Abstract: To study the influence of cross sectional shear deformation and moment of inertia on transverse vibration of elastic foundation beam, the finite element analysis method for variable cross-sectional Timoshenko beam on Pasternak elastic foundation model was developed and improved, and the modal analysis method for arbitrary cross-section of Timoshenko beam was established. In specific, the motion differential equations of foundation beam were derived based on Timoshenko beam theory and Newton’s second law; in the light of piecewise equivalent idea, the variable cross-sections were discretized into many simple uniform beam sections, which corresponded respectively with each finite element with four degrees of freedom. Furthermore, with beam of simply supported boundary which is fully supported on elastic foundation as an example, the characteristics of free vibration were analyzed and compared with those obtained from reliable semi-analytical approach. The results showed that the present method is effective and accuracy and therefore a new insight is provided to the analysis of variable cross-sectional foundation-beam.

Key words: Pasternak elastic foundation model, Timoshenko beam, finite element analysis, variable cross-section, modal analysis