International Journal of Structural Stability and Dynamics

Introduced herein is a new structural damping identification approach based on a two-dimensional (2D) amplitude and phase estimation (APES) method. The original APES method is suitable for application to an undamped and complex harmonic vibration signal. Hence, it has to be modified for application to real damped vibration signals such as the vibration test signals in engineering structures. This modified approach will be named as dr_APES. It can transform one-dimensional (1D) signals in time domain into their corresponding signals in the 2D domain of frequency and damping factor. By applying this dr_APES approach, the three-dimensional (3D) amplitude spectrum, with peaks corresponding to the vibration modes, can be obtained for any given vibration signals. By accurately locating the coordinates of the peaks, modal frequencies and damping factors can be identified. Owing to the high-resolution of the location of 2D ordinates of the spectral line and the value of spectrum, the accurate location of peaks can be estimated, and therefore, the modal frequencies and damping factor can be accurately determined. This is demonstrated by a numerical case study. Moreover, by applying the proposed approach to a real onsite dynamic test on two cables in a cable-stayed bridge, the inherent damping of the two cables was identified accurately, thereby verifying the ability of proposed damping identification approach in meeting the requirement of weak damping characteristics identification in flexible structures such as naked cables.

The wavelet transform and Lipschitz exponent perform well in detecting signal singularity. With the bridge crack damage modeled as rotational springs based on fracture mechanics, the deflection time history of the beam under the moving load is determined with a numerical method. The continuous wavelet transformation (CWT) is applied to the deflection of the beam to identify the location of the damage, and the Lipschitz exponent is used to evaluate the damage degree. The influence of different damage degrees, multiple damage, different sensor locations, load velocity and load magnitude are studied. Besides, the feasibility of this method is verified by a model experiment.

A numerical approach is presented to calculate the dynamic response of a group of rigid surface foundations. The formulation is unconditionally stable and has the computational simplicity with only the algebraic calculations involved. It imposes no limit to the foundation shape, foundation separations, thickness of the layered medium and magnitude of frequency. In the analysis, the foundation–ground interface is discretized into a number of sub square-regions. The Green’s function, which is obtained by the Fourier–Bessel transform and precise integration method, is employed to calculate the dynamic response of each sub-region. Finally, a system of linear algebraic equation in terms of the contact forces within each sub-region is observed, which leads to the desired dynamic impedance functions of the foundations. Comparison is carried out between the proposed method and the solutions available in the literature. Parametric studies on the dynamic interaction between adjacent foundations are also described. Addressed in this study are the effects of the distance and direction of foundation alignment. Several conclusions are drawn the significance of each factor. Illustrative results for a case of several closely-spaced foundations are also presented. Although the dynamic interaction analysis of foundations is concerned here, further applications of this approach can be extended to the interaction analysis of structures.

In order to evaluate the dynamic response of the train running on long-span cable-stayed bridges under uniform seismic excitations, a time-domain framework of analysis for the train–bridge system is established. The rail irregularities are treated as internal excitation and seismic loads as external excitation considering the inertia forces induced by the 3D seismic waves. The vehicles are modeled as mass-spring-damper systems, and the cable-stayed railway bridge is simulated by finite elements. A comprehensive analysis of the train–bridge system subjected to earthquake is conducted, focused on the effect of seismic ground motions on the dynamic response of the running train. Four kinds of seismic waves, each with three components, are simulated, with their spectral characteristics taken into account. To consider the stochastic characteristic of actual seismic waves, the effect of the incident angle and occurrence time of earthquakes on the bridge and vehicles is analyzed. Moreover, the earthquakes with various occurrence probability levels are also studied and the safety of the train running under the seismic action is evaluated, which may be used as the operation reference for the railway authority. The results demonstrate that the seismic ground motions have significant effects on the dynamic response of railway vehicles running on the long-span cable-stayed bridge under various spectrum characteristics, incident angles, occurrence times, and occurrence probabilities.

The transverse vibrations of cracked beams with rectangular cross sections resting on Pasternak and generalized elastic foundations are considered. Both the Euler–Bernoulli (EB) and Timoshenko beam (TB) theories are used. The open edge crack is represented as a rotational spring whose compliance is obtained by the fracture mechanics. By applying the compatibility conditions between the beam segments at the crack location and the boundary conditions, the characteristic equations are derived, from which the nondimensional natural frequencies are solved as the roots. Sample numerical results showing the effects of crack depth, crack location, foundation type and foundation parameters on the natural frequencies of the beam are presented. It is observed that the existence of crack reduces the natural frequencies, whereas the elasticity of the foundation increases the stiffness of the system and thus the natural frequencies. It is also observed that the type of elastic foundation has a significant effect on the natural frequencies of the cracked beam.

The free vibration of rotating tapered Timoshenko beams (TBs) made of the axially functionally graded materials (FGMs) is studied. The Chebyshev polynomials multiplied by the boundary functions are selected as the admissible functions in the Ritz minimization procedure, which is called the Chebyshev–Ritz method. As such, the geometric boundary conditions are satisfied, while the numerical robustness is guaranteed through use of the Chebyshev polynomials. The Ritz approach provides an upper bound of the exact frequencies. The effectiveness of the method is confirmed in the convergence and comparison studies. The effects of hub radius ratio, rotational speed ratio, taper ratios, rotary inertia and material gradient on the natural frequencies of the TBs for six different sets of boundary conditions are studied in detail.

Under ambient excitation of white noise, structural modal parameters can be identified from cross-power spectrum calculated from structural outputs, without known input. The minimization of difference between theoretical value and test value of cross-power spectrum — the former is an equation including modal parameters to be identified, and the latter is computed based on the output-only data of structure — is adopted as an objective function for optimization. The optimal objective function value can be obtained through optimal modal parameter search. Quantum-behaved particle swarm optimization (QPSO) — swarm intelligence optimization algorithm based on particle swarm optimization (PSO) — is used for optimization to identify the modal parameters of structure under the ambient excitation. Then, the modal parameter identification method based on QPSO presented herein had been demonstrated by a numerical simulation of three-span continuous beam and experimental results of a three story structure. The computed results indicated that QPSO can be effectively used in the structural modal parameter identification under ambient excitation.

Complex structural dynamic problems are normally analyzed by finite element and numerical integration techniques. An explicit time integration algorithm with second-order accuracy and unconditional stability is presented for dynamic analysis. Utilizing weighted factors, the current displacement and velocity relations are defined in terms of the accelerations of two previous time steps. The concept of discrete transfer function and the pole mapping rule from the control theory are exploited to develop the new algorithm. Several linear and nonlinear dynamic analyses are performed to verify the efficiency of the method compared with the well-known Newmark method.

This paper studies the time-dependent seismic fragility of reinforced concrete bridges with chloride induced corrosion under spatially varying ground motions. The time-varying characteristic of the chloride corrosion current density and the uncertainties related to the structural, material and corrosion parameters are both considered in the probabilistic finite element modeling of the example RC bridge at different time steps during its life-cycle. Spatially varying ground motions at different bridge supports are stochastically simulated and used as inputs in the fragility analysis. Seismic fragility curves of the corroded RC bridge at different time steps are generated using the probabilistic seismic demand analysis (PSDA) method. Numerical results indicate that both chloride induced corrosion and ground motion spatial variations have a significant effect on the bridge structural seismic fragility. As compared to the intact bridge, the mean peak ground accelerations (PGAs) of the fragility curves of the RC bridge decrease by approximately 40% after 90 years since the initiation of corrosion. Moreover, the effect of ground motion spatial variations changes along with the process of chloride induced corrosion owing to the structural stiffness degradation. Neglecting seismic ground motion spatial variations may not lead to an accurate estimation of the lifetime seismic fragility of RC bridges with chloride induced corrosion.

Based on force equilibrium and rigid body considerations, a novel approach is proposed for deriving the state equations and then the buckling equations of pretwisted spatially curved beams. Based on statical consideration of an infinitesimal element from the last calculated configuration $C_1$ to the current configuration $C_2$, a set of condition equations for the state matrix is derived. Next, by enforcing the rigid body rule for the beam, another set of condition equations for the state matrix is derived. From these two sets of equations, the state matrix of the beam is derived that leads directly to the buckling differential equations. The merit of the proposed approach is that it only requires simple differential and matrix operations. No hidden errors are possible because no higher-order terms need to be treated. In addition, a direct link is established between the straight and curved beam theories. Finally, examples are provided to demonstrate the application of the theory to the buckling analysis of various curved beams, including the helical ones.

In this paper, the seismic performance of offshore reinforced concrete (RC) bridges during their life cycle periods is assessed by the pushover analysis based on the concept of the force analogy method (FAM). The governing equations and implementation process of the proposed pushover method are first derived. The material nonlinearity is modeled by the local plastic mechanism, which is capable of simulating the monotonic strength hardening and softening behaviors of RC piers. The chloride ions corrosion effect for the RC bridges located in coastal areas is considered by using the deterioration model for the mechanical property of reinforcement steel. Besides, structural stability against overturning is considered by incorporating the geometric nonlinearity with the FAM. Since the initial stiffness matrices remain constant through the computation process, the advantages of the FAM, such as high efficiency and stability, are retained. A numerical example is carried out to illustrate the process of seismic performance assessment for offshore RC bridges with the FAM.