研究了两端简支不可移、轴向运动梁在热冲击作用下的横向振动特性,根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制方程,采用微分求积法求解了梁的横向振动问题,分析了热冲击和轴向运动效应对梁固有特性的影响。研究发现:热冲击引起的梁的等效热轴力、热弯矩和弹性模量变化三因素中,热轴力对梁固有频率的影响起主导作用,材料的弹性模量变化和热弯矩起次要作用;当热冲击载荷大于或等于梁的临界压力时,达到梁的第一阶失稳模态;热冲击和轴向运动效应都会降低梁的固有频率,它们的联合作用会导致模态之间的耦合现象,使梁更易达到失稳状态。
Abstract
The transverse vibration characteristics of an axially moving beam immovably simply supported at both ends and subjected to a thermal shock were studied. Based on Timoshenko beam theory and Hamilton principle, the governing equations of its transverse vibration were established. The transverse vibration problem of the beam was solved by using the differential quadrature method. The effects of thermal shock and axially moving speed on its natural frequencies were analyzed. The results shwoed that among three factors including equivalent thermal axial force, equivalent thermal bending moment and changing of elastic modulus dut to thermal shock, equivalent thermal axial force plays a dominant role to affect natural frequencies of the beam, while changing of elastic modulus and equivalent thermal moment play a secondary role; when the thermal shock loads reach the critical load of the beam, the first order buckling mode is excited; thermal shock and axial moving speed can both reduce natural frequencies of the beam, and their joint action leads to the phenomenon of modal coupling to make the beam easily reach an unstable status.
关键词
Timoshenko梁 /
热冲击 /
轴向运动效应 /
微分求积法
{{custom_keyword}} /
Key words
Timoshenko beam /
thermal shock /
axial motion effects /
Differential Quadrature Method
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Simpson A. Transverse modes and frequencies of beams translating between fixed end supports[J]. Journal of Mechanical Engineering Science, 1973, 15:159~164.
[2] Wang L, Chen H. H, He X. D. Modal frequency characteristics of axially moving beam with Supersonic/Hypersonic speed[J]. Transactions of Nanjing University of Aeronautics & Astronautics, 2011, 28(2):163~168.
[3] 黄世勇,王智勇.热环境下的结构模态分析[J].导弹与航天运载技术,2009(5):50~56.
HUANG Shi-yong, WANG Zhi-yong. The structure modal analysis with thermal environment[J]. Missile and Space Vehcile, 2009(5):50~56.
[4] 雷桂林,陈方,张胜涛,等.持续气动加热环境下的结构热载荷分析与应用[J].科学技术与工程,2013,13(12):3343~3349.
LEI Gui-lin, CHEN Fang, ZHANG Sheng-tao, et al. Structure thermal load analysis and application research in the continuous aeroheating environment[J]. Science Technology and Engineering, 2013,13(12):3343~3349.
[5] Wang B. L, Mai Y. W, Zhang X. H. Thermal shock resistance of functionally graded materials[M]. Acta Materialia, 2004, 52:4961~4972.
[6] Tian X. G. A direct finite element method study of generalized thermoelastic problems[J]. International Journal of Solids and Structures. 2006, 43:2050~2063, 232~239.
[7] Ghayesh M.H, Khadem S.E. Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity[J]. International Journal of Mechanical Sciences, 50(2008) 389~404.
[8] Guo X. X, Wang Z. M, Wang Y, et al. Analysis of the coupled thermoelastic vibration for axially moving beam [J]. Journal of Sound and Vibration, 325(2009) 597~608.
[9] Manoach E, Ribeiro P. Coupled, thermoelastic, large amplitude vibrations of Timoshenko beams[J]. International Journal of Mechanical Sciences, 2004, 46:1589~1606.
[10] 李世荣,范亮亮.Timoshenko梁在热冲击下的瞬态动力响应[J].振动与冲击,2008,21(7):118~121.
LI Shi-rong, FAN Liang-liang. Transient dynamic response of Timoshenko beams under thermal shock[J]. Journal of Vibration and Shock, 2008, 21(7):118~121.
[11] 王亮,陈怀海,贺旭东.轴向高速运动梁的热冲击动力学响应及控制[J].振动工程学报,2011,24(6):590~594.
WANG Liang, CHEN Huai-hai, HE Xu-dong. Dynamic response and control of an axially moving beam with supersonic speed under thermal shock[J]. Journal of Vibration Engineering, 2011, 24(6):590~594.
[12] 陈红永,陈海波,张培强.轴向受压运动梁横向振动特性的数值分析[J].振动与冲击,2014,33(24):101-105.
CHEN Hong-yong, CHEN Hai-bo, ZHANG Pei-qiang, et al. Numerical analysis of free vibration of an axially moving beam under compressive load[J]. Journal of Vibration and Shock, 2014,33(24):101~105.
[13] Chen H. Y, Chen H. B. A research on the dynamic characteristics of axially moving Timoshenko beam with compressive load[J]. Journal of Vibroengineering, 2014, 16(2):656~673.
[14] 陈红永,陈海波.轴压作用下自由-自由运动梁振动特性研究[J].工程力学,2015,32(3):233~240.
CHEN Hong-yong, CHEN Hai-bo. Vibration Characteristics of free-free moving beam under axial compressive loads. Engineering Mechanics, 2015, 32(3):233~240.
[15] 吕海炜,李映辉,李亮,等.轴向运动软夹层梁横向振动分析[J].振动与冲击,2014,33(2):41-46.
LU Hai-wei, LI Ying-hui, LI Liang, et al. Analysis of transverse vibration of axially moving soft sandwich beam[J]. Journal of Vibration and Shock, 2014,33(2):41~46.
[16] 姜任秋.热传导、质扩散与动量传递中的瞬态冲击效应[M].北京:科学出版社,1997.
[17] Vosteen. L. F. Effect of temperature on dynamic modulus of elasticity of some structural alloys[R]. AIAA-TR-4348.1958.
[18] Bellmall. R. E, Casti J. Differential quadrature and long-term integration[J]. Journal of Mathematical Analysis and Applications, 1971, 34(2):235~238.
[19] 王鑫伟.微分求积法在结构力学中的应用[J].力学进展,1995,25(2):232~239.
WANG Xin-wei. Differential quadrature in the analysis of structural components[J]. Advances in Mechanics. 1995, 25(2):232~239.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}