Buckling of parabolic shallow arches when support stiffens under compression

2010 ◽  
Vol 37 (5) ◽  
pp. 467-471 ◽  
Author(s):  
Jianguo Cai ◽  
Jian Feng
Keyword(s):  
Shallow Arches

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.

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.

Non-Standard Reduction of Noisy Structural Systems: Shallow Arches

2000 ◽  
Author(s):  
Lalit Vedula ◽  
N. Sri Namachchivaya
Keyword(s):  
Markov Process ◽  
Random Perturbation ◽  
Exit Time ◽  
Stochastic Averaging ◽  
Dimensional System ◽  
Shallow Arches ◽  
Higher Dimensional ◽  
Mean Exit Time ◽  
Stationary Probability Density Function ◽  
Low Dimensional

Abstract The dynamics of a shallow arch subjected to small random external and parametric excitation is invegistated in this work. We develop rigorous methods to replace, in some limiting regime, the original higher dimensional system of equations by a simpler, constructive and rational approximation – a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results such as mean exit time, stationary probability density function.

Sensitivity in the structural behavior of shallow arches

2014 ◽  
Vol 58 ◽  
pp. 212-221 ◽  
Author(s):  
L.N. Virgin ◽  
R. Wiebe ◽  
S.M. Spottswood ◽  
T.G. Eason
Keyword(s):  
Structural Behavior ◽  
Shallow Arches

Exploration of the Response of Electrically Actuated MEMS Arches Under the Effect of Mechanical Shock Loads

2017 ◽  
Author(s):  
Jihad E. Alqasimi ◽  
Hassen M. Ouakad
Keyword(s):  
Dynamic Response ◽  
Abrupt Change ◽  
Combined Effects ◽  
Mechanical Shock ◽  
Reliability Study ◽  
Shock Loads ◽  
Shallow Arches ◽  
Electrically Actuated ◽  
Predicted Values ◽  
Stable Structures

This work investigates the modeling and simulation of the dynamic response of MEMS shallow arches under the combined effects of mechanical shock waves and electrostatic actuating forces. The possible instabilities and/or failures that can be considered in any reliability study of such bi-stable structures are numerically examined. The results demonstrate that the simultaneous effects of shock loads and the actuating force can make the bi-stability and/or the instability thresholds of electrically actuated MEMS arches devices much lower than the predicted values when considering their effects independently. The outcomes of this investigation can be very useful to design smart MEMS bi-stable sensors/accelerometers activated at a pre-programmed level of shock and/or abrupt change in the acceleration.

scholarly journals Exploring the design space of nonlinear shallow arches with generalised path-following

2018 ◽  
Vol 143 ◽  
pp. 1-10 ◽  
Author(s):  
B.S. Cox ◽  
R.M.J. Groh ◽  
D. Avitabile ◽  
A. Pirrera
Keyword(s):  
Design Space ◽  
Path Following ◽  
Shallow Arches

Localization and Propagation of Instabilities in Long Shallow Panels Under External Pressure

1994 ◽  
Vol 61 (4) ◽  
pp. 755-763 ◽  
Author(s):  
T. L. Power ◽  
S. Kyriakides
Keyword(s):  
Constant Pressure ◽  
Limit Load ◽  
Solution Procedure ◽  
External Pressure ◽  
Uniform Pressure ◽  
Membrane Tension ◽  
Pressure Loading ◽  
Shallow Arches ◽  
Subsequent Deformation ◽  
Static Conditions

This paper discusses the response of long, shallow, elastic panels to uniform pressure loading. Under quasi-static conditions, the deformation of such panels is initially uniform along their length, and their response has the nonlinearity and instabilities characteristic of shallow arches. Shallower panels deform symmetrically about the midspan and exhibit a limit load instability. For less shallow panels, the response bifurcates into an unsymmetric mode before the limit load is achieved. A formulation and a solution procedure are developed and used to analyze the response of such panels beyond first instability. It is demonstrated in both cases that following the first instability the deformation ceases to be axially uniform and locqlizes to a region a few arch spans in length. A drop in pressure accompanies this localized collapse and causes unloading in the remainder of the panel. Subsequent deformation is confined to this region until membrane tension arrests the local collapse. Further deformation can occur at a constant pressure and takes the form of spreading of the collapsed region along the length of the panel. The lowest pressure at which this can take place (propagation pressure) can be significantly lower than the pressure associated with first instability.

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