Effects of movement and rotation of supports on nonlinear instability of fixed shallow arches

2020 ◽  
Vol 155 ◽  
pp. 106909 ◽  
Author(s):  
Hanwen Lu ◽  
Lulu Liu ◽  
Airong Liu ◽  
Yong-Lin Pi ◽  
Mark Andrew Bradford ◽  
...  
Keyword(s):  
Nonlinear Instability ◽  
Shallow Arches

Weakly nonlinear instability of planar viscoelastic sheets

2015 ◽  
Vol 27 (1) ◽  
pp. 013103 ◽  
Author(s):  
Chen Wang ◽  
Li-jun Yang ◽  
Luo Xie ◽  
Pi-min Chen
Keyword(s):  
Nonlinear Instability ◽  
Weakly Nonlinear

Experimental and analytical investigation on the in-plane dynamic instability of arches owing to parametric resonance

2017 ◽  
Vol 24 (19) ◽  
pp. 4419-4432 ◽  
Author(s):  
Airong Liu ◽  
Zhicheng Yang ◽  
Hanwen Lu ◽  
Jiyang Fu ◽  
Yong-Lin Pi
Keyword(s):  
Parametric Resonance ◽  
Dynamic Instability ◽  
Damping Ratio ◽  
Analytical Investigation ◽  
Engineering Practice ◽  
Test Results ◽  
Periodic Load ◽  
Shallow Arches ◽  
Excitation Frequencies ◽  
Critical Regions

When an arch is subjected to a periodic load, it may lose in-plane stability dynamically owing to parametric resonance. Previous investigations have been concentrated on in-plane dynamic buckling of pin-ended shallow arches. However, in engineering practice, fixed arches with different rise-to-span ratios are often encountered. Little research on in-plane dynamic instability of deep fixed arches has been reported in the literature. This paper is concerned with experimental and analytical investigations for in-plane dynamic instability of fixed circular arches with rise-to-span ratios 1/8–1/2 under a central periodic load owing to parametric resonance. Experiments are carried out to determine the in-plane frequency and damping ratio of arches, to investigate critical regions of frequencies and amplitudes of the periodic load for in-plane dynamic instability of arches, and to explore effects of the rise-to-span ratio and additional weights on dynamic instability. The analytical method for determining the region of excitation frequencies and amplitudes of the periodic load causing in-plane instability of the arch is established using the Hamilton’s principle by accounting for effects of additional concentrated weights. Comparisons of analytical solutions with test results show that they agree with each other quite well. These results show that the rise-to-span ratio significantly influences the bandwidth of regions of critical excitation frequencies for in-plane dynamic instability of arches. The critical frequencies of the periodic load and their bandwidth increase with a decrease of the rise–span ratio of the arch, whereas the corresponding amplitude of the periodic load decreases at the same time. It is also found that the central concentrated weight influences in-plane dynamic instability of arches significantly. As the weight increases, the critical frequencies of excitation and their bandwidth for in-plane dynamic instability of arches decreases, whereas the corresponding amplitude of excitation increases.

Nonlinear instability of Phillips model

2016 ◽  
Vol 32 (3) ◽  
pp. 669-684 ◽  
Author(s):  
Rong-fang Wang ◽  
Hong-jun Gao
Keyword(s):  
Nonlinear Instability ◽  
Phillips Model

The nonlinear instability of Hill's vortex

1986 ◽  
Vol 168 (-1) ◽  
pp. 337 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Nonlinear Instability

Effect of Temperature Gradient on the Mechanical Buckling Resistance of FGM Shallow Arches

2014 ◽  
Author(s):  
M. Bateni ◽  
M. R. Eslami
Keyword(s):  
Temperature Gradient ◽  
Thermal Environment ◽  
Mechanical Load ◽  
Functionally Graded ◽  
Effect Of Temperature ◽  
Power Law Distribution ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Buckling Resistance ◽  
Graded Material

This work presents a closed form investigation on the effect of temperature gradient on the buckling resistance of functionally graded material (FGM) shallow arches. The constituents are assumed to vary smoothly through the thickness of the arch according to the power law distribution and they are assumed to be temperature dependent. The arches subjected to the both uniform distributed radial load and central concentrated load and both boundary supports are supposed to be pinned. The temperature field is approximated by one-dimensional linear gradient through the thickness of the arch and the displacement field approximated by classical arches model. Also, Donnell type kinematics is utilized to extract the suitable strain-displacement relations for shallow arches. Adjacent equilibrium criterion is used to buckling analysis, and, critical bifurcation load is obtain in the complete presence of pre-buckling deformations. Results discloses the usefulness of using the FGM shallow arches in thermal environment because the temperature gradient enhances the buckling resistance of these structures when they are subjected to a lateral mechanical load.

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