Parameter studies on impact in a lap joint

doi:10.1007/s11465-014-0322-x

Front. Mech. Eng.

2015, Vol. 10

Issue (1) : 64-77 https://doi.org/10.1007/s11465-014-0322-x

RESEARCH ARTICLE

Parameter studies on impact in a lap joint

Amir M. RAHMANI¹, Elizabeth K. ERVIN²(

)

¹. Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11790, USA
². Department of Civil Engineering, University of Mississippi, University, MS 38677, USA

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Abstract

To represent a loose lap joint, a beam impacting four springs with gaps is modeled. Modal analysis with base excitation is solved, and time histories of contact points are closely monitored. Using the impulse during steady state response, six influential parameters are studied: damping ratio, contact stiffness, intermediate contact position, gap, excitation amplitude and beam height. For all parameters, the system response is highly controlled by modes with two contacting springs. Each parameter’s effect on system response is presented including unstable regions, unique trend behaviours result. Recommendations for structural designers are also noted.

Keywords impact mechanics contact joint behaviour modal analysis parameter study

Corresponding Author(s): Elizabeth K. ERVIN

Online First Date: 26 December 2014 Issue Date: 01 April 2015

Cite this article:

Amir M. RAHMANI,Elizabeth K. ERVIN. Parameter studies on impact in a lap joint[J]. Front. Mech. Eng., 2015, 10(1): 64-77.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0322-x
https://academic.hep.com.cn/fme/EN/Y2015/V10/I1/64

Fig.1 Cantilever beam and four contact springs

	Parameter	Value
Fixed	Length, L/m	2.5
	Breadth, b/mm	300
	Density, ρ/( $kg ? m − 3$ )	7890
	Modulus of elasticity, E/( $N ? m − 2$ )	2.05e+11
Varied	Damping ratio, ζ	0.08, 0.04, 0.02
	Dimensionless stiffness, k^*	1200, 3000, 6000
	Intermediate spring position, a/m	1.2500, 1.5625, 1.8750
	All gaps G/mm	0.5, 1.0, 2.0
	Excitation amplitude, A/m	0.03, 0.06, 0.12
	Height, h/mm	50, 60, 70

Tab.1 Studied numerical parameters with basis parameters shown in boldface

Fig.2 Relative response at point P2. (a) Damping ratio of 8%; (b) damping ratio of 4%; (c) damping ratio of 2%; (d) Table displacement at excitation frequency of 650?rad/s

Fig.3 Impulses at point P4 versus frequency for damping ratio of 2% (red color), 4% (blue color) and 8% (black color)

Fig.4 Region from Fig. 3 for damping ratios of 2% (red color), 4% (blue color) and 8% (black color). (a) Region one; (b) Region two

Fig.5 Relative response at excitation frequency of 604?rad/s for damping ratio of 8% (blue color) and 4% (red color) at point P4

Fig.6 Impulses at point P4 versus frequency for nondimensional stiffness of 6000 (red color), 3000 (blue color) and 1200 (black color)

Tab.2 First five natural frequencies of State 6 for different nondimensional longitudinal position of intermediate springs

Fig.7 Impulses at point P4 versus frequency for intermediate springs at 3/4 L (red color), 5/8 L (blue color) and 1 /2 L (black color)

Tab.3 Time percentage of one full cycle for three different gaps at excitation frequency of 650?rad/s

Fig.8 Impulses at point P4 versus frequency for gaps equal to 2?mm (red color), 1?mm (black color) and 0.5?mm (blue color)

Fig.9 Region one from Fig. 8

Fig.10 Impulses at point P4 versus frequency for excitation amplitude of 0.12?m (red color), 0.06?m (black color) and 0.03?m (blue color)

Fig.11 Region one from Fig. 10

Tab.4 Time percentage of one full cycle for system with three different heights at excitation frequency of 880?rad/s

Fig.12 Impulses at point P4 versus frequency for heights of 0.07?m (red color), 0.06?m (black color) and 0.05?m (blue color)

Tab.5 Time percentage of one full cycle surrounding the unstable region for system with h=0.07?m

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