Summary
The objective of the present paper is to analyze the dynamic flexural behavior of elastic two-layer beams with interlayer slip. The Bernoulli-Euler hypothesis is assumed to hold for each layer separately, and a linear constitutive equation between the horizontal slip and the interlaminar shear force is considered. The governing sixth-order initial-boundary value problem is solved by separating the dynamic response in a quasistatic and in a complementary dynamic response. The quasistatic portion that may also contain singularities or discontinuities due to sudden load changes is determined in a closed form. The remaining complementary dynamic part is non-singular and can be approximated by a truncated modal series of fast accelerated convergence. The solution of the resulting generalized decoupled single-degree-of-freedom oscillators is given by means of Duhamel,s convolution integral, whereby the velocity and acceleration of the loads are the driving terms. Light damping is considered via modal damping coefficients. The proposed procedure is illustrated for dynamically loaded layered single-span beams with interlayer slip, and the improvement in comparison to the classical modal analysis is demonstrated.
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Vinson, J. R., Sierakowski, R. I.: The behavior of structures composed of composite materials. Amsterdam: Martinus Nijhoff 1987.
Reddy, J. N.: An evaluation of equivalent-single-layer and layerwise theories of composite laminates. Comp. Struct.26, 21–35 (1993).
Yu, Y.-Y.: A new theory of elastic sandwich plates-one-dimensional case. J. Appl. Mech.26, 415–421 (1959).
Swift, G. W., Heller, R. A.: Layered beam analysis. J. Eng. Mech. Div., ASCE100, 267–282 (1974).
Heuer, R.: Static and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy. Acta Mech.91, 1–9 (1992).
Whitney, J. M., Pagano, N. J.: Shear deformation in heterogeneous anisotropic plates. J. Appl. Mech.37, 1031–1036 (1970).
Reddy, J. N.: A simple higher-order theory for laminated composite plates. J. Appl. Mech.51, 745–752 (1984).
Homberg, H.: Brücke mit elastischem Verbund zwischen Stahlhauptträger und der Betonfahrbahntafel. Bauingenieur27, 213–216 (1952).
Hoischen, A.: Verbundträger mit elastischer und unterbrochener Verdübelung. Bauingenieur29, 241–244 (1954).
Pischl, R.: Ein Beitrag zur Berechnung hölzener Biegeträger. Bauingenieur43, 448–451 (1968).
Goodman, J. R., Popov, E. P.: Layered beam systems with interlayer slip. J. Struct. Div., ASCE94, 2535–2547 (1968).
Girhammar, U. A., Gopu, V. K. A.: Composite beam — columns with interlayer slip-exact analysis. J. Struct. Eng.119, 1265–1282 (1993).
Mistakis, E. S., Thomopoulos, K., Avdelas, A., Panagiotopoulos, P. D.: On the nonmonotone slip effect in the shear connectors of composite beams. Int. J. Eng. Anal. Des.1, 395–409 (1994).
Girhammar, U. A., Pan, D.: Dynamic analysis of composite members with interlayer slip. Int. J. Solids Struct.30, 797–823 (1993).
Boley, B. A., Barber, A. D.: Dynamic response of beams and plates to rapid heating. J. Appl. Mech.24, 413–416 (1957).
Ziegler, F., Irschik, H.: Dynamic analysis of elastic plastic beams by means of thermoelastic solutions. Int. J. Solids Struct.21, 819–829 (1985).
Fotiu, P. A., Irschik, H., Ziegler, F.: Modal analysis of elastic-plastic plate vibrations by integral equations. EABE14, 81–97 (1994).
Adam, C., Ziegler, F.: Forced flexural vibrations of elastic-plastic composite beams with thick layers. Comp. Part B28B, 201–213 (1997).
Irschik, H., Ziegler, F.: Dynamics of linear elastic structures with selfstress: a unified treatment for linear and nonlinear problems. ZAMM68, 199–205 (1988).
Ziegler, F.: Developments in structural dynamic viscoplasticity including ductile damage. ZAMM72, T5-T15 (1992).
Irschik, H., Ziegler, F.: Dynamic processes in structural thermo-viscoplasticity. AMR48, 301–316 (1995).
Jeschko, A.: Biegeschwingungen zweischichtiger elastischer Balken mit nachgiebigem Verbund — ein analytisches Lösungsverfahren. Master's Thesis, Technical University of Vienna, Dept. of Civil Eng., Vienna 1996.
Weaver, W., Timoshenko, S., Young, D. H.: Vibration problems in engineering, 5th ed. New York: Wiley 1990.
Clough, R. W., Penzien, J.: Dynamics of structures, 2th ed. New York: McGraw-Hill 1993.
Ziegler, F.: Mechanics of solids and fluids, 2nd ed. New York: Springer 1995.
Holl, H. J.: Ein effizienter Algorithmus für nichtlineare Probleme der Strukturdynamik mit Anwendung in der Rotordynamik. Doctoral Thesis, University of Linz, Linz 1995.
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Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday
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Adam, C., Heuer, R. & Jeschko, A. Flexural vibrations of elastic composite beams with interlayer slip. Acta Mechanica 125, 17–30 (1997). https://doi.org/10.1007/BF01177296
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DOI: https://doi.org/10.1007/BF01177296