Large-amplitude vibration of rotating functionally graded blades including geometrical nonlinearity and stress stiffening effects

Abstract

The nonlinear frequency responses of functionally graded (ceramic/metal/ceramic) straight/curved blade-type structures are examined under rotation and thermal environment. Here, the geometrical nonlinearity is introduced using Green-Lagrange’s strain via the higher-order shear deformation theory. The constituent materials, i.e. ceramic and metal-alloy, are considered to be temperature-dependent, whereas, the overall blade material properties are evaluated using Voigt’s homogenization scheme via a modified power-law function. The equations of motion are obtained using Hamilton’s principle by including the geometrical nonlinearity and stress stiffening effects. The linear and the nonlinear frequency responses are computed through the developed nonlinear finite element method and Picard’s successive iteration scheme. An exhaustive computation is carried out to report the linear and the nonlinear vibrational behavior of the proposed composite straight/curved blade model at small-to-large amplitudes for various sets of combinations of geometric and material parameters, such as blade span, blade thickness, volume fractions, rotational speed, and temperature.

Keywords:

• Nonlinear finite element method
• large-amplitude vibration
• straight/curved blades
• functionally graded materials
• Green-Lagrange kinematics
• stress stiffening

Disclosure statement

The authors have no relevant financial or non-financial interests to disclose.