Abstract
Forced vibrations of moderately thick plates on two-parameter, Pasternak-type foundations are considered. Influence of plate shear and rotatory inertia are taken into account according to Mindlin. Excitations are of the force as well as of the support motion type. Formulation is in the frequency domain. An analogy to thin plates without foundations is given. This analogy to classical plate theory is complete in the case of polygonal plan-forms and hinged support conditions. In that case the higher order Mindlin-problem is reduced to two (second order) Helmholtz-Klein- Gordon boundary value problems. An advanced BEM using Green's functions of rectangular domains is applied to the latter, thereby satisfying boundary conditions exactly as far as possible. This problem oriented strategy provides the frequency response functions for the deflection of the undamped Mindlin plate with high numerical accuracy. Structural damping is built in subsequently, and Fast Fourier Transform is applied for calculation of the transient response.
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References
Altiero, N. J.; Sikarskie, D. L. (1978): A boundary integral method applied to plates of arbitrary plan form. Comput. Struct. 9, 163–168
Brebbia, C. A.; Telles, J. C. F.; Wrobel, L. C. (1984): Boundary element techniques. Berlin, Heidelberg, New York: Springer
Federhofer, K. (1935): Biegeschwingungen der in ihrer Mittelebene belasteten Kreisplatte. Ing. Arch. 6, 68–74
Heuer, R.; Irschik, H. (1987): A boundary element method for eigenvalue problems of polygonal membranes and plates. Acta Mech. 66, 9–20
Höllinger, F. (1983): Time-harmonic and nonstationary stochastic vibrations of arch dam-reservoir-systems. Acta Mech. 49, 153–167
Irschik, H. (1981): Zur Berechnung thermisch beanspruchter dünner linear elastischer Platten. Z. Angew. Math. Mech. 61, T97–99
Irschik, H. (1982): Eine Analogie zwischen Lösungen für schubstarre und schubelastische Platten. Z. Angew. Math. Mech. 62, T129–131
Irschik, H. (1983a): Ein Randintegralgleichungsverfahren für temperaturmomentbeanspruchte Platten. Ing. Arch. 53, 197–207
Irschik, H. (1983b): Erweiterung eines Randintegralgleichungsverfahrens auf Platten mit elastisch gelagerten Rändern. Z. Angew. Math. Mech. 63, T174–177
Irschik, H. (1984): A Boundary integral equation method for bending of orthotropic plates. Int. J. Solids Struct. 20, 244–255
Irschik, H. (1985): Membrane-type eigenmotions of Mindlin plates. Acta Mech. 55, 1–20
Irschik, H.; Heuer, R. (1988): Static and dynamic analysis of moderately thick plates on Pasternak foundation using classical plate theory. Proc. ICONMIG 88, Innsbruck, Austria. Numerical Methods in Geomechanics (Swoboda, G., ed). Rotterdam: Balkema
Irschik, H.; Ziegler, F. (1981): Application of the Green's function method to thin elastic polygonal plates. Acta Mech. 39, 155–169
Irschik, H.; Heuer, R.; Ziegler, F. (1987): BEM using Green's functions of rectangular domains: Static and dynamic problems of bending of plates. In: Boundary elements IX, Proc. BEM-Conf. Stuttgart 1987 (Brebbia, C. A.; Wendland, W. L.; Kuhn, G. eds.), vol. 2, pp. 35–49. Berlin, Heidelberg, New York: Springer
Irschik, H.; Heuer, R.; Ziegler, F. (1988): Free and forced vibrations of Mindlin plates by an advanced BEM. Proc. IUTAM-Conf. on Advanced Boundary Element Methods, 1987. Berlin, Heidelberg, New York: Springer
Marcus, M. (1924): Die Theorie elastischer Gewebe und ihre Anwendung auf die Berechnung biegsamer Platten. Berlin: Springer
Melnikov, YU. A. (1977): Some applications of the Green's function method in mechanics. Int. J. Solids Struct. 13, 1045–1058
Mindlin, R. D. (1951): Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. J. Appl. Mech. 18, 31–38
Reissner, E. (1985): Reflections on the theory of elastic plates. Appl. Mech. Rev. 38, 1453–1464
Vlasov, V. Z.; Leontèv, U. N. (1966): Beams, plates and shells on elastic foundations. Israel Progr. for Sci. Transl., Jerusalem
Ziegler, F. (1983): The elastic-viscoelastic correspondence in case of numerically determined discrete elastic response spectra. Z. Angew. Math. Mech. 63, T135–137
Ziegler, F. (1985): Technische Mechanik der festen und flüssigen Körper. Wien, New York: Springer
Ziegler, F.; Irschik, H.; Heuer, R. (1986): Nonstationary response of polygonally shaped membranes to random excitations. In: Crandall-Festschrift (Elishakoff, I.; Lyon, R. H. eds.), pp. 555–565. New York: Elsevier
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Irschik, H., Heuer, R. & Ziegler, F. Dynamic analysis of polygonal Mindlin plates on two-parameter foundations using classical plate theory and an advanced BEM. Computational Mechanics 4, 293–300 (1989). https://doi.org/10.1007/BF00301387
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DOI: https://doi.org/10.1007/BF00301387