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A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

This paper studies the vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving concentrated load. The volume fraction of constituent materials is assumed to vary in both the thickness and longitudinal directions by power-law functions. The governing equations of motion based on Timoshenko beam theory are constructed from Hamilton’s principle. A finite element formulation is derived and used in combination with the Newmark method in computing the vibration response. A parametric study is carried out to highlight the effect of the material distribution and moving load speed on the vibration characteristics of the beams. The numerical results show that the two grading indexes which govern the variation of the effective material properties have opposite effect on the natural frequencies, dynamic magnification factor and mid-span axial stress. The influence of the aspect ratio on the dynamic behavior of the beams is also examined and discussed.

This paper investigates the dynamic behavior of functionally graded beam in the thermal environment due to a moving harmonic load. The material properties are assumed to be graded in the thickness direction by a power-law function, and they are considered to be temperature dependent. Two types of temperature distribution, namely uniform and nonlinear temperature rises, are considered. Equations of motion based on Euler-Bernoulli beam theoryare derived from Hamilton’s principle and they are solved by a simple finite element formulation in combination with Newmark time-integration procedure. Numerical results show that the dynamic deflection and dynamic amplification factor is decreased with increasing the temperature rise, and the decreasein the uniform temperature rise is more significant that by the nonlinear temperature rise. The excitation frequency plays an important role in the dynamic behavior of the beams, and the frequency at which resonant phenomenon can occur depends on the temperature. A parametric study is carried out to highlight the effect of the temperature rise and moving load parameters on the dynamic behavior of the beams.