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.

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.

Effects of Clearance on Normal Mode Frequencies of a Nonsmooth System

1999 ◽  
Author(s):  
Eric A. Butcher
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Nonsmooth System ◽  
Single Degree ◽  
Equivalent Linear ◽  
Frequency Relation

Abstract The effects of a clearance or interference on the normal mode frequencies of a two-dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation. First, the exact bilinear natural frequencies of a single degree-of-freedom system are analytically obtained in terms of the amount of clearance and the strength of nonlinearity, and an equivalent linear system is derived. These results are in turn used to construct three methods which approximate the bilinear frequencies for the 2-dof system in which the resulting approximate frequencies are compared with those obtained from numerical simulations. The results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance/interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation.

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.

Understanding Damping in Acoustic and Mechanical Systems

2014 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Linear System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Degree Of Freedom ◽  
Vibration Modes ◽  
Acoustic System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Modes Of Vibration ◽  
Straightforward Extension

A system with damping is much more difficult to model than an undamped system. In particular, the effect of damping on a multi-degree-of-freedom system is not a straightforward extension of the damping found in a single-degree-of-freedom system. The complications of a multi-degree-of-freedom system are first examined by investigating the acoustic modes of a pipe with energy leaking from the boundaries. This system can be modelled exactly and identifies the complexities that need to be understood. Although this is a linear system it is found that in contradistinction to an undamped system it cannot be separated into individual modes of vibration. Modes which bear some similarity to undamped modes can be found but these are always coupled by damping effects which, to add more complications, may involve some modes being active and supplying energy to other modes. The original acoustic system is simplified to systems of finite and eventually two-degrees-of-freedom in an effort to understand the effects of damping. It is found that when damping is added to a system some damping ratios may decrease moving the system into an unfavourable state. Overall some general properties of damping, for example, the constancy of average damping, are deduced.

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