Approximate Min-Max Equivalent Linearization

1971 ◽  
Vol 38 (4) ◽  
pp. 1070-1073
Author(s):  
R. E. Jonckheere
Keyword(s):  
Analytical Approach ◽  
Autonomous Systems ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Single Degree Of Freedom ◽  
Single Degree

A new analytical approach to approximate min-max equivalent linearization is presented for symmetrical autonomous systems with a single degree of freedom. It also serves as a foundation for previously suggested min-max methods.

Linearization Equations for Vibration Induced by Oscillatory Flow

1979 ◽  
Vol 46 (4) ◽  
pp. 946-948 ◽  
Author(s):  
P-T. D. Spanos ◽  
T. W. Chen
Keyword(s):  
Linear System ◽  
Oscillatory Flow ◽  
Degree Of Freedom ◽  
Approximate Determination ◽  
Equivalent Linearization ◽  
Mean Velocity ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonzero Mean

Equations are presented for the approximate determination through equivalent linearization of the response of a single-degree-of-freedom linear system to excitation induced by oscillatory flow with nonzero mean velocity. The reliability of the proposed methodology is examined.

Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

Design Tool for Base-Isolated Structures Modeled as Single-Degree-of-Freedom Oscillators

1997 ◽  
Vol 50 (11S) ◽  
pp. S125-S132
Author(s):  
Gustavo O. Maldonado
Keyword(s):  
Response Spectrum ◽  
Time History ◽  
Design Tool ◽  
Degree Of Freedom ◽  
Iteration Step ◽  
Complex Conjugate ◽  
Equivalent Linearization ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Isolated Structures

A stochastic equivalent linearization technique combined with a ground response spectrum approach is proposed to approximate the inelastic response of base-isolated structures. These structures are modeled by nonlinear oscillators with a single degree of freedom. The main advantage of the proposed methodology is the fast calculation of approximate results in comparison with the slow, but more accurate time history analyses. The Bouc-Wen constitutive model is used to represent the inelastic behavior of the isolators. The equations of motion are linearized by an iterative stochastic technique involving the a-priori unknown response statistics. At each iteration step, the modal contributions from one real and one pair of complex conjugate modes are combined by a response spectrum approach to obtain the maximum responses of interest. The process requires the use of conventional spectra (pseudo-acceleration and relative velocity) as well as the relative displacement spectrum of a massless oscillator. Floor response spectrum results above the isolators are calculated by the proposed approach and are compared against the results obtained by a simulation involving time history analyses.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait
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