scholarly journals Influence of Longitudinal Inertia of Mass Element on Non-Linear Component of Beam Natural Frequency

2020 ◽  
Vol 138 (2) ◽  
pp. 302-304
Author(s):  
S. Uzny ◽  
Ł. Kutrowski ◽  
M. Osadnik
Keyword(s):  
Natural Frequency ◽  
Linear Component ◽  
Mass Element ◽  
Non Linear

scholarly journals Influence of Time Delay on Controlling the Non-Linear Oscillations of a Rotating Blade

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 85
Author(s):  
Yasser Salah Hamed ◽  
Ali Kandil
Keyword(s):  
Time Delay ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Control Process ◽  
Control Force ◽  
Specific Level ◽  
Loop Control ◽  
Positive Displacement ◽  
Non Linear ◽  
Linear Vibrations

Time delay is an obstacle in the way of actively controlling non-linear vibrations. In this paper, a rotating blade’s non-linear oscillations are reduced via a time-delayed non-linear saturation controller (NSC). This controller is excited by a positive displacement signal measured from the sensors on the blade, and its output is the suitable control force applied onto the actuators on the blade driving it to the desired minimum vibratory level. Based on the saturation phenomenon, the blade vibrations can be saturated at a specific level while the rest of the energy is transferred to the controller. This can be done by adjusting the controller natural frequency to be one half of the blade natural frequency. The whole behavior is governed by a system of first-order differential equations gained by the method of multiple scales. Different responses are included to show the influences of time delay on the closed-loop control process. Also, a good agreement can be noticed between the analytical curves and the numerically simulated ones.

A stochastic model for two interacting populations

1970 ◽  
Vol 7 (3) ◽  
pp. 544-564 ◽  
Author(s):  
Niels G. Becker
Keyword(s):  
Stochastic Model ◽  
Linear Models ◽  
Death Process ◽  
Linear Component ◽  
Birth And Death Process ◽  
Linear Interaction ◽  
Interacting Populations ◽  
Non Linear ◽  
The Subject ◽  
Interaction Component

To explain the growth of interacting populations, non-linear models need to be proposed and it is this non-linearity which proves to be most awkward in attempts at solving the resulting differential equations. A model with a particular non-linear component, initially proposed by Weiss (1965) for the spread of a carrier-borne epidemic, was solved completely by different methods by Dietz (1966) and Downton (1967). Immigration parameters were added to the model of Weiss and the resulting model was made the subject of a paper by Dietz and Downton (1968). It is the aim here to further generalize the model by introducing birth and death parameters so that the result is a linear birth and death process with immigration for each population plus the non-linear interaction component.

The non-linear vibrations of simply supported column loaded by the mass element

2021 ◽  
Vol 89 ◽  
pp. 700-709
Author(s):  
Sebastian Uzny ◽  
Łukasz Kutrowski ◽  
Michał Osadnik
Keyword(s):  
Simply Supported ◽  
Mass Element ◽  
Non Linear ◽  
Linear Vibrations

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.

Comparison of human ictal, interictal and normal non-linear component analyses

2000 ◽  
Vol 111 (7) ◽  
pp. 1282-1292 ◽  
Author(s):  
Hongkui Jing ◽  
Morikuni Takigawa
Keyword(s):  
Linear Component ◽  
Non Linear

Identification of Natural Frequency of Bearing Rotor Based on GA-SVM

2012 ◽  
Vol 443-444 ◽  
pp. 27-33
Author(s):  
Tian Ran Ma ◽  
Fei Hu Qin ◽  
Rui Xue Liu ◽  
Feng Jie Zhang
Keyword(s):  
Experimental Data ◽  
Support Vector Machine ◽  
Natural Frequency ◽  
Rolling Bearing ◽  
Linear Mapping ◽  
Support Vector ◽  
Non Linear ◽  
Experimental Values ◽  
Rotor Structure ◽  
Good Agreement

During identify natural frequency of bearing rotor, due to the complex non-linear relationship among the factors which influence natural frequency, so it is hard to establish a complete and accurate theoretical model. Based on the generalization and approximation of non-linear mapping capability of support vector machine (SVM) and the powerful ability of global optimization of the genetic algorithm (GA), the paper through optimizing the SVM by GA, establishes combined Genetic Support Vector Machine (GA-SVM). The method establishes the mapping between the natural frequency of a rolling bearing rotor and the various parameters, which reduces the rotor structure for the study similar to the natural frequency of the calculation of the workload greatly. Using the model to indentify the natural frequency of bearing rotor under different parameters, then compare identification value with experimental values shows that projections in good agreement with the experimental data.

Experimental study on condition assessment of reinforced concrete structure using a dynamics response approach

2014 ◽  
Vol 32 (2) ◽  
pp. 89-101
Author(s):  
Chun Pong Sing ◽  
P.E.D. Love ◽  
P.R. Davis
Keyword(s):  
Reinforced Concrete ◽  
Natural Frequency ◽  
Time Domain ◽  
Damping Ratio ◽  
Content Type ◽  
Rc Structures ◽  
Random Decrement ◽  
Rc Structure ◽  
Non Linear ◽  
Linear Damping

Purpose – Condition assessment on reinforced concrete (RC) structures is one of the critical issues as a result of structure degradation due to aging in many developed countries. The purpose of this paper is to examine the sensitivity and reliability of the conventional dynamic response approaches, which are currently applied in the RC structures. The key indicators include: natural frequency and damping ratio. To deal with the non-linear characteristics of RC, the concept of random decrement is applied to analyze time domain data and a non-linear damping curve could be constructed to reflect the condition of RC structure. Design/methodology/approach – A full-scale RC structure was tested under ambient vibration and the impact from a rubber hammer. Time history data were collected to analyze dynamics parameters such as natural frequency and damping ratio. Findings – The research demonstrated that the measured natural frequency is not a good indicator for integrity assessment. Similarly, it was revealed that the traditional theory of viscous damping performed poorly for the RC with non-linear characteristics. To address this problem, a non-linear curve is constructed using random decrement and it can be used to retrieve the condition of the RC structure in a scientific manner. Originality/value – The time domain analysis using random decrement can be used to construct a non-linear damping curve. The results from this study revealed that the damage of structure can be reflected from the changes in the damping curves. The non-linear damping curve is a powerful tool for assessing the health condition of RC structures in terms of sensitivity and reliability.

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