Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams

By Mergen H. Ghayesh. Applied Mathematical Modelling, 2018

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Abstract This paper aims at investigating the nonlinear vibration characteristics of axially functionally graded (AFG) shear deformable tapered beams subjected to external harmonic excitations. A coupled nonlinear longitudinal-transverse-rotational set of equations governing the motion of the AFG system is derived utilising the third-order shear deformation beam theory via Hamilton's energy principle. The beam under consideration is tapered; i.e. the width of the beam varies along the length. The tapered geometry along with the nonuniform material properties arising from the AFG nature of the beam increases the complexity in the modelling and numerical simulations. The expressions for the kinetic and potential energies of the AFG shear-deformable tapered beam together with the expressions for the work of damping and external excitation are derived and implemented in Hamilton's principle. The nonlinear partial differential equations are discretised making use of the Galerkin technique and solved with the aid of a continuation scheme. The effect of different parameters such as the gradient index and the tapered ratios on the force- and frequency-amplitude diagrams of the AFG system is examined.

Subfields: Control and Systems Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ab8de54cec1895a5ae030520f5aaf197a9fe89ec

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In Control and Systems Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A review on the mechanics of nanostructures (2018, background): “In this section, size-dependent [60-69] elasticity theories including the nonlocal elasticity and the nonlocal strain gradient elasticity, which are commonly applied to nanoscale structures, are reviewed.”