Porosity-dependent thermoelastic free vibration response of sigmoid functionally graded sandwich rotor blade with varying thickness
摘要
This paper investigates free vibration characteristics of rotating functionally graded (FG) sandwich blade, which is modeled as cantilevered pre-twisted shallow cylindrical shell with thickness variation mounted on a rotating rigid hub. The tapered blade consists of one isotropic core layer and two symmetric porous FG face sheet layers, which contain internal pores following different porosity distributions. The material properties of the FG layers are temperature-dependent and graded in the thickness direction in accordance with a modified sigmoid law. An isoparametric finite element (FE) formulation is established in the framework of the higher-order shear deformation theory (HSDT) for the present investigation, considering various configurations of the FG sandwich blade. Lagrange’s equation of motion is employed to derive the dynamic equilibrium equation that accounts for the nonlinear strains due to rotational and thermal loads. Comparisons with the benchmark results are provided to verify the present FE formulation. Parametric studies are performed to analyze the effects of volume fraction index, porosity coefficient, thickness variation ratio, pre-twist angle, radius-to-span length ratio, rotational speed, and temperature of the environment on the natural frequency of the blade considering different porosity distributions and sandwich configuration schemes. Also, some representative mode shapes are depicted for different values of thickness variation ratios of the FG blades. The study reveals that ceramic enrichment and chordwise thickness variation enhance frequencies, while increased porosity, spanwise variation, pre-twist angle, radius-to-span length ratio, and thermal gradients reduce stiffness and frequencies; additionally, rotational speed induces centrifugal stiffening, thereby increasing the fundamental frequencies.