scholarly journals On the analytical approximation of the quadratic non-linear oscillator by modified extended iteration method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
B. M. Ikramul Haque ◽  
Shajia Afrin Flora
Keyword(s):  
Analytical Solution ◽  
Iteration Method ◽  
Analytical Approximation ◽  
Linear Oscillator ◽  
Algebraic Complexity ◽  
Non Linear ◽  
Approximate Frequency ◽  
Non Linear Oscillator ◽  
Good Agreement

AbstractA modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier terms have been used in each step of iterations. The frequencies obtained by this technique show good agreement with the exact frequency. The percentage of error between the exact frequency and our third approximate frequency is as low as 0.001%. There is no algebraic complexity in our calculation, which is why this technique is very easy. The results have been compared with the exact and other existing results, which are both convergent and consistent.

On Categorization of Seismic Load As Primary or Secondary for Piping Systems With Hardening Capacity

2018 ◽  
Author(s):  
Pierre B. Labbé
Keyword(s):  
Natural Frequency ◽  
Response Spectrum ◽  
A Priori ◽  
Effective Stiffness ◽  
Linear Oscillator ◽  
Seismic Load ◽  
Wide Range ◽  
Non Linear ◽  
Piping Systems ◽  
Non Linear Oscillator

The concept of primary/secondary categorization is first reviewed and generalized for its application to a non-linear oscillator subjected to a seismic load. Categorizing the seismic load requires calculating the input level associated with the oscillator ultimate capacity and comparing it to the level associated with the plastic yield. To resolve this problem, it is assumed that the non-linear oscillator behaves like a linear equivalent oscillator, with an effective stiffness (or frequency) and an effective damping. However, as it is not a priori possible to predict the equivalent stiffness and damping, a wide range of possibilities is systematically considered. The input motion is represented by its conventional response spectrum. It turns out that key parameters for categorization are i) the “effective stiffness factor” (varying from 0 for perfect damage behaviour to 1 for elastic-perfectly plastic) and the slope of the response spectrum in the vicinity of the natural frequency of the oscillator. Effective damping and spectrum sensitivity to damping play a second order role. A formula is presented that enables the calculation of the primary part of a seismically induced stress as a function of both the oscillator and input spectrum features. The formula is also presented in the form of a diagram. This paper follows-up on a similar paper presented by the author at the PVP 2017 Conference [1]. The new development introduced here is that the oscillator exhibits hardening capacity, while no hardening was assumed in [1]. It appears that the conclusions are slightly modified but the trend is very similar to the non-hardening case. Regarding piping systems, it appears that even when experiencing large plastic strains under beyond design input motions, their observed effective frequency is very close to their natural frequency, decreasing only by a few percents (experimental data from USA, Japan and India are processed). These observations lead to the conclusion that the seismic load, or the seismically induced inertial seismic strains, should basically be regarded as secondary.

J024013 Research on estimation of epileptic brainwave according to the band using a non-linear oscillator

2013 ◽  
Vol 2013 (0) ◽  
pp. _J024013-1-_J024013-5
Author(s):  
Takahiro MURAKAMI ◽  
Yasumi UKIDA ◽  
Koji MORI ◽  
Takashi SAITO ◽  
Hiroyuki KIDA ◽  
...  
Keyword(s):  
Linear Oscillator ◽  
Non Linear ◽  
Non Linear Oscillator
Sign in / Sign up

Export Citation Format

Share Document