Evaluation of first transition foundation stiffness for simply supported beams on Pasternak foundation

摘要

The vibration and buckling analysis of beams on elastic foundation is of importance in many fields of engineering. In general, the Winkler type of elastic foundation' is the simplest and is widely used by engineers because of the simplicity of the model. The Winkler type of foundation acts as if it consists of an infinitely closely spaced elastic springs. However, in the actual situation the Winkler hypothesis neglects the interaction of shear between the adjacent springs and hence cannot represent the characteristics of many practical foundations. While consideration of continuous medium to represent an elastic foundation is more accurate, it is not easily amenable for theoretical or numerical analysis. To over come this, two parameter elastic foundations have been suggested by many investigators. These are less restrictive than the Winkler foundation and take care of the realistic situation more accurately. A review of the various types of two parameter foundations is given by Zhaohua and Cook~2. In the present study, the more frequently used two parameter Pasternak foundation~3 is considered.Buckling of beams on the Winkler foundation and its practical significance is well discussed by Timoshenko and Gere~4 and Column Research Committee of Japan~5. Some studies on the buckling and free vibration behaviour of beams on the Pasternak foundation are presented by Pantelides~6, Karamanlidis and Prakash~7, Naidu and Rao~8, De Rosa~9 and De Rosa and Maurizi~(10,11).