Dynamic snap-through of a laterally loaded arch under prescribed end motion

Lin, Jian-San; Chen, Jen‐San

doi:10.1016/s0020-7683(03)00181-1

Cited by 23 publications

(10 citation statements)

References 19 publications

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“…The d'Alembert principle and the basic assumptions applied, the nonlinear governing equation of the shallow arch can be obtained: (2) where A is the section area of arch; I is the moment of inertia for section area; ρ is mass density of arch; E is the Young's modulus of elasticity; y 0 (x) and y(x, t) are the initial shape of the shallow arch and the deformed shape of the loaded arch respectively; and S is the initial thrust of the shallow arch. …”

Section: Mechanical Modelmentioning

confidence: 99%

“…Although the shallow arch is relatively simple, it is a very useful structural element. Moreover, one can understand the complicated structures that are analogous to shallow arch such as shallow shell and curved plate further, through the research of shallow arch whose structural characteristics have been extensively studied [1][2][3][4][5][6][7][8][9][10][11][12]. When a shallow arch is subject to lateral static load it may become prime buckling or bifurcation buckling under certain conditions.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Stability of Shallow Arches with the Geometrical Imperfections

Wang

2009

2009 International Joint Conference on Computational Sciences and Optimization

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The dynamic stability of the hinged-hinged sinusoidal shallow arch with geometrical imperfection under time wise distributed load is investigated in this paper. First, the nonlinear governing equation of shallow arch is derived from the d'Alembert principle andEuler-Bernoulli assumption. And the dimensionless type of the equations, which is used to investigate the equilibrium configurations of shallow arch, is obtained by the Fourier series expansion and the Galerkin integration. Then, with the application of both the nonlinear equation and sufficient condition for stability, the stability of shallow arch with geometrical imperfection is studied. The emphasis is placed on the influences of root locus of critical points and sufficient condition for dynamic stability on the second harmonic imperfection, which is similar to the buckling mode-shape of arch structure. To compare the stability property of imperfect shallow arch with that of perfect arch, the sinusoidal shallow arch with no imperfection is studied before the analysis of effect on imperfection.

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Section: Mechanical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Stability of Shallow Arches with the Geometrical Imperfections

Wang

2009

2009 International Joint Conference on Computational Sciences and Optimization

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“…This type of research have also been done in engineering. In fact, stability of the shallow arch from an engineering point of view is studied in [4,5,8,15,16,17,21], and in their references. This work dealt with the subject of chaotic motion, global behavior, accurate solutions, dynamic critical load, internal resonance, and stability with various boundary conditions and load type.…”

Section: Introductionmentioning

confidence: 99%

“…This work dealt with the subject of chaotic motion, global behavior, accurate solutions, dynamic critical load, internal resonance, and stability with various boundary conditions and load type. Generally, the methodologies used in estimating critical loads can be classified as the energy approach, and the direct approach by obtaining dynamic response in a wide parameter range [17].…”

Section: Introductionmentioning

confidence: 99%

Stability of shallow arches under constant load

Ha¹,

Gutman²,

Shon³

et al. 2014

International Journal of Non-Linear Mechanics

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“…In the case when the lateral load is applied dynamically instead of in the quasi-static manner, the critical load will be different from the one predicted statically, see Hoff and Bruce (1954), Humphreys (1966), Lock (1966), Hsu (1967Hsu ( , 1968, Hsu et al (1968), Huang and Nachbar (1968), Fulton and Barton (1971), Sundararajan and Kumani (1972), Lo and Masur (1976), Johnson and Mclvor (1978), Johnson (1980), Gregory and Plaut (1982), Donaldson and Plaut (1983), Patricio et al (1998), Xu et al (2002), Lin and Chen (2003), Chen and Lin (2004a), and Chen and Liao (2005). A comprehensive review on the dynamic instability of shallow arches can be found in the book by Simitses (1990).…”

Section: Introductionmentioning

confidence: 99%

Effects of elastic foundation on the snap-through buckling of a shallow arch under a moving point load

Chen

2006

International Journal of Solids and Structures

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In this paper we study the effects of elastic foundation on the static and dynamic snap-through of a shallow arch under a point load traveling at a constant speed. The deformation of the arch is expressed in a Fourier series. For static analysis when the moving speed of the point load is almost zero, the first four modes in the expansion are sufficient in predicting the equilibrium positions and the critical loads. Unlike the case without elastic foundation, static snapthrough can occur even when the arch is in another stable (P À 1 ) position before the point load moves onto the arch. In the dynamic case when the moving speed of the point load is significant, the numerical simulation of the response does not converge well, especially long after the point load leaves the arch. However, the total energy of the arch converges quite well when only the first eight modes are used in the Fourier series. This observation allows us to establish a sufficient condition against dynamic snap though, although we are unable to predict precisely, with finite number of modes in the series, at what time it will occur when this sufficient condition is not fulfilled.

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Dynamic snap-through of a laterally loaded arch under prescribed end motion

Cited by 23 publications

References 19 publications

Dynamic Stability of Shallow Arches with the Geometrical Imperfections

Dynamic Stability of Shallow Arches with the Geometrical Imperfections

Stability of shallow arches under constant load

Effects of elastic foundation on the snap-through buckling of a shallow arch under a moving point load

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