Fluctuation and Frequency of the Oscillators with Exponential Spring Using Accurate Approximate Analytical Solutions

This paper examines the fluctuation and frequency of the motion of a homogeneous solid on a horizontal plane on an exponential crisscross spring. The governing equations of this oscillator are investigated using a modified Homotopy Perturbation method, Energy balance method and artificial parameter–Linstedt–Poincare’ method. A comparison of solutions shows that the fluctuation and frequency of the system solved by the presented methods are effective with a minor error of 0.1%.

Approximate Boundary Value Problems of a Deformed Flexible Closed Torso Shell with Excited Edges

A boundary value problem solution is presented to treatment the deformations of a closed flexible elastic torso shell having perturbations at its axial edges. A so-called artificial parameter technique is applied to obtain a solution in the form of a double asymptotic series further summed using two-dimensional fractional rational approximations. Convergence of the approximations to the exact solution is proven.

A Methodology for Online Fatigue Monitoring With Consideration of Temperature-Dependent Material Properties Using Artificial Parameter Method

Following the basis of the ASME codes, the major nuclear components are designed to successfully avoid the fatigue failure. However, such design is generally very conservative and it is necessary to accurately assess the fatigue life of the components for the optimal life. The assessment of fatigue damage accumulation due to the thermal transients is currently performed via online fatigue monitoring systems. The algorithms for online calculation of thermal stress are one of the main components of these systems and are often based on the Green function technique (GFT), in which machine parameters such as fluid temperatures, pressures, and flow rates are converted into metal temperature transients and thermal stresses. However, since the GFT is based upon the linear superposition principle, it cannot be directly used when the temperature-dependent material properties are considered. This paper presents a methodology to consider the temperature- dependent material properties using artificial parameter method. Two cases are presented to compare the results calculated from the proposed models with those calculated by finite element method (FEM). It is found that the temperature-dependent material properties have significant influence on the maximum peak stresses which can be accurately captured by the models proposed in this work.