A dynamic homogenization model for long-wavelength wave propagation in corrugated sandwich plates

Abstract In the present work, a new dynamic homogenization model is developed to investigate the long-wavelength wave propagation in a corrugated sandwich plate. With the harmonic motion assumption and using a shifting operator, the governing equations of the plate are firstly represented in a state-space form. Then, a dynamic homogenization model is developed via the two-scale homogenization method. Based on this model and considering the propagation of sinusoidal waves, the dispersion relations and corresponding wave modes can be easily obtained. In order to validate the developed homogenization model, the obtained dispersion relations are compared with those predicted by the spectral element method. It is found that the present method gives accurate results in low frequency range. Furthermore, the effects of some geometric and material parameters on the dispersion relations for the corrugated sandwich plate are also discussed. The developed homogenization model is expected to be helpful in the prediction and control of dynamic responses of corrugated or even lattice sandwich structures.

[1]  V. Rubino,et al.  The three-point bending of Y-frame and corrugated core sandwich beams , 2010 .

[2]  Chun H. Wang,et al.  Improving the bending strength and energy absorption of corrugated sandwich composite structure , 2013 .

[3]  E. Hinton,et al.  A review of homogenization and topology optimization III—topology optimization using optimality criteria , 1998 .

[4]  N. Jacques,et al.  Modelling of micro-inertia effects in closed-cell foams with application to acoustic and shock wave propagation , 2016 .

[5]  I. D. Abrahams,et al.  Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves. , 2006 .

[6]  Dieter Weichert,et al.  Higher order asymptotic homogenization and wave propagation in periodic composite materials , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Li Ma,et al.  Mechanical properties and failure mechanisms of sandwich panels with ultra-lightweight three-dimensional hierarchical lattice cores , 2018 .

[8]  Li Ma,et al.  Fabrication and crushing behavior of low density carbon fiber composite pyramidal truss structures , 2010 .

[9]  Li Ma,et al.  Modal response of all-composite corrugated sandwich cylindrical shells , 2015 .

[10]  Yi-Ze Wang,et al.  Vibration band gap behaviors of sandwich panels with corrugated cores , 2013 .

[11]  Hyun Gyu Kim,et al.  An equivalent plate model for corrugated-core sandwich panels , 2015 .

[12]  Li Ma,et al.  Free vibration analysis of simply supported sandwich beams with lattice truss core , 2012 .

[13]  Tong Hui,et al.  A nonlocal homogenization model for wave dispersion in dissipative composite materials , 2013 .

[14]  Paul D. Wilcox,et al.  Ultrasonic arrays for non-destructive evaluation: A review , 2006 .

[15]  Z. Ayub,et al.  Experimental investigation of single phase convective heat transfer coefficient in a corrugated plate heat exchanger for multiple plate configurations , 2010 .

[16]  Massimo Ruzzene,et al.  Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos , 2011 .

[17]  Damiano Pasini,et al.  Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods , 2013 .

[18]  S. Rokhlin,et al.  Floquet wave homogenization of periodic anisotropic media. , 2002, The Journal of the Acoustical Society of America.

[19]  C. Jianchun,et al.  Homogenization of Two-Dimensional Phononic Crystals at Low Frequencies , 2005 .

[20]  N. Fleck,et al.  Collapse of truss core sandwich beams in 3-point bending , 2001 .

[21]  Tao Zeng,et al.  Mechanical response of carbon/epoxy composite sandwich structures with three-dimensional corrugated cores , 2018 .

[22]  J. Fish,et al.  A Dispersive Model for Wave Propagation in Periodic Heterogeneous Media Based on Homogenization With Multiple Spatial and Temporal Scales , 2001 .

[23]  Lin-zhi Wu,et al.  Low-velocity impact characteristics and residual tensile strength of carbon fiber composite lattice core sandwich structures , 2011 .

[24]  Bogdan Vernescu,et al.  Homogenization methods for multiscale mechanics , 2010 .

[25]  R. M. Manglik,et al.  Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels , 2004 .

[26]  S. Wu.  Classical solutions of forced vibration of rod and beam driven by displacement boundary conditions , 2005 .

[27]  O. Oleinik.  On homogenization problems , 1984 .

[28]  Chuanzeng Zhang,et al.  Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm , 2014 .

[29]  C. Sun,et al.  Modeling micro-inertia in heterogeneous materials under dynamic loading , 2002 .

[30]  Osamu Matsuda,et al.  Complex band structures of two dimensional phononic crystals: Analysis by the finite element method , 2013 .

[31]  Bo Wang,et al.  Honeycomb–corrugation hybrid as a novel sandwich core for significantly enhanced compressive performance , 2016 .

[32]  Li Ma,et al.  Mechanical behavior of the sandwich structures with carbon fiber-reinforced pyramidal lattice truss core , 2010 .

[33]  Ying Liu,et al.  The plastic behavior of sandwich beams with core gradation , 2017 .

[34]  Vikram Deshpande,et al.  Hierarchical Corrugated Core Sandwich Panel Concepts , 2007 .

[35]  H. W. Lv,et al.  Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam , 2018 .

[36]  I. Andrianov,et al.  Dynamic homogenization and wave propagation in a nonlinear 1D composite material , 2013 .

[37]  V. K. Nema,et al.  Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger , 2012 .

[38]  Lin-zhi Wu,et al.  Experimental investigation of 3D sandwich structure with core reinforced by composite columns , 2010 .

[39]  E. Magnucka-Blandzi,et al.  Experimental and numerical investigations of five-layered trapezoidal beams , 2016 .

[40]  O. Poncelet,et al.  Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates , 2005 .