Elastic impact of sphere on large plate

doi:10.1016/j.jmps.2021.104604

CORC > 力学研究所 > 中国科学院力学研究所 > 非线性力学国家重点实验室

	Elastic impact of sphere on large plate
	Peng, Qing 2,3; Liu, Xiaoming 2,3; Wei, Yueguang 1
刊名	JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
	2021-11-01
卷号	156 页码:22
关键词	Elastic impact Homotopy analysis method Sphere on plate Coefficient of restitution
ISSN号	0022-5096
DOI	10.1016/j.jmps.2021.104604
通讯作者	Liu, Xiaoming(xiaomingliu@imech.ac.cn)
英文摘要	Different from the Hertz impact, a sphere impacting on a plate has an extra dissipation by the flexural wave propagating on the plate. This wave dissipation has been noticed by Zener (1941), who introduced this dissipation term into the governing equation. Because of this extra dissipation term by the flexural wave, the Zener equation cannot be treated as the same way as in the Hertz impact problem. As a result, in the past 80 years, except few numerical tries for Zener equation, no analytical solution has been provided for the evolution of compressive displacement or contact force during the Zener impact. In this paper, by using homotopy analysis method, we analytically solved the Zener impact problem. After constructing an auxiliary linear operator, we derived an analytical solution for the evolution of contact force up to the first order of the embedding homotopy parameter. Present model can take full account of the elongation of contact time by plate compliance, which is impossible by using Hertz impact model. Comparisons with finite element simulation show that the prediction of the contact force history is of high accuracy. With the solution of force history, we derived an explicit expression for the energy loss of Zener type, this Zener loss has a different dependence on the impact velocity as the Hunter loss does. Also, both the motions of the sphere and the plate are able to be predicted with high accuracy. In addition, with the zeroth-order solution, we derived explicit expressions for both the coefficient of restitution and the contact duration.
资助项目	National Natural Science Foundation of China[11772334] ; National Natural Science Foundation of China[11890681] ; National Natural Science Foundation of China[12022210] ; National Natural Science Foundation of China[12032001] ; Youth Innovation Promotion Association CAS[2018022] ; Strategic Priority Research Program of the Chinese Academy of Sciences[XDB22040501]
WOS关键词	HOMOTOPY ANALYSIS METHOD ; ELASTOPLASTIC IMPACT ; ENERGY-DISSIPATION ; WAVE-PROPAGATION ; CONTACT ; COEFFICIENT ; RESTITUTION ; COLLISIONS ; MODEL
WOS研究方向	Materials Science ; Mechanics ; Physics
语种	英语
WOS记录号	WOS:000743553400005
资助机构	National Natural Science Foundation of China ; Youth Innovation Promotion Association CAS ; Strategic Priority Research Program of the Chinese Academy of Sciences
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/88426]
专题	力学研究所_非线性力学国家重点实验室
通讯作者	Liu, Xiaoming
作者单位	1.Peking Univ, Coll Engn, Beijing 100871, Peoples R China 2.UCAS, Sch Engn Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Inst Mech, LNM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Peng, Qing,Liu, Xiaoming,Wei, Yueguang. Elastic impact of sphere on large plate[J]. JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS,2021,156:22.
APA	Peng, Qing,Liu, Xiaoming,&Wei, Yueguang.(2021).Elastic impact of sphere on large plate.JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS,156,22.
MLA	Peng, Qing,et al."Elastic impact of sphere on large plate".JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 156(2021):22.