Vibration of stiffened skew Mindlin plates. (English) Zbl 0855.73046
Summary: This paper presents a formulation for the free vibration analysis of skew Mindlin plates with intermediate parallel stiffeners attached in two directions. The Mindlin theory is used to account for the effects of transverse shear deformations and rotary inertia of the plate while the Engesser theory associated with the consideration of torsion is employed for stiffeners. Based on these two theories, the energy functionals for the plate system have been derived. To obtain the vibration frequencies, these energy functionals are minimized with the shape functions assumed in a set of two-dimensional mathematically complete polynomials. This procedure has been implemented numerically to compute the vibration solutions. Convergence studies have been performed to verify the accuracy of this method. Sets of first known results have been presented for several stiffened plate structures.
Keywords:
convergence; parallel stiffeners; transverse shear deformations; rotary inertia; Engesser theory; energy functionals; shape functionsReferences:
| [1] | Leissa, A. W.: Recent research in plate vibration: 1981-1985 Part II: Complicating effects. Shock Vibr. Dig.19, 10-24 (1987). · doi:10.1177/058310248701900304 |
| [2] | Mindlin, R. D.: Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates. ASME J. Appl. Mech.18, 31-38 (1951). · Zbl 0044.40101 |
| [3] | Engesser, F.: Die Knickfestigkeit gerader St?be. Zentralbl. Bauverwaltung11, 483-486 (1891). · JFM 23.1035.01 |
| [4] | Liew, K. M., Xiang, Y., Wang, C. M., Kitipornchai, S.: Vibration of thick skew plates based on Mindlin shear deformation plate theory. J. Sound Vibr.168, 39-69 (1993). · Zbl 0925.73419 · doi:10.1006/jsvi.1993.1361 |
| [5] | Morley, L. S. D.: Skew plates and structures. Oxford: Pergamon Press 1963. · Zbl 0124.17704 |
| [6] | Shastry, B. P., Rao, G. V.: Vibrations of thin rectangular plates with arbitrarily oriented stiffeners. Comput. Struct.7, 627-629 (1977). · Zbl 0365.73061 · doi:10.1016/0045-7949(77)90005-0 |
| [7] | Mizusawa, T., Kajita, T., Naruoka, M.: Vibration of stiffened skew plates by using B-spline functions. Comput. Struct.10, 821-826 (1979). · Zbl 0413.73069 · doi:10.1016/0045-7949(79)90046-4 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
