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Exact frequency equations of free vibration of exponentially functionally graded beams

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WOS被引频次:56
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成果类型:
期刊论文
作者:
Li, X. -F.*;Kang, Y. -A.;Wu, J. -X.
通讯作者:
Li, X. -F.
作者机构:
[Li, X. -F.; Wu, J. -X.; Kang, Y. -A.] Cent S Univ, Sch Civil Engn, Changsha 410075, Hunan, Peoples R China.
通讯机构:
[Li, X. -F.] Cent S Univ, Sch Civil Engn, Changsha 410075, Hunan, Peoples R China.
语种:
英文
关键词:
Functionally graded beams;Exponential gradient;Natural frequency;Free vibration;Frequency equation;Critical frequency
期刊:
Applied Acoustics
ISSN:
0003-682X
年:
2013
卷:
74
期:
3
页码:
413-420
文献类别:
WOS:Article;EI:Journal article (JA)
所属学科:
ESI学科类别:物理学;WOS学科类别:Acoustics
入藏号:
WOS:000312975600013;EI:20124815740258
机构署名:
本校为第一且通讯机构
院系归属:
土木工程学院
摘要:
Free vibration of axially inhomogeneous beams is analyzed. For exponentially graded beams with various end conditions, characteristic equations are derived in closed form. These characteristic or frequency equations can analytically reduce to the classical forms of Euler-Bernoulli beams if the gradient index disappears. The gradient has a strong influence on the frequency spectrum, and the natural frequencies noticeably depend on the variation of the gradient parameter and end support conditions. For certain beams with exponential gradients, there exists a critical frequency depending on the gradient parameter. Vibration can be only excited by propagating waves with frequencies in excess of the critical frequency, and otherwise vibration is prohibited for pseudo-frequencies lower than the critical frequency. For some gradient index with small change, the natural frequencies have an abrupt jump when across its critical frequencies. Obtained results can serve as a benchmark for other numerical procedures for analyzing transverse vibration of axially functionally graded beams. The minimal natural frequency can be sought for certain gradient index, and this helps engineers to optimally design vibrating nonhomogeneous beam structures. Obtained results also apply to free vibration of nonuniform beams with constant thickness and exponentially decaying width. ©2012 Elsevier Ltd. All rights reserved.
参考文献:
Atmane HA, 2011, J VIB CONTROL, V17, P311, DOI 10.1177/1077546310370691
Aydogdu M, 2007, MATER DESIGN, V28, P1651, DOI 10.1016/j.matdes.2006.02.007
Chakrabarti A, 2010, J VIB ACOUST, V132, DOI 10.1115/1.3025825
Cranch E. T., 1956, J APPLIED MECHANICS, V23, P103
Ding HJ, 2007, INT J SOLIDS STRUCT, V44, P176, DOI 10.1016/j.ijsolstr.2006.04.026

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