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Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Żur K. K.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 1

87--101

Free vibration analysis of homogeneous and isotropic thin circular and annular plates with discrete elements such as elastic ring supports is considered. The general form of quasi- -Green’s function for thin circular and annular plates is obtained. The nonlinear characteristic equations are defined for thin circular and annular plates with different boundary conditions and different combinations of the core and support radius. The continuity conditions at the ring supports are omitted based on the properties of Green’s function. The fundamental frequency of axisymmetric vibration has been calculated using the Newton-Raphson method and calculation software. The obtained results are compared with selected results presented in literature. The exact frequencies of vibration presented in a non-dimensional form can serve as benchmark values for researchers to validate their numerical methods when applied for uniform thin circular and annular plate problems.

Drgania układu wielokondygnacyjnych ram połączonych więzami sprężystymi

Stojek Z., Burak J.

Zeszyty Naukowe Politechniki Rzeszowskiej. Budownictwo i Inżynieria Środowiska

2000

z. 32[180], cz.1

515-524

The paper is devoted to horizontal vibrations of the system of two multi-storey plane frames with elastic constraints. In the analysis, macro-models of the frames, are represented by bars acting on pure shearing and connected by an elastic layer of the Winkler type. There were analysed free vibrations as well as forced and damped ones. The last part of the paper contains issues referring to optimisation of the constraints with respect to kinematic energy, as well as an example for shock wave load.