An elliptic averaging method for harmonically excited oscillators with a purely non-linear non-negative real-power restoring force

2013 ◽  
Vol 18 (7) ◽  
pp. 1888-1901 ◽  
Author(s):  
Zvonko Rakaric ◽  
Ivana Kovacic
Keyword(s):  
Averaging Method ◽  
Restoring Force ◽  
Real Power ◽  
Non Linear ◽  
Elliptic Averaging

Effect of Static Deflection on the Natural Frequency of a System with a Hardening Non-Linear Spring

1967 ◽  
Vol 9 (3) ◽  
pp. 177-181 ◽  
Author(s):  
Z. F. Reif
Keyword(s):  
Natural Frequency ◽  
Averaging Method ◽  
Analogue Computer ◽  
Static Deflection ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
First Approximation ◽  
Non Linear ◽  
Linear Spring

The effect of the static deflection on the natural frequency response is investigated for a single-degree-of-freedom system with a positive cubic non-linearity in the restoring force. The Ritz averaging method is used for the theoretical analysis, and by comparison with analogue computer solutions the first approximation, consisting of two terms, is shown to be satisfactory for most applications. Results indicate that in systems with a non-linear restoring force the existence of a static deflection produces significant effects and cannot be neglected in a theorectical analysis.

scholarly journals Seismic Strengthening Effects of Full-Size Reinforced Concrete Frame Retrofitted with Novel Concrete-Filled Tube Modular Frame by Pseudo-Dynamic Testing

2021 ◽  
Vol 11 (11) ◽  
pp. 4898
Author(s):  
Jin-Seon Kim ◽  
Ju-Seong Jung ◽  
Dong-Keun Jung ◽  
Eui-Yong Kim ◽  
Kang-Seok Lee
Keyword(s):  
Dynamic Analysis ◽  
Shear Failure ◽  
Dynamic Testing ◽  
Seismic Intensity ◽  
Seismic Retrofitting ◽  
Restoring Force ◽  
Rc Structures ◽  
Linear Dynamic ◽  
Non Linear ◽  
Force Characteristics

The present study proposes a new seismic retrofitting method using a concrete-filled tube modular frame (CFT-MF) system, a novel technique to overcome and improve the limitations of existing seismic strengthening methods. This CFT-MF seismic retrofitting method makes the most of the advantages of both concrete and steel pipes, thereby significantly improving constructability and increasing integration between the existing structure and the reinforcement joints. This method falls into the category of typical seismic retrofitting methods that focus on increasing strength, in which the required amount of seismic reinforcement can be easily estimated. Therefore, the method provides an easy solution to improving the strength of existing reinforced concrete (RC) structures with non-seismic details that are prone to shear failure. In the present study, a full-size two-story test frame modeled from existing domestic RC structures with non-seismic details was subjected to pseudo-dynamic testing. As a result, the effect of the CFT-MF system, when applied to existing RC structures, was examined and verified, especially as to its seismic retrofitting performance, i.e., restoring force characteristics, stiffness reinforcement, and seismic response control. In addition, based on the pseudo-dynamic testing results, a restoring force characteristics model was proposed to implement non-linear dynamic analysis of a structure retrofitted with the CFT-MF system (i.e., the test frame). Finally, based on the proposed restoring force characteristics, non-linear dynamic analysis was conducted, and the results were compared with those obtained by the pseudo-dynamic tests. The results showed that the RC frame (building) with no retrofitting measures applied underwent shear failure at a seismic intensity of 200 cm/s2, the threshold applied in seismic design in Korea. In contrast, in the frame (building) retrofitted with the CFT-MF system, only minor earthquake damage was observed, and even when the maximum seismic intensity (300 cm/s2) that may occur in Korean was applied, small-scale damage was observed. These results confirmed the validity of the seismic retrofitting method based on the CFT-MF system developed in the present study. The non-linear dynamic analysis and the pseudo-dynamic test showed similar results, with an average deviation of 10% or less in seismic response load and displacement.

Non-linear threshold autoregressive models for non-linear random vibrations

1981 ◽  
Vol 18 (02) ◽  
pp. 443-451 ◽  
Author(s):  
Tohru Ozaki
Keyword(s):  
Real Data ◽  
Time Series Models ◽  
Random Vibrations ◽  
Restoring Force ◽  
Threshold Autoregressive ◽  
Threshold Autoregressive Model ◽  
Linear Threshold ◽  
Non Linear ◽  
Stationarity Conditions ◽  
Structural Aspects

Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models. Stationarity conditions and some structural aspects of the model are briefly discussed. Applications of the model in the statistical analysis of real data are also shown with numerical results.

D11 Elliptic Averaging Method for Nonlinear Oscillator Having Two-Degree-of-Freedom

2011 ◽  
Vol 2011 (0) ◽  
pp. 97-98
Author(s):  
Tadashi OKABE ◽  
Takahiro KONDOU ◽  
Jumpei OHNISHI ◽  
Hideo TORIHARA
Keyword(s):  
Nonlinear Oscillator ◽  
Averaging Method ◽  
Degree Of Freedom ◽  
Elliptic Averaging ◽  
Two Degree Of Freedom

On the Forced Vibration with Non-linear Restoring Force by the Unbarmonic Force

1948 ◽  
Vol 51 (360) ◽  
pp. 347-348
Author(s):  
Toshio NISHIHARA ◽  
Yoshikazu SAWARAGI ◽  
Hirokazu NAKAMURA ◽  
Sadami NISHIDA
Keyword(s):  
Forced Vibration ◽  
Restoring Force ◽  
Non Linear

On the Non-Linear Characteristics of Automotive Shock Absorbers

1992 ◽  
Vol 206 (1) ◽  
pp. 3-16 ◽  
Author(s):  
C Surace ◽  
K Worden ◽  
G R Tomlinson
Keyword(s):  
Experimental Data ◽  
Restoring Force ◽  
Shock Absorbers ◽  
Surface Method ◽  
First Case ◽  
Non Linear ◽  
Realistic Representation ◽  
Linear System Identification ◽  
Stiffness Characteristics ◽  
Non Linear System

The objectives of this paper are essentially twofold. In the first case an experimental study of a number of shock absorbers is presented; the restoring force surface method of non-linear system identification is applied in order to determine the non-linear characteristics of the absorbers in an easily visualizable manner. In the second part, a new physical model for the absorber is presented which incorporates effects due to compressibility of the fluid in the absorber; this provides a more realistic representation of the stiffness characteristics than previous simple models. The new model is compared with the experimental data.

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