Abstract
The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.
Highlights
The dynamic behaviour of the plates on elastic foundations has been the subject of intensive studies for many years due to their great importance in many engineering applications such as mat and raft foundations, highways and airfield pavements
It should be noted that the decrease in the frequency parameters with increasing l y/lx ratios for a constant value of H and γ gets larger for larger values of the frequency parameters
The Modified Vlasov Model and Mindlin plate theory have been effectively applied to the free vibration analysis of plates on elastic foundations
Summary
The dynamic behaviour of the plates on elastic foundations has been the subject of intensive studies for many years due to their great importance in many engineering applications such as mat and raft foundations, highways and airfield pavements. The main shortcoming of Winkler Model is discontinuity of the elastic springs and necessity of determining coefficient of the elastic springs To overcome this problem, some researches developed two parameter models connecting the top ends of vertical springs by a fictitious membrane or shear layer or elastic plate. The investigators modified the two parameter models by proposing a computational technique to calculate these two soil parameters iteratively They introduced another parameter, γ, to characterize the vertical deformation profile within the subsoil, and called the model as Modified Vlasov Model. The advantages of this model is the elemination of the necessity to determine the values of soil parameters, k and 2t, arbitrarily because these values can be computed as a function of the vertical deformation parameter, γ. The model is called as “three parameter model” by some other researchers [1]
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