Random dynamics of structures with gaps: Simulation and spectral linearization

This paper deals with the prediction of the response of strutures with gaps excited by a white noise. This model is frequently introduced for practical analysis of dynamic systems such as pipings having a clearance into the supporting device, mechanical equipments subjected to impact disturbance with the basements, and so on. It is impliccitly assumed throughout that the systems have been discretized, so that its motion can be represented in terms of a finlte number of coordinates. Some DOF will be subjected to limitations represented by a hard spring without damping.The first section deals with the numerical aspects of the problem. Two classical algorithms for MDOF systems are considered: the pseudo-static formulation, and the modal decomposition, Comparison of the results leads to the selection of the more effective method.In the second section some limitations of the statistical linearization method are established and a new linearization method based upon an ARMA representation of the response is proposed. The main point is in the relation between the coefficients of the ARMA model and the parameters of the system which is studied in this paper.The third section is the core of the paper. It presents a method for identifying a linear structure whose displacement response is close to the response of the lumped structure with gaps in terms of power spectra. Results are illustrated by some examples on MDOF oscillators. Only cases with a single excitation (corresponding to scismic analysis) are considered.

[1]  Thomas J. R. Hughes,et al.  Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics , 1976 .

[2]  Pierre Bernard.  Methodes mathematiques d'etude des vibrations aleatoires et analyse sur les espaces gaussiens , 1990 .

[3]  P. Whittle,et al.  Estimation and information in stationary time series , 1953 .

[4]  Edward L. Wilson,et al.  Numerical methods in finite element analysis , 1976 .

[5]  H. Akaike.  Markovian Representation of Stochastic Processes by Canonical Variables , 1975 .

[6]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[7]  I. Elishakoff,et al.  Probabilistic Methods in the Theory of Structures , 1984 .

[8]  Anant R. Kukreti,et al.  Dynamic response analysis of nonlinear structural systems subject to component changes , 1984 .

[9]  Thomas Kailath,et al.  Linear Systems , 1980 .

[10]  Hiroe Kobayashi,et al.  Dynamic response of piping system on rack structure with gaps and frictions , 1989 .

[11]  T. K. Caughey,et al.  On the response of non-linear oscillators to stochastic excitation , 1986 .

[12]  Frank Kozin,et al.  Structural parameter identification techniques , 1988 .

[13]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[14]  André Preumont.  Frequency domain analysis of time integration operators , 1982 .

[15]  A. Kiureghian,et al.  Methods of stochastic structural dynamics , 1986 .

[16]  Christian Soize,et al.  Mathematics of random phenomena , 1986 .

[17]  Thomas J. R. Hughes,et al.  Implicit-explicit finite elements in nonlinear transient analysis , 1979 .

[18]  A. J. Hartmann,et al.  Nonlinear Dynamic Analysis of a Structure Subjected to Multiple Support Motions , 1981 .

[19]  M. J. Pettigrew,et al.  Vibration damping of heat exchangertubes in liquids: Effects of support parameters , 1988 .

[20]  W. Rudin.  Real and complex analysis , 1968 .

[21]  Paul C. Jennings,et al.  Digital calculation of response spectra from strong-motion earthquake records , 1969 .

[22]  Howard I. Epstein,et al.  An experimental-modal computational technique to find dynamic stresses , 1986 .

[23]  T. Caughey.  Nonlinear Theory of Random Vibrations , 1971 .

[24]  Mustapha Taazount.  Etude dynamique des structures a chocs sous sollicitations aleatoires , 1991 .

[25]  Christian Soize,et al.  Steady state solution of Fokker-Planck equation in higher dimension , 1988 .

[26]  Thomas K. Caughey,et al.  Derivation and Application of the Fokker-Planck Equation to Discrete Nonlinear Dynamic Systems Subjected to White Random Excitation , 1963 .