Linear and nonlinear damping identification in helicopter rotor systems

The dynamic torsional analysis of gear train systems has implemented many practical system designs. A computer analysis to predict the steady-state torsional response of a gear train system is presented in reference [1]. The current paper extends this work to the linear and nonlinear transient analysis of complex torsional gear train systems. Factors considered in the formulation are time-varying gear tooth stiffness, gear web rigidity, gear tooth backlash, shafts of nonuniform cross section, linear and nonlinear damping elements, multishock loadings, and complex-geared branched systems. For linear systems, the equations of transient motion are derived and closed-form solutions can be obtained by the state transition method [2]. For nonlinear systems, numerical methods are also presented. The method may be used as a means to analyze gear train start/stop operational problems, as well as constant speed response subject to internal and external disturbances.

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Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

Journal of Microelectromechanical Systems ◽

10.1109/jmems.2015.2411747 ◽

2015 ◽

Vol 24 (5) ◽

pp. 1462-1470 ◽

Cited By ~ 5

Author(s):

Zahra Nourmohammadi ◽

Sankha Mukherjee ◽

Surabhi Joshi ◽

Jun Song ◽

Srikar Vengallatore

Keyword(s):

Nonlinear Damping ◽

Atomistic Simulations ◽

Nanomechanical Resonators ◽

Linear And Nonlinear

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A Truncated Low Approach of Intrinsic Linear and Nonlinear Damping in Thin Structures

Journal of Vibration and Acoustics ◽

10.1115/1.2358153 ◽

2006 ◽

Vol 129 (1) ◽

pp. 32-38

Author(s):

Yves Gourinat ◽

Victorien Belloeil

Keyword(s):

Experimental Data ◽

Damping Ratio ◽

Vibrational Analysis ◽

Nonlinear Damping ◽

Thin Structures ◽

Adaptive Approach ◽

Equivalent Damping ◽

Linear And Nonlinear ◽

Algebraic Representations

An adaptive approach of vibrating thin structures is proposed here. The method consists in applying an equivalent adimensional damping ratio to each potential resonance. This ratio is deduced from experimental data obtained in vacuum facility, in relation with frequencies, for several structural technologies. Consequently, it is possible to calculate the structure in a linear nondissipative context, valid out of resonance bands, and truncated in those bands. Thus, the equivalent damping ratio is directly used to define adimensional resonance truncation bandwith and level. The contribution consists in tested and applied modal methodology and algebraic representations of damping including several dissipations—viscous and internal microfrictions—inducing a nonmonotonous model. The here aim is to provide realistic recommendations for simple vibrational analysis of aerospace thin structures—panels and stiffeners.

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Design and analysis trends of helicopter rotor systems

Sadhana ◽

10.1007/bf02812163 ◽

1994 ◽

Vol 19 (3) ◽

pp. 427-466 ◽

Cited By ~ 1

Author(s):

Inderjit Chopra

Keyword(s):

Helicopter Rotor ◽

Rotor Systems

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Hard-Spring Bistability and Effect of System Parameters in a Two-Degree-of-Freedom Vibration System with Damping Modeled by a Fractional Derivative

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416500784 ◽

2016 ◽

Vol 26 (05) ◽

pp. 1650078 ◽

Cited By ~ 2

Author(s):

Zhongjin Guo ◽

Wei Zhang

Keyword(s):

Steady State ◽

Fractional Derivative ◽

Numerical Integration ◽

Nonlinear Damping ◽

Homotopy Continuation ◽

Saddle Node Bifurcation ◽

Damping Coefficients ◽

Linear And Nonlinear ◽

Two Degree Of Freedom ◽

Derivative Order

The harmonic balance coupled with the continuation algorithm is a well-known technique to follow the periodic response of dynamical system when a control parameter is varied. However, deriving the algebraic system containing the Fourier coefficients can be a highly cumbersome procedure, therefore this paper introduces polynomial homotopy continuation technique to investigate the steady state bifurcation of a two-degree-of-freedom system including quadratic and cubic nonlinearities subjected to external and parametric excitation forces under a nonlinear absorber. The fractional derivative damping is considered to examine the effects of different fractional order, linear and nonlinear damping coefficients on the steady response. By means of polynomial homotopy continuation, all the possible steady state solutions are derived analytically, i.e. without numerical integration. Coexisting periodic solutions, saddle-node bifurcation and various effects of fractional damping on the steady state response are found and investigated. It is shown that the fractional derivative order and damping coefficient change the bifurcating curves qualitatively and eliminate the saddle-node bifurcation during resonance. Moreover, the system response depicts bigger and bigger region of hard-spring bistability with increasing fractional derivative order, but the region of hard-spring bistability of steady response becomes gradually small and then disappears when we increase the linear and nonlinear damping coefficients. In addition, the analytical results are verified by comparison with the numerical integration ones, it can be found that the present approximate resonance responses are in good agreement with numerical ones.

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