A New 2D Local Vibrational Model for Unidirectional Clamped—Clamped Sandwich Structure with Edge Stiffeners

Abstract

Flexural vibration of a clamped—clamped, three-layer, one-span sandwich, unidirectional structure composed of isotropic layers is considered in the article. A new single series model of the 2D problem, obtained within the local theory of linear elastodynamics, is presented. Very realistic boundary conditions at edges of the structure, which correspond to the engineering solution with the edge stiffeners, are introduced and satisfied. Eight eigenfrequencies of the structure for two sets of input data are calculated, according to the new model, and compared with numerical and experimental results existing in the literature. A detail comparative analysis of the results is done and some conclusions are presented.

Keywords

flexural vibration eigenfrequencies sandwich beam edge stiffeners 2D local model linear elastodynamics single series expansion.

Get full access to this article

View all access options for this article.

References

Frostig, Y. and Baruch, M. ( 1994). Free Vibrations of Sandwich Beams with a Transversely Flexible Core: a High Order Approach, Journal of Sound and Vibration, 176(2): 195-208.

Fasana, A. and Marchesiello, S. ( 2001). Rayleigh-Ritz Analysis of Sandwich Beams, Journal of Sound and Vibration, 241(4): 643-652.

Kapuria, S. , Dumir, P.C. and Jain, N.K. ( 2004). Assessment of Zigzag Theory for Static Loading, Buckling, Free and Forced Response of Composite and Sandwich Beams , Composite Structures, 64: 317-327.

Frostig, Y. and Thomsen, O.T. ( 2004). High-order Vibration of Sandwich Panels with a Flexible Core, International Journal of Solids and Structures, 41: 1697-1724.

Backstrom, D. and Nilsson, A. (2006). Modeling Flexural Vibration of a Sandwich Beam Using Modified Fourth-order Theory, Journal of Sandwich Structures and Materials, 8: 465-476.

Backstrom, D. and Nilsson, A. (2007). Modeling the Vibration of Sandwich Beams Using Frequency-dependent Parameters, Journal of Sound and Vibration, 300: 589-611.

Hu, H. , Belouettar, S. , Daya, El.M. and Potier-Ferry, M. ( 2006). Evaluation of Kinematic Formulations for Viscoelastically Damped Sandwich Beam Modeling, Journal of Sandwich Structures and Materials, 8: 477-495.

Hu, H. , Belouettar, S. , Potier-Ferry, M. and Daya, E. l.M. (2008). Review and Assessment of Various Theories for Modeling Sandwich Composites, Composite Structures, 84: 282-292.

Wu, Z. and Chen, W. ( 2007). An Assessement of Several Displacement-based Theories for the Vibration. and Stability Analysis of Laminate Composite and Sandwich Beams, Composite Structures, 84: 337-349.

10.

Raville, M.E. , Ueng, E.S. and Lei, M.M. (1961). Natural Frequencies of Vibrations of Fixed-fixed Sandwich Beams, ASME Journal of Applied Mechanics, 28: 367-371.

11.

Sakiyama, T. , Matsuda, H. and Morita, C. ( 1996). Free Vibration Analysis of Continuous Sandwich Beams with Elastic or Viscoelastic Cores by Applying the Discrete Green Function , Journal of Sound and Vibration, 198: 439-454.

12.

Nilsson, E. and Nilsson, A.C. ( 2002). Prediction and Measurement of Some Dynamic Properties of Sandwich Structures with Honeycomb and Foam Cores, Journal of Sound and Vibration, 251(3): 409-430.

13.

Sokolinsky, V.S. and Nutt, S.R. (2002). Boundary Condition Effects in Free Vibrations of Higher-order Soft Sandwich Beams, AIAA Journal, 40: 1220-1227.

14.

Howson, W.P. and Zare, A. (2005). Exact Dynamic Stiffness Matrix for Flexural Vibration of Three-layered Sandwich Beams, Journal of Sound and Vibration, 282: 753-767.

15.

Karczmarzyk, S. (2005). An Effective 2D Linear Elasticity Vibrational Model for Layered and Sandwich Clamped-clamped Unidirectional Strips, In: Thomsen, O.T , Bozhevolnaya, E. and Lyckegaard, A. (eds), Proceedings of the 7th International Conference on Sandwich Structures, Vol. 2, Springer, Aalborg University, pp. 577-586.

16.

Karczmarzyk, S. (1996). An Exact Elastodynamic Solution to Vibration Problems of a Composite Structure in the Plane Stress State, Journal of Sound and Vibration, 196(1): 85-96.

17.

Karczmarzyk, S. (1999). An Analytic Model of Flexural Vibrations and the Static Bending of Plane Viscoelastic Composite Structures, Scientific Works, Mechanics Series, Vol. 172, Publishing House of the Warsaw University of Technology, Warsaw.

18.

Karczmarzyk, S. (2004). New 2D Approach and Solution to the Static Transverse Bending Problem for a Sandwich Strip with Realistic Clampings of the Edges, Journal of Sandwich Structures and Materials, 6: 7-45.

19.

Karczmarzyk, S. , Meyer-Piening, H.-R. and Caviezel , M. (2003). Numerical and Experimental Analysis of the Influence of Edge Conditions on the Deflection of a Clamped-clamped Asymmetric Sandwich Strip, Journal of Sandwich Structures and Materials, 5: 119-145.

20.

Bert, C.W. , Wilkins Jr, D.J. and Crisman, W.C. ( 1967). Damping in Sandwich Beams with Shear-flexible Cores, Journal of Engineering for Industry, 89: 662-670.