Abstract
A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials is proposed and its dynamic behavior due to nonuniform motion of a moving point load is investigated for the first time. The beam consists of three layers, a homogeneous core, and two functionally graded face sheets with material properties varying in both the thickness and longitudinal directions by power gradation laws. Based on the first-order shear deformation beam theory, a finite beam element is derived and employed in computing dynamic response of the beam. The element which used the shear correction factor is simple with the stiffness and mass matrices evaluated analytically. The numerical result reveals that the material distribution plays an important role in the dynamic response of the beam, and the beam can be designed to meet the desired dynamic magnification factor by appropriately choosing the material grading indexes. A parametric study is carried out to highlight the effects of the material distribution, the beam layer thickness and aspect ratios, and the moving load speed on the dynamic characteristics. The influence of acceleration and deceleration of the moving load on the dynamic behavior of the beam is also examined and highlighted.
Highlights
Investigations on vibration of beams made of functionally graded materials (FGMs), a new type of composite materials initiated by Japanese researchers in 1984 [1], have been extensively carried out in the last two decades
A bidirectional functionally graded Sandwich (BFGSW) beam model made from three distinct materials has been proposed and its dynamic response to nonuniform motion of a moving load was studied. e beam consists of three layers, a homogeneous core, and two bidirectional FGM face sheets with material properties varying in both the thickness and length directions by the power gradation laws
E conventional transverse FGM Sandwich beam is a special case of the present BFGSW beam
Summary
Investigations on vibration of beams made of functionally graded materials (FGMs), a new type of composite materials initiated by Japanese researchers in 1984 [1], have been extensively carried out in the last two decades. Wang et al [36] considered the material properties varying by an exponential function along the beam length and a power law though the thickness in their free vibration study of bidirectional FGM Euler-Bernoulli beams. E beams were considered to be made from four materials with volume fraction varying in both the thickness and length directions by the power gradation laws It is clear from the above literature review that, except for the work in [38], the mechanical behavior of bidirectional functionally graded Sandwich (BFGSW) beams has not been studied so far. In addition to the BFGSW beam model, the main novelty of this paper is that the effect of variation of the material properties in both the thickness and longitudinal directions on the dynamic behavior of FGM Sandwich beams under moving loads is taken into consideration for the first time. Based on the first-order shear deformation beam theory, a finite beam element is formulated and employed in computing the dynamic response of the beam. e first-order shear deformation beam theory requires a shear correction factor [41, 42], but it leads to a simple element. e element with stiffness and mass matrices evaluated analytically is derived using quadratic and cubic polynomials to interpolate the rotation and transverse displacement, respectively. e effects of the material distribution, the layer thickness and aspect ratios, and the moving load parameters on the dynamic behavior of the beam are investigated in detail. e influence of the acceleration and deceleration of the moving load on the dynamic response of the beam is examined and discussed
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