Airong Liu

Nonlinear Equilibrium and Buckling of Fixed Shallow Arches Subjected to an Arbitrary Radial Concentrated Load

This paper is concerned with an analytical study of the nonlinear in-plane equilibrium and buckling of fixed shallow circular arches that are subjected to an arbitrary radial concentrated load. The structural behavior of an arch under an arbitrary radial concentrated load is quite different from that of an arch under a central concentrated load. It is shown that a fixed arch under an arbitrary radial concentrated load can buckle in a limit point instability mode, but cannot buckle in a bifurcation mode, which is different from that of a fixed arch under a central concentrated load that can buckle in a bifurcation mode or in a limit point instability mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling load of shallow circular arches under an arbitrary radial concentrated load are derived. It is found that the load position influences the buckling load significantly and the influence is much related to the modified slenderness of the arch defined in the paper. It is also found that when the modified slenderness of an arch is smaller than a specific value, the arch has no typical buckling behavior. The analytical solution for the relationship of the specific modified slenderness with the load position is also derived. Comparisons with finite element (FE) results show that the analytical solutions can accurately predict the nonlinear equilibrium and buckling load of shallow fixed arches under an arbitrary radial concentrated load.

Dynamic Stability of Euler Beams under Axial Unsteady Wind Force

Dynamic instability of beams in complex structures caused by unsteady wind load has occurred more frequently. However, studies on the parametric resonance of beams are generally limited to harmonic loads, while arbitrary dynamic load is rarely involved. The critical frequency equation for simply supported Euler beams with uniform section under arbitrary axial dynamic forces is firstly derived in this paper based on the Mathieu-Hill equation. Dynamic instability regions with high precision are then calculated by a presented eigenvalue method. Further, the dynamically unstable state of beams under the wind force with any mean or fluctuating component is determined by load normalization, and the wind-induced parametric resonant response is computed by the Runge-Kutta approach. Finally, a measured wind load time-history is input into the dynamic system to indicate that the proposed methods are effective. This study presents a new method to determine the wind-induced dynamic stability of Euler beams. The beam would become dynamically unstable provided that the parametric point, denoting the relation between load properties and structural frequency, is located in the instability region, no matter whether the wind load component is large or not.

Unified Practical Formulas for Vibration-Based Method of Cable Tension Estimation:

In this paper, unified practical formulas are proposed to estimate cable tension for vibrations under different boundaries. Correction coefficients are applied to the cable tensions calculated from the taut string theory. In these formulas, a dimensionless parameter η is introduced to represent the relative bending stiffness of the cable in lieu of the dimensionless parameter ξ in the previous formulas found in practice. Results have shown that the proposed formulas are accurate. For the fixed-fixed boundaries, the error in the estimated cable tensions for various frequencies is less than 3% for η ≤ 0.88, and less than 1% for η ≤ 0.55. For the fixed-hinged boundaries, the error in the estimated cable tensions for various frequencies is less than 1% for η ≤ 0.9. If there are multiple frequencies in the in-situ measurement, the proposed formulas can be used to identify the cable tension and bending stiffness simultaneously by solving a quadratic equation. The proposed formulas have been validated against several numerical examples as well as practical test cases.

Lateral-Torsional Buckling of Circular Steel Arches under Arbitrary Radial Concentrated Load

AbstractSteel arches are applied in many engineering structures because of their excellent capacity to resist various transverse loadings. Modified (or normalized) slenderness plays an important ro...

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

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.

A Method of Reinforcement and Vibration Reduction of Girder Bridges Using Shape Memory Alloy Cables

Bending and torsional vibrations caused by moving vehicle loads are likely to affect the traffic safety and comfort for girder bridges with limited torsional rigidity. This paper studies the use of cables made of shape memory alloy (SMA) as the devices of reinforcement and vibration reduction for girder bridges. The SMA cables are featured by their small volume, expedient installation. To investigate their effect on the vibration of girder bridges, theoretical analysis, numerical simulation and experimental study were conducted in this paper. For bending vibration, the governing equations of the girder with and without SMA cables subjected to moving vehicle loads were derived, while for torsional vibration, the finite element (FE) simulations were used instead. The results of bending and torsional vibrations obtained by the analytical approach and FE simulations, respectively, were compared with the experimental ones from model testing. It was confirmed that the SMA cables can restrain the vibration of the girder bridge effectively.

An Analytical Solution for Lateral Buckling Critical Load Calculation of Leaning-Type Arch Bridge

An analytical solution for lateral buckling critical load of leaning-type arch bridge was presented in this paper. New tangential and radial buckling models of the transverse brace between the main and stable arch ribs are established. Based on the Ritz method, the analytical solution for lateral buckling critical load of the leaning-type arch bridge with different central angles of main arch ribs and leaning arch ribs under different boundary conditions is derived for the first time. Comparison between the analytical results and the FEM calculated results shows that the analytical solution presented in this paper is sufficiently accurate. The parametric analysis results show that the lateral buckling critical load of the arch bridge with fixed boundary conditions is about 1.14 to 1.16 times as large as that of the arch bridge with hinged boundary condition. The lateral buckling critical load increases by approximately 31.5% to 41.2% when stable arch ribs are added, and the critical load increases as the inclined angle of stable arch rib increases. The differences in the center angles of the main arch rib and the stable arch rib have little effect on the lateral buckling critical load.

Nonlinear Buckling Analysis of Functionally Graded Graphene Reinforced Composite Shallow Arches with Elastic Rotational Constraints under Uniform Radial Load

The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL’s dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

Out-of-Plane Parametric Resonance of Arches Under an In-Plane Central Harmonic Load

Arches have been widely used in infrastructures such as bridges. This paper presents an experimental investigation of the out-of-plane dynamic instability of shallow circular arches under an in-plane central concentrated harmonic load owing to parametric resonance. The effects of central concentrated weight and the amplitude of the periodic load on the out-of-plane dynamic instability of arches are also investigated. It is found that as the weight increases, the bandwidth of the critical frequency region for out-of-plane dynamic instability decreases. It is also found that the bandwidth of the critical frequency region increases with an increase of the amplitude of the harmonic load. It is shown that the curve of the excitation frequency vs. amplitude of out-of-plane resonance bends toward the low frequency region and that the “traction” out-of-plane instability may occur owing to the “amplitude” perturbation.

Parametric Instability of Euler Beams under Random Wind Loads

The present study discusses the approach of dynamic stability analysis for pin-ended beams under random wind loads. The Schwarz’s inequality is adopted to determine the boundary of dynamic instability, and analyses under a real time history of wind forces are carefully carried out. Studies show that the relationship of variance and mean of wind load determines the state of parametric stability of the beam. Increase of the variance or the mean will make the beam be subject to instability. The beam becomes more stable with stronger elasticity, higher damping and density.