LOCALIZATION OF WAVE PROPAGATION IN DISORDERED PERIODIC STRUCTURES

A structure designed to be spatially periodic in its configuration cannot be exactly periodic due to material, geometric, and manufacturing variabilities. Such variabilities are random, and their presence (often referred to as disorder) can reduce the ability of the structure to transmit waves from one location to another. The phenomenon is known as vibration confinement or localization. A new perturbation scheme is developed in this paper on the basis of probability theory to calculate the average exponential decay rate of wave transmission with respect to the distance of transmission, called the localization factor. Account is also taken of structural damping. The new scheme permits successive improvement of accuracy, making it applicable to either weak, strong, or moderate localization. Moreover, the analysis is based on a generic periodic structure; thus, it is not restricted to a specific set of governing equations. These are achieved by taking into account reflections from nearby disordered cell-units successively and substituting the ensemble average for the sequential average of certain statistical properties of the cell units on the basis of spatial ergodicity. Application of the method is illustrated by an example, and the results are compared with Monte Carlo simulations.

[1]  J. N. Yang,et al.  Free Vibration of a Disordered Periodic Beam , 1974 .

[2]  Y. K. Lin,et al.  Statistical Distribution of Frequency Response in Disordered Periodic Structures , 1992 .

[3]  D. J. Mead.  Wave propagation and natural modes in periodic systems: I. Mono-coupled systems , 1975 .

[4]  Y. K. Lin,et al.  Free vibrations of a continuous beam on elastic supports , 1962 .

[5]  Y. K. Lin,et al.  Dynamics of Beam-Type Periodic Structures , 1969 .

[6]  T. T. Soong,et al.  On the impulsive admittance and frequency response of a disordered linear chain of N degrees of freedom , 1964 .

[7]  Effects of random fluctuations in ply mechanical properties on ultrasound propagation in a laminated solid layer , 1992 .

[8]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[9]  D. J. Mead.  Free wave propagation in periodically supported, infinite beams , 1970 .

[10]  H. Furstenberg.  Noncommuting random products , 1963 .

[11]  Y. K. Lin,et al.  Propagation of decaying waves in periodic and piecewise periodic structures of finite length , 1989 .

[12]  J. Woodhouse,et al.  Confinement of vibration by structural irregularity , 1981 .

[13]  Glen James Kissel,et al.  Localization in disordered periodic structures , 1988 .

[14]  J. Woodhouse,et al.  Vibration isolation from irregularity in a nearly periodic structure: Theory and measurements , 1983 .

[15]  C. Pierre.  Weak and strong vibration localization in disordered structures: A statistical investigation , 1990 .

[16]  T. T. Soong,et al.  On the natural frequencies of a disordered linear chain of N degrees of freedom , 1963 .

[17]  J. N. Yang,et al.  Frequency response functions of a disordered periodic beam , 1975 .