Abstract:Based on the Timoshenko beam theory, free vibrations of axially moving functionally graded material (FGM) beams under thermal shock were investigated for three different conditions with clamped-clamped, clamped-simply supported and simply supported-simply supported boundary. Using the Hamilton principle, the governing differential equation of free vibration of an axially moving FGM beam under thermal shock was derived and the one-dimensional heat conduction equation was solved by variable separation method. The beam was discretized along the length direction by using differential quadrature method (DQM) and the original equation was turned into fourth order generalized characteristic value problem, then the dimensionless natural frequencies of free vibration of the FGM beam were solved and analyzed. The influences of the different heat flow input, graded index and dimensionless axially moving speed on natural frequencies of free vibration of the FGM beam were presented. The results show that the larger the thermal shock load is, the more obvious the effect is to reduce the natural frequency of the FGM beam. Under the condition of certain axially moving speeds and heat flow input, increasing gradient indexes of functionally graded material gradually will reduce the dimensionless natural frequencies of the beams. The FGM beam will slow down the thermal shock in a short period of time and the first order instability will take long time relative to homogeneous material. Under thermal shock, the FGM beam easier reach an instability state in axially moving.
林鹏程,滕兆春. 热冲击下轴向运动FGM梁的自由振动分析[J]. 振动与冲击, 2020, 39(12): 249-256.
LIN Pengcheng, TENG Zhaochun. Free vibration analysis of axially moving FGM beams under thermal shock. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(12): 249-256.
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