Review Evaluation of the dynamic properties of PVC foams under flexural vibrations Mustapha Assarar a,⇑ , Abderrahim El Mahi b , Jean-Marie Berthelot c a Université de Reims Champagne-Ardenne, GRESPI, EA 4301, IUT de Troyes, 9 rue de Québec 10026 Troyes Cedex, France b Université du Maine, LAUM, UMR CNRS No. 6613, Avenue Olivier Messiaen, 72085 Le Mans Cedex 9, France c ISMANS, Institute for Advanced Materials and Mechanics, 44 Avenue Bartholdi, 72000 Le Mans, France article info Article history: Available online 2 February 2012 Keywords: PVC foams Damping Finite element analysis Vibration testing abstract The paper presents an investigation of the damping of PVC foams under flexural vibrations of clamped- free beams. The PVC foams are constrained by two aluminium beams and different densities of the PVC foams are studied. An experimental investigation is implemented using an impulse technique. The nat- ural frequencies and the damping of the beams are modelled by using a finite element analysis based on the sandwich theory. Next, the numerical and experimental results are used to derive the shear mod- ulus and the damping of PVC foams as functions of the frequency. Finally, the experimental investigation and the developed modelling show how the damping of aluminium–foam beams must be corrected to estimate the damping of PVC foams. Ó 2012 Elsevier Ltd. All rights reserved. Contents 1. Introduction ........................................................................................................ 1919 2. Materials and tests ................................................................................................... 1921 2.1. Materials ..................................................................................................... 1921 2.2. Test specimens ................................................................................................ 1921 2.3. Determination of the dynamic properties of the test specimens ......................................................... 1921 3. Modelling the damping of aluminium/PVC foam/aluminium beams ........................................................... 1922 3.1. Stress field in aluminium–foam material ........................................................................... 1922 3.2. In-plane strain energy ........................................................................................... 1923 3.2.1. In-plane strain energy stored in the foam core ............................................................... 1923 3.2.2. In-plane strain energy stored in the aluminium beams ......................................................... 1924 3.2.3. Total in-plane strain energy stored in the test specimens ....................................................... 1925 3.3. Transverse shear strain energy .................................................................................... 1925 3.3.1. Transverse shear energy stored in the foam core .............................................................. 1925 3.3.2. Transverse shear energy stored in the aluminium beams ....................................................... 1925 3.3.3. Total transverse shear strain energy stored in the test specimens ................................................ 1925 3.4. Damping of the test specimens ................................................................................... 1926 4. Results and discussion ................................................................................................ 1926 4.1. Mode shapes and natural frequencies .............................................................................. 1926 4.2. Shear modulus of foams as a function of frequency ................................................................... 1926 4.3. Energies stored in the foam core and skins .......................................................................... 1927 4.4. Damping properties of aluminium ................................................................................. 1927 4.5. Damping properties of the foams.................................................................................. 1928 5. Conclusion ......................................................................................................... 1931 References ......................................................................................................... 1931 1. Introduction The vibration damping properties of foams make them extre- mely attractive in many applications, ranging from architectural 0263-8223/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2012.01.017 ⇑ Corresponding author. Tel.: +33 325 42 46 15; fax: +33 325 42 70 98. E-mail address: mustapha.assarar@univ-reims.fr (M. Assarar). Composite Structures 94 (2012) 1919–1931 Contents lists available at SciVerse ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct