Dynamic Stability of Fluttered Systems Subjected to Parametric Random Excitations

Abstract

A general solution for dynamic stability of the fluttered mode of damped, fluttered systems subjected to parametric random excitations is presented in this paper. First, the system equations are pairwisely uncoupled by a modal analysis based on normal modes of the system at the onset of fluttering. The stochastic averaging method is then applied to obtain Ito's equation governing the amplitude of the fluttered mode. Finally, the Lyapunov exponent of the fluttered mode is derived, from which the criterion for asymptotic sample stability of the mode is determined. A cantilevered beam acted upon by a static follower force and a white noise parametric excitation at the free end, and a skew panel subjected to an aerodynamic force in the chordwise direction and a white noise excitation in the spanwise direction are demonstrated as examples. Numerical results show that, although the static follower force or the aerodynamic force exceeds the flutter load, the fluttered mode of the beam or the panel may remain stable in the sense of asymptotic sample stability due to the presence of the white noise excitation.

Vibration control of an elastic strip by a singular force

“…Applying control theory to simpler models which use ordinary differential equations has been considered in a number of studies. The approximate ordinary differential equations have been obtained by finite element or RayleighRitz methods in a number of studies pertaining to control of flutter in aerospace structures and other vibration problems (Moon & Kim 2005;Frampton et al 1996;Döngi et al 1996;Forster & Yang 1998;Han et al 2006;Kwak & Heo 2007;Walker & Yaneske 1976;Bingham et al 2001;Young et al 2002;De Matteis et al 2008;Bos & Casagrande 2003;Bolotin et al 2001;Shen & Homaifar 2001;Ro & Baz 2002;Hurlebaus et al 2008) using piezoelectric actuators. (Benjeddou 2000;Sunar & Rao 1999) are surveys of piezoelectric control of flexible structures.…”

Parametric instability of delaminated composite plates subjected to periodic in-plane loading

“…Biswas et al (2011) examined the static and dynamic instability characteristics of curved laminates with internal damage subjected to follower loading. The dynamic stability of fluttered systems subjected to parametric random excitations were investigated by Young et al (2002) applying a stochastic averaging method. Recently Ruan et al (2012) studied the dynamic stability of functionally graded materials (FGM) skew plates subjected to tangential follower forces using Kirchoff's thin plate theory.…”

Controlling resonance frequencies of a rectangular plate by a discrete applied force

“…The overwhelming majority of work revolves around using piezoelectric actuators. The approximate ordinary differential equations have been obtained by finite element or Rayleigh‐Ritz methods in a number of studies pertaining to control of flutter in aerospace structures and other vibration problems (Moon and Kim, 2005; Frampton et al , 1996; Döngi et al , 1996; Forster and Yang, 1998; Han et al , 2006; Kwak and Heo, 2007; Walker and Yaneske, 1976; Bingham et al , 2001; Young et al , 2002; de Matteis et al , 2008; Bos and Casagrande, 2003; Luo et al , 2008a, b; Bolotin et al , 2001; Shen and Homaifar, 2001; Ro and Baz, 2002; Hurlebaus et al , 2008) using piezoelectric actuators. Benjeddou (2000) and Sunar and Rao (1999) are surveys of piezoelectric control of flexible structures.…”