Global plate vibration reduction using a periodic grid of vibration absorbers

This paper studies the potential of a periodic grid of vibration absorbers to achieve global plate vibration reduction. The global plate vibration reduction is pursued by applying the principles of resonance based stop bands. This principle is investigated both by infinite structure theory and by an example of a finite plate with a periodic grid of tuned resonators. Specific attention is paid to the effect of the level of damping in the tuned resonators. The tuned resonators are shown to have a strong effect on the plate vibrations in the frequency region corresponding to the resonance frequency of the resonators. Furthermore, it is shown that the damping in the resonators leads to a wider stop band at the cost of the level of vibration reduction inside the stop band. A guideline for the required number of resonators to achieve global plate vibration reduction is derived based on the finding that the distance between the tuned resonators should be smaller than half a wavelength.

[1]  Ping Sheng,et al.  Classical wave localization and spectral gap materials , 2005 .

[2]  Anthony M. Waas,et al.  Analysis of wave propagation in a thin composite cylinder with periodic axial and ring stiffeners using periodic structure theory , 2010 .

[3]  Bert Pluymers,et al.  A wave based prediction technique for the dynamic response analysis of plates with random point mass distributions , 2008 .

[4]  Wim Desmet,et al.  An efficient wave based prediction technique for plate bending vibrations , 2007 .

[5]  Robin S. Langley,et al.  A note on the force boundary conditions for two-dimensional periodic structures with corner freedoms , 1993 .

[6]  L. Brillouin,et al.  Wave Propagation in Periodic Structures , 1946 .

[7]  D. M. Mead,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES: RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON, 1964–1995 , 1996 .

[8]  C. Kittel.  Introduction to solid state physics , 1954 .

[9]  W. Desmet.  A wave based prediction technique for coupled vibro-acoustic analysis , 1998 .

[10]  A. Diaz,et al.  Design of bandgap grid structures , 2004 .

[11]  D. J. Mead.  A general theory of harmonic wave propagation in linear periodic systems with multiple coupling , 1973 .

[12]  Gengkai Hu,et al.  Wave propagation characterization and design of two-dimensional elastic chiral metacomposite , 2011 .

[13]  Steven J. Cox,et al.  Maximizing Band Gaps in Two-Dimensional Photonic Crystals , 1999, SIAM J. Appl. Math..

[14]  Bert Pluymers,et al.  On the use of a Wave Based prediction technique for steady-state structural-acoustic radiation analysis , 2003 .

[15]  Gang Wang,et al.  Two-dimensional locally resonant phononic crystals with binary structures. , 2004, Physical review letters.

[16]  M D.J.,et al.  WAVE PROPAGATION IN CONTINUOUS PERIODIC STRUCTURES : RESEARCH CONTRIBUTIONS FROM SOUTHAMPTON , 1964 – 1995 , 2022 .

[17]  José Sánchez-Dehesa,et al.  Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials , 2003 .

[18]  Yong Li,et al.  A sonic band gap based on the locally resonant phononic plates with stubs , 2010 .

[19]  Wim Desmet,et al.  A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions , 2010 .

[20]  A. Haddow,et al.  Design of band-gap grid structures , 2005 .

[21]  Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[22]  Karel Vergote.  Dynamic Analysis of Structural Components in the Mid Frequency Range using the Wave Based Method: Non-Determinism and Inhomogeneities (Dynamische analyse van constructiecomponenten in het middenfrequentiebereik met behulp van de golfgebaseerde methode: niet-determinisme en inhomogeniteiten) , 2012 .

[23]  Sergey Sorokin,et al.  Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading , 2004 .

[24]  Bhisham Sharma,et al.  Dynamic behaviour of sandwich structure containing spring-mass resonators , 2011 .

[25]  F. Bloch.  Über die Quantenmechanik der Elektronen in Kristallgittern , 1929 .

[26]  Wim Desmet,et al.  ON THE POTENTIAL OF LOCAL RESONATORS TO OBTAIN LOW-FREQUENCY BAND GAPS IN PERIODIC LIGHTWEIGHT STRUCTURES , 2011 .