An Energetic Criterion for Dynamic Instability of Structures Under Arbitrary Excitations

An energetic criterion for identifying the global dynamic instability of structures subjected to any kind of excitations is proposed in the paper. The concept of dynamic stability for structures is firstly interpreted and distinguished from the stability concept in the Lyapunov sense. It is demonstrated that the dynamic instability depends not only on the properties of the structure, but also relates to the change of external excitations on the structure, which distinguishes the essence of dynamic instability from the pseudo static stiffness criterion. This background leads to a novel energetic criterion with which the first passage of the variation of intrinsic energy over the input energy manifests the dynamic instability of structures. The proposed criterion has been extensively tested and verified in the numerical examples, with its advantages clearly illustrated.

[1]  Eric B. Williamson,et al.  Dynamic stability of structural systems subjected to base excitation , 1998 .

[2]  R. Batra,et al.  Dynamic buckling of thin thermoviscoplastic cylindrical shell under radial impulsive loading , 2006 .

[3]  P. Nawrotzki,et al.  Numerical stability analysis in structural dynamics , 2000 .

[4]  A. Teter.  Dynamic critical load based on different stability criteria for coupled buckling of columns with stiffened open cross-sections , 2011 .

[5]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories , 2010 .

[6]  Thomas Most,et al.  Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading , 2004 .

[7]  S. K. Sahu,et al.  PARAMETRIC RESONANCE CHARACTERISTICS OF ANGLE-PLY TWISTED CURVED PANELS , 2008 .

[8]  Z. Bažant,et al.  Stability Of Structures , 1991 .

[9]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[10]  Udo Peil,et al.  Numerical Analysis of Dynamic Stability of Elastic Truss Structures , 1998 .

[11]  Ichiro Ario,et al.  Homoclinic bifurcation and chaos attractor in elastic two-bar truss , 2004 .

[12]  P. K. Datta,et al.  PARAMETRIC COMBINATION RESONANCE CHARACTERISTICS OF DOUBLY CURVED PANELS SUBJECTED TO NON-UNIFORM HARMONIC EDGE LOADING , 2005 .

[13]  J. Hutchinson,et al.  An introduction to the elastic stability of structures , 1976 .

[14]  Wei-Ren Chen,et al.  DYNAMIC STABILITY CHARACTERISTICS OF FUNCTIONALLY GRADED PLATES UNDER ARBITRARY PERIODIC LOADS , 2013 .

[15]  M. A. Bradford,et al.  ENERGY APPROACH FOR DYNAMIC BUCKLING OF AN UNDAMPED ARCH MODEL UNDER STEP LOADING WITH INFINITE DURATION , 2010 .

[16]  C. Q. Ru,et al.  AN ENERGY CRITERION FOR THE DYNAMIC PLASTIC BUCKLING OF CIRCULAR CYLINDERS UNDER IMPULSIVE LOADING , 1985 .

[17]  Marcelo A. Savi,et al.  Nonlinear dynamics and chaos in a pseudoelastic two-bar truss , 2010 .

[18]  Carmelo E. Majorana,et al.  Dynamic stability of elastic structures: a finite element approach , 1998 .

[19]  C. Hsu,et al.  Stability of Shallow Arches Against Snap-Through Under Timewise Step Loads , 1968 .

[20]  J. L. Meek,et al.  A REVIEW OF THE INSTABILITY PROBLEM FOR FRAME STRUCTURES , 2001 .

[22]  Cheng-Wu Chen,et al.  Stability analysis of an oceanic structure using the Lyapunov method , 2010 .

[23]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[24]  J. Thompson,et al.  Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists , 1986 .

[25]  Feng Fan,et al.  Elasto-plastic instability of single-layer reticulated shells under dynamic actions , 2010 .

[26]  Liqun Chen,et al.  BIFURCATIONS AND CHAOS OF AN AXIALLY MOVING PLATE UNDER EXTERNAL AND PARAMETRIC EXCITATIONS , 2012 .

[27]  Charles McSween Blackmon,et al.  Dynamic snap-through buckling of eccentrically stiffened shallow spherical caps , 1969 .