Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

On modal analysis of axially functionally graded material beam under hygrothermal effect

This investigation focuses on the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam are supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution. A finite element analysis with COMSOL Multiphysics® (version 5.2) package is used to find the Eigen frequencies of the beam. The accuracy of the technique is authenticated by relating the results with the prior investigation for reduced case. The effects of moisture changes, temperature, and volume fraction index, length-to-thickness ratio on the Eigen frequencies are investigated in detail. It is believed that the present investigation may be useful in the design of highly efficient environmental sensors for structural health monitoring perspective.

Effects of Support Conditions to the Post-Buckling Behaviors of Axially Functionally Graded Material Rods

The effects of support conditions to the post-buckling behaviors of rod structures made of Axially Functionally Graded Material (AFGM) are presented. The material property of the rod member is assumed to vary linearly in the axis direction of the member. The non-linear material property of the rod element is formulated in the Finite Element context. The consistent shape functions for the rod element were developed to take into account the varying material property in the finite element formulation. The geometrically non-linear behavior of the rod element is formulated in the context of the updated co-rotational formulation. The non-linear equilibrium equations are solved by using the incremental and iterative procedures in combination with the arc-length control method. The influences of the material distribution on the post-buckling behaviors of the AFGM Williams’ toggle frames under various support conditions are highlighted. As a result, the graded between two materials can increase the post-buckling behaviors of the AFGM rod element regardless of the types of support conditions. The orientation of material distributions combined with the type of support condition can increase the performance of the rod element. The fixed-fixed support condition showed the highest performance of the AFGM rod element.