Frequency Response of Laminated Glass Elements: Analytical Modeling and Effective Thickness

Laminated glass elements are sandwich structures where the glass presents linear-elastic behavior, whereas the polymer interlayer is, in general, a linear-viscoelastic material. Several analytical models have been proposed since the 1950s to determine the response of laminated glass elements to both frequency and thermal conditions. In this paper, it is proved that Ross, Kerwin, and Ungar's model can be considered as a particular case of the Mead and Markus model when the exponential decay rate per unit length is neglected. The predictions of these models are compared with those obtained from operational modal tests carried out on a laminated glass beam at different temperatures. Finally, a new effective thickness for the dynamic behavior of laminated glass beams, which allows the determination of the dynamic response using a simple monolithic elastic model, is proposed.

[1]  D. J. Mead,et al.  Loss factors and resonant frequencies of encastré damped sandwich beams , 1970 .

[2]  J. R. McGraw,et al.  Vibratory Bending of Damped Laminated Plates , 1969 .

[3]  Ivelin V. Ivanov,et al.  Analysis, modelling, and optimization of laminated glasses as plane beam , 2006 .

[4]  Yao Koutsawa,et al.  Static and free vibration analysis of laminated glass beam on viscoelastic supports , 2007 .

[5]  Gianni Royer-Carfagni,et al.  Laminated beams with viscoelastic interlayer , 2012 .

[6]  N. Tschoegl.  The Phenomenological Theory of Linear Viscoelastic Behavior , 1989 .

[7]  J. Ferry.  Viscoelastic properties of polymers , 1961 .

[8]  L. Galuppi,et al.  The effective thickness of laminated glass plates , 2012 .

[9]  R. Ditaranto.  Theory of Vibratory Bending for Elastic and Viscoelastic Layered Finite-Length Beams , 1965 .

[10]  D. J. Mead,et al.  The measurement of the loss factors of beams and plates with constrained and unconstrained damping layers: A critical assessment , 2007 .

[11]  José Manuel Abete,et al.  Relaxation modulus—complex modulus interconversion for linear viscoelastic materials , 2013 .

[12]  Palle Andersen,et al.  Modal Identification from Ambient Responses using Frequency Domain Decomposition , 2000 .

[13]  Mehmet Zülfü Aşık,et al.  A mathematical model for the behavior of laminated glass beams , 2005 .

[14]  D.I.G. Jones.  REFLECTIONS ON DAMPING TECHNOLOGY AT THE END OF THE TWENTIETH CENTURY , 1996 .

[15]  R. Landel,et al.  The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids , 1955 .

[16]  Anand Jagota,et al.  Analysis of Glass/Polyvinyl Butyral Laminates Subjected to Uniform Pressure , 1999 .

[17]  É. Hermida,et al.  Scaling concept and the Williams-Landel-Ferry relationship , 1988 .

[18]  B. E. Douglas,et al.  On the forced vibrations of three-layer damped sandwich beams† , 1974 .

[19]  E. Kerwin.  Damping of Flexural Waves by a Constrained Viscoelastic Layer , 1959 .

[20]  B. C. Nakra,et al.  Vibrations of unsymmetrical sandwich beams and plates with viscoelastic cores , 1974 .

[21]  D. K. Rao,et al.  Frequency and Loss Factors of Sandwich Beams under Various Boundary Conditions , 1978 .

[22]  A. Fernández‐Canteli,et al.  Study of the interconversion between viscoelastic behaviour functions of PMMA , 2011 .

[23]  Anand Jagota,et al.  Fracture of Glass/Poly(vinyl butyral) (Butacite®) Laminates in Biaxial Flexure , 1999 .

[24]  L. Galuppi,et al.  Effective Thickness of Laminated Glass Beams.New expression via a variational approach. , 2012 .

[25]  D. J. Mead,et al.  The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions , 1969 .

[26]  S. W. Park,et al.  Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series , 1999 .

[27]  H. Scott Norville,et al.  Behavior and strength of laminated glass , 1998 .

[28]  David I. G. Jones.  Handbook of Viscoelastic Vibration Damping , 2001 .

[29]  J. E. Minor,et al.  Structural Behavior of Architectural Laminated Glass , 1993 .

[30]  W. T. Read,et al.  Stress Analysis for Compressible Viscoelastic Materials , 1950 .

[31]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[32]  J. Hooper,et al.  On the bending of architectural laminated glass , 1973 .