation of a shallow conical shell subjected to linear loads is obtained and the characteristic curves of load-deflection on a perturbing point are portrayed. The similar questions of other kind of shell and plate can be discussed by using this paper's method. As the examples, the large deflection of plate and shallow conical shells with different initial deflections is discussed.