Abstract
The chapter presents a detailed study into dynamic behaviour of axially functionally graded (AFG) tapered Timoshenko beam on linear elastic foundation. Geometric nonlinearity is induced in the system through Von Karman strain–displacement expressions, which are inherently nonlinear. The material model is such that it exhibits continuous gradation of material properties along the length of the beam. A set of linear springs is assumed to be attached to the bottom of the beam to mathematically replicate the foundation behaviour. Governing equations of motion are derived through suitable energy principle. The free vibration study is carried out on statically deflected configuration to plot the backbone curves of the system. Forced vibration problem is solved by assuming dynamic equilibrium under maximum amplitude of excitation. Amplitude and frequency of excitation of the external transverse harmonic excitation are the controlling factors of the system response. Frequency response curves pertaining to different combinations of system parameters are furnished as benchmark results.
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