The problem of the aperiodic vibration of a thick non-prismatic circular plate resting on an inertial elastic half-space

• Autorzy: Ruta P.
• Języki publikacji: EN

Abstrakty

EN

The problem of the vibration of an axially symmetrical thick circular non-prismatic plate subjected to an axially symmetrical aperiodic normal load is solved in this paper. The plate rests on an inertial elastic half-space and is joined to the foundation by bilateral constrains. The problem is solved by the approximation method, using Chebyshev series. As a result, closed analytical formulas for the coefficients of an infinite system of equations for calculating the Laplace transforms of the sought solution’s coefficients – the passive foundation pressure function and the displacement function – are obtained. In order to illustrate the proposed method, the problem of the vibration of the plate under a uniformly distributed aperiodic load is solved. The inverse transform is calculated using the Zakian method.

Słowa kluczowe

EN

thick non-prismatic plate; inertial elastic half-space; aperiodic vibration; Chebyshev series; Legendre series

PL

wibracje; nierówność Czebyszewa; drgania osiowo symetryczne

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2012
• Tom: Vol. 12, no. 1
• Strony: 74--82
• Opis fizyczny: Bibliogr. 26 poz., wykr.

Twórcy

autor

Ruta P.

• Institute of Civil Engineering, Wrocław University of Technology, Wyb. Stanisława Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

• [1] Q.S. Li, Free vibration of elastically restrained flexural-shear plates with varying cross-section, Journal of Sound and Vibration 235 (2000) 63–85.
• [2] E. Efraim, M. Eisenberger, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 299 (2007) 720–738.
• [3] Y.K. Cheung, D. Zhou, Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions, Journal of Sound and Vibration 260 (2003) 693–709.
• [4] Y. Xiang, L. Zhang, Free vibration analysis of stepped circular Mindlin plates, Journal of Sound and Vibration 280 (2005) 633–655.
• [5] I. Shufrin, M. Eisenberger, Vibration of shear deformable plates with variable thickness first-order and higher-order analyses, Journal of Sound and Vibration 290 (2006) 465–489.
• [6] F. Ju, H.P. Lee, K.H. Lee, Free vibration of plates with stepped variations in thickness on non-homogeneous elastic foundations, Journal of Sound and Vibration 183 (1995) 533–545.
• [7] Mihir Chandra Manna, Free vibration analysis of isotropic rectangular plates using a high-order triangular finite element with shear, Journal of Sound and Vibration 281 (2005) 235–259.
• [8] H.R.D. Taher, M. Omidi, A.A. Zadpoor, A.A. Nikooyan, Free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions, Journal of Sound and Vibration 296 (2006) 1084–1092.
• [9] F.L. Liu, K.M. Liew, Free vibration analysis of Mindlin sector plates: numerical solutions by differential quadrature method, Computer Methods in Applied Mechanics and Engineering 177 (1999) 77–92.
• [10] P. Malekzadeh, G. Karami, Vibration of non-uniform thick plates on elastic foundation by differential quadrature method, Engineering Structures 26 (2004) 1473–1482.
• [11] T. Sakiyama, M. Huang, Free-vibration analysis of right triangular plates with variable thickness, Journal of Sound and Vibration 234 (2000) 841–858.
• [12] T. Sakiyama, M. Huang, Free vibration analysis of rectangular plates with variable thickness, Journal of Sound and Vibration 216 (1998) 379–397.
• [13] M. Huang, X.Q. Ma, T. Sakiyama, H. Matuda, C. Morita, Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions, Journal of Sound and Vibration 288 (2005) 931–955.
• [14] W.M. Sejmow, Application of orthogonal polynomials method to dynamic contact problems, Prikladnaja Mechanika 8 (1972) 69–77 (in Russian).
• [15] Mithu Mukherjee, Forced vertical vibrations of an elastic elliptic plate on an elastic half space a direct approach using orthogonal polynomials, International Journal of Solids and Structures 38 (2001) 389–399.
• [16] S.A. Savidis, T. Richter, Dynamic response on elastic plates on the surface of the half-space, International Journal for Numerical and Analytical Methods in Geomechanics 3 (1979) 245–254.
• [17] M. Iguchi, J.E. Luco, Dynamic response of flexible rectangular foundations on an elastic half-space, Earthquake Engineering and Structural Dynamics 9 (1981) 239–249.
• [18] R.K.N.D. Rajapakse, Dynamic response of elastic plates on viscoelastic half space, Journal of Engineering Mechanics 115 (1989) 1867–1881.
• [19] Jin Bo, The vertical vibration of an elastic circular plate on a fluid-saturated porous half space, International Journal of Engineering Science 37 (1999) 379–393.
• [20] S.L. Chen, L.Z. Chen, J.M. Zhang, Dynamic response of a flexible plate on saturated soil layer, Soil Dynamics and Earthquake Engineering 26 (2006) 637–647.
• [21] S.L. Chen, L.Z. Chen, E. Pan, Vertical vibration of a flexible plate with rigid core on saturated ground, Journal of Engineering Mechanics ASCE 133 (2007) 326–337.
• [22] P. Ruta, The vibration of a non-prismatic beam on an inertial elastic half-plane, Journal of Sound and Vibration 275 (2004) 533–556.
• [23] S. Paszkowski, Numerical Applications of Chebyshev Poly-nomials, PWN, Warsaw, 1975 (in Polish).
• [24] W.M. Ewing, W.S. Jardetzky, F. Press, Elastic Waves in Layered Media, McGraw-Hill Book Company, New York, Toronto, London, 1957.
• [25] P. Ruta, The application of Chebyshev polynomials to the solution of the nonprismatic Timoshenko beam vibration problem, Journal of Sound and Vibration 296 (2006) 243–263.
• [26] V. Zakian, Numerical inversion of Laplace transform, Electronics Letters 6 (21) (1970) 120–121.