The Galloping Response of a Two-Degree-of-Freedom System

1974 ◽  
Vol 41 (4) ◽  
pp. 1113-1118 ◽  
Author(s):  
R. D. Blevins ◽  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Natural Frequencies ◽  
Analytic Solutions ◽  
Degree Of Freedom ◽  
Approximate Analysis ◽  
Stability Criteria ◽  
Integer Multiple ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

The galloping response of a two-degree-of-freedom system is investigated using asymptotic techniques to generate approximate steady-state solutions. Simple closed-form analytic solutions and stability criteria are presented for the case where the two structural natural frequencies are harmonically separated. Examples of the nature of the galloping response of a particular section are presented for the case where the frequencies are harmonically separated as well as for the case where the two natural frequencies are near an integer multiple of each other. The results of the approximate analysis are compared with experimental and numerical results.

Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation

2014 ◽  
Vol 14 (04) ◽  
pp. 1450009 ◽  
Author(s):  
Andrew Yee Tak Leung ◽  
Hong Xiang Yang ◽  
Ping Zhu
Keyword(s):  
Steady State ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Homotopy Continuation ◽  
Response Curves ◽  
System A ◽  
Structural Responses ◽  
Voigt Model ◽  
Two Degree Of Freedom ◽  
Steady State Solutions

This paper is concerned with the steady state bifurcations of a harmonically excited two-member plane truss system. A two-degree-of-freedom Duffing system having nonlinear fractional derivatives is derived to govern the dynamic behaviors of the truss system. Viscoelastic properties are described by the fractional Kelvin–Voigt model based on the Caputo definition. The combined method of harmonic balance and polynomial homotopy continuation is adopted to obtain steady state solutions analytically. A parametric study is conducted with the help of amplitude-response curves. Despite its seeming simplicity, the mechanical system exhibits a wide variety of structural responses. The primary and sub-harmonic resonances and chaos are found in specific regions of system parameters. The dynamic snap-through phenomena are observed when the forcing amplitude exceeds some critical values. Moreover, it has been shown that, suppression of undesirable responses can be achieved via changing of viscosity of the system.

Effects of Chip Seizure on Steady State Motion of a Machine-Tool

2009 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Machine Tool ◽  
Systems Theory ◽  
Degree Of Freedom ◽  
Continuous Systems ◽  
Discontinuous Systems ◽  
Mechanical Analogy ◽  
Steady State Motion ◽  
Two Degree Of Freedom

The steady state motion of a machine-tool is numerically predicted with interaction of the chip/tool friction boundary. The chip/tool friction boundary is modeled via a discontinuous systems theory in effort to validate the passage of motion through such a boundary. The mechanical analogy of the machine-tool is shown and the continuous systems of such a model are governed by a linear two degree of freedom set of differential equations. The domains describing the span of the continuous systems are defined such that the discontinuous systems theory can be applied to this machine-tool analogy. Specifically, the numerical prediction of eccentricity amplitude and frequency attribute the chip seizure motion to the onset or route to unstable interrupted cutting.

Technical Note: A two-degree-of-freedom ambulance stretcher suspension: Part 3: Laboratory and road test performance

1998 ◽  
Vol 212 (5) ◽  
pp. 401-407 ◽  
Author(s):  
R. J. Henderson ◽  
J. K. Raine
Keyword(s):  
Test Performance ◽  
Natural Frequencies ◽  
Low Cost ◽  
Mechanical Systems ◽  
Technical Note ◽  
Suspension System ◽  
Degree Of Freedom ◽  
Road Test ◽  
Pneumatic Suspension ◽  
Two Degree Of Freedom

Parts 1 and 2 of this paper gave a design overview and described the dynamics of a prototype two-degree-of-freedom pneumatic suspension for an ambulance stretcher. This concluding part briefly reviews laboratory shaker table and ambulance road test performance of the suspension with passive pneumatic damping. The suspension system is found to offer compact low-cost isolation with lower natural frequencies than achieved in earlier mechanical systems.

Experimental Determination of the Complete Dynamical Properties of a Two-Degree-Of-Freedom Model Having Nearly Coincident Natural Frequencies

1967 ◽  
Vol 9 (5) ◽  
pp. 402-413 ◽  
Author(s):  
R. W. Traill-Nash ◽  
G. Long ◽  
C. M. Bailey
Keyword(s):  
Experimental Investigation ◽  
Experimental Determination ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Influence Coefficients ◽  
Stiffness Properties ◽  
Modes Of Vibration ◽  
Dynamical Properties ◽  
Two Degree Of Freedom

Existing techniques of resonance testing have shown a marked inability to find the principal modes, natural frequencies and levels of damping in a structure which possesses two or more close natural frequencies (1)§. This paper describes an experimental investigation on a two-degree-of-freedom model of a technique which makes use of dynamical influence coefficients (or receptances) measured at a number of stations on the structure (2) (3) (4) (5). The measured coefficients are used to calculate natural frequencies and modes of vibration, and the mass, damping and stiffness properties of the system. Several model configurations having different natural frequency separations were tested and no special difficulty resulted when natural frequencies were close or even coincident.

Hydrodynamics Loads on Two Degree-of-Freedom Cylinder With Uncertain Natural Frequencies Subject to VIV

2009 ◽  
Author(s):  
Didier Lucor
Keyword(s):  
Natural Frequencies ◽  
Numerical Study ◽  
Spectral Element ◽  
Numerical Approach ◽  
Response Surfaces ◽  
Degree Of Freedom ◽  
Two Dimensional ◽  
Wide Range ◽  
Two Dimensional Flow ◽  
Two Degree Of Freedom

In this numerical study, we build response surfaces of two degree-of-freedom vortex-induced vibrations (VIV) of flexibly mounted cylinders for a wide range of transverse and in-line natural frequencies. We consider both the structure and the flow to be two-dimensional and the structure has a low mass damping. The emphasis is put on the representation of the hydrodynamic loads acting on the cylinder in response to the change in the natural frequencies of the structure. The system is sampled for a wide range of natural frequencies within the synchronization region, totaling 149 two-dimensional flow-structure simulations. The parametric range of the in-line frequency is chosen to be larger than the one of the transverse frequency in order to favor multi-modal responses. No preferred frequencies are emphasized within the intervals of study. The fully spectral numerical approach relies on a stochastic collocation method coupled to a spectral element-based deterministic solver.

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