Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method

Abstract

This study is to analyse the dynamical instability (or the buckling) of a steel space truss using the accurate solutions obtained by the high-order Taylor series method. One is used to obtain numerical solutions for analysing instability, because it is difficult to find the analytic solution for a geometrical nonlinearity system. However, numerical solutions can yield incorrect analyses in the case of a space truss model with high nonlinearity. So, we use the semi-analytic solutions obtained by the high-order Taylor series to analyse the instability of the nonlinear truss system. Based on the semi-analytic solutions, we investigate the dynamical instability of the truss systems under step, sinusoidal and beating excitations. The analysis results show that the reliable attractors in the phase space can be observed even though various forces are excited. Furthermore, the dynamic buckling levels with periodic sinusoidal and beating excitations are lower, and the responses react sensitively according to the beating and the sinusoidal excitation.

A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

“…The periodic parameters and of 1.0 and 0.05, respectively, were applied as shown in Figure 15. In (34) and (35), 0 is the first natural angular frequency of the model, and the excitation is applied at the same period as the natural frequency of the case of = 1.0. This study considered the case of = 1.0 only.…”

“…In particular, when we need to perform long-time numerical simulations and sometimes to look for high precision solutions of differential systems, the family of ordinary differential equation solvers that can answer the requirements is the Taylor Series Method (Barrio et al [34]). Additionally, it has been reported that appropriately adjusting the number of terms and error limit is advantageous in computing the error limit and attaining an accurate solution fairly easily (Barrio et al [27]; Shon et al [35]). Traditional Taylor series method requires an infinite series expansion for attaining periodic response of a dynamic system and can be inappropriate for discrete nonlinear governing equations.…”

Dynamics of Multilink Rod System With Constraints: A Plane Problem in Finite Element Formulation

“…Пронумеруем конечные элементы от 1 до N и обозначим через ( ) k q вектор обобщен-ных координат k-го элемента (24). Тогда вариационное уравнение (2) для k-го элемента можно записать в виде…”