International Journal of Structural Stability and Dynamics

Fast tracking is one of the most important performance indices in servo systems. To ensure fast tracking performance, many design methodologies have been established. This note proposes yet another new method based on the idea of intended instability. This is essentially a framework within which a variety of design approaches can be developed. Specifically, fast tracking through slow switching, fast switching, as well as compound control is explained. Refinement of the design approaches is also brought up. Numerical simulations are performed for the illustration of the corresponding designs.

The existing prediction methods of penetration depth do not take the influence of attack angle or angular velocity of projectile (i.e. effect of attack angle) into account. The main purpose of this work is to develop an approximate approach to predict the penetration depth for a rigid projectile into concrete target covered with yaw-inducing overlays. A quasi-static, elastic–plastic contact model of projectile impacting on irregular barrier is built based on Hertz’s contact theory, and the expression of effect of attack angle are also presented. The stress on projectile–target interface is derived according to spherical cavity expansion model and mechanical property of target, where reduction coefficient is introduced to consider the effect of free surface, and the penetration resistances are further obtained. Differential equations of motion for projectile arbitrarily oblique into target covered with yaw-inducing overlays are given by employing the initial conditions of projectile striking on irregular barrier. Then a simplified formula of depth-of-penetration (DOP) with effect of attack angle is presented by introducing an influence coefficient of oblique impact and an influence coefficient of yaw-inducing overlays into the depth of normal penetration. Predictions from the simplified formula are validated by comparison with ballistic experimental data for a 57mm diameter, 4.44kg, and ogive-nose, semi-armor-piercing with striking velocities between 320 and 705m/s.

The mode shapes of a bridge are important modal properties for many purposes, such as damage detection and model updating. Traditional methods for constructing mode shapes often require installation of instruments on the bridge for collection of dynamic responses. However, these methods are not only costly but also inconvenient. Therefore, a method is developed for constructing the mode shapes of girder bridges using the dynamic responses extracted from a moving vehicle under impact excitation. This paper reports some numerical simulations based on finite element modeling. First, the dynamic responses of a moving vehicle under impact excitation are generated for simulation. Then the component response associated with each natural frequency of the bridge is extracted by using a suitable filter. Finally, the mode shape associated with each natural frequency identified is constructed from the extracted component response and its Hilbert transform pair. The proposed method uses only the information measured from the moving vehicle, which acts both as a sensor and an exciter. Moreover, the additional impact excitation on the vehicle helps to excite the bridge. This helps to improve the accuracy by overcoming the adverse effects of measurement noise and road surface roughness. The effects of measurement noise, road surface roughness and vehicle speed on the accuracy of results are evaluated. A numerical study is presented to verify the feasibility of the proposed method.

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.

Structural health monitoring (SHM) has received increasing attention in the research community over the past two decades. Most of the relevant research focuses on linear structural damage detection. However, the majority of the damage in civil engineering structures is nonlinear, such as fatigue cracks that open and close under dynamic loading. In this study, a new hybrid AR/ARCH model in the field of economics and a proposed damage indicator (DI) which is the second-order variance indicator (SOVI) based on the model have been used for detecting structural nonlinear damage. The data from an experimental three-storey structure and a simulated eight-storey shear building structure model have been used to verify the effectiveness of the algorithm and SOVI. In addition, a traditional linear DI: cepstral metric indicator (CMI) has also been used to diagnose the nonlinear damage. The results of the CMI and SOVI were compared and it is found that there are advantages in using the SOVI in the field of nonlinear structural damage.

The dynamic stability of bidirectional woven fiber laminated glass/epoxy composite shallow shells subjected to harmonic in-plane loading in hygrothermal environment is considered. An eight-noded isoparametric shell element with five degrees of freedom is used in the analysis. In the present finite element formulation, a composite doubly curved shell model based on first-order shear deformation theory (FSDT) is used for the dynamic stability analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for the parametric study on the dynamic stability of shell panels under the hygrothermal field. The effects of various parameters like static load factor, curvature, shallowness, temperature, moisture, stacking sequence and boundary conditions on the dynamic instability regions of woven fiber glass/epoxy shell panels are investigated. The location of dynamic instability regions is shown to affect significantly due to presence of the hygrothermal field.

Presented herein is a functionally graded piezoelectric energy harvester using a thin cylindrical shell. The torsional mode for the thin cylindrical shell is studied and the effects of the functionally graded parameters on the power density are discussed. The analytical expressions for the power density are derived. From the results obtained, it can be observed that the functionally graded constant has obvious influences on the peak value of the power density. Moreover, larger values of the power density may be obtained by increasing the elastic parameter and the mass density. This work is expected to be useful in the analysis and design of energy harvester as well as new kinds of energy systems.

Touchdown bearing (TDB) is one of the key elements in active magnetic bearings (AMBs). When the magnetic bearing fails or is exposed to an overload, touchdown events will occur. According to ISO 14839, three typical orbit responses (pendulum vibration, combined rub and bouncing, and full rub) can be detected in touchdown events. The magnitude of the dynamic forces between the rotor and TDBs has been considered as an indicator to identify these orbit responses. However, the contact forces may not be easy to measure with precision. The instantaneous frequency of the rotor vibration is another significant difference between them. In this paper, a performance analysis model has been established that considers the dynamic and thermal effects in touchdown events. Simulations under different working conditions have been conducted and a recommendation for safety working conditions of the AMB system has been developed. The instantaneous frequency of the rotor vibration has been computed using Hilbert transform and the frequency characteristics of the three orbit responses have been analyzed and discussed. The results reveal that the instantaneous frequency of the pendulum vibration is almost fixed. The instantaneous frequency of the combined rub and bouncing fluctuates vehemently in most cases. The instantaneous frequency of the backward whirl shows periodic regularity.

The self-centering energy-dissipative (SCED) brace is a novel bracing element that can substantially reduce the residual deformation and enhance the reparability of structures. In this paper, nonlinear dynamic analyses have been conducted on a 4- and a 12-story steel-braced frame with SCED braces to study the effect of four important design parameters on the seismic performance of the SCED frames and recommendations are given for selection of the parameters. The parameters considered include the response modification coefficient $R$, the stiffness ratio of the brace $\alpha$, the strength ratio of the brace $\beta$, and the fuse activation story drift ${\theta }_a$. The relationship between the residual story drift and the peak story drift of the SCED frames is obtained based on these statistics. Finally, based on the equivalent linearization theory, a direct displacement-based design method applicable to the SCED frames, regarding both the peak story drift and residual story drift as the design objectives, is proposed.

Cable-arch structures, having features of the flexibility of cable and rigidity of arch, have often been used in structural and bridge engineering. It is important to fully understand the behavior of such a structure under various conditions. For this purpose, in this paper, linear and nonlinear elastic buckling analysis of four cable-arch related structures, including tied cable-arch structure, pure arch, tied arch and cable-arch, were conducted using the finite element methods under different boundary and load conditions with the stability of these structures compared. Furthermore, the parametric analysis was carried out to investigate the influence of numbers and inclined angles of hangers and cables, materials of cables and stiffness of tie beam on the buckling behavior of tied cable-arch. The results indicate that the stability of pure arch and tied arch can be enhanced by anchoring cables on the arch rib due to the increase in stiffness. Moreover, the weaker the stiffness of an arch, the greater the cable’s contribution to structural stiffness. The stability of a tied cable-arch is quite sensitive to the inclined angle of hangers and cables, the number and materials of cables, and tie bar, but not to the fracture of two hangers. The study gives us a complete understanding of the elastic buckling behavior of circular tied cable-arch structures.

Experimental and numerical studies are performed to analyze a concrete bridge under moving vehicular loads considering the effects of the damage cracks, stochastic traffic flows, and bridge surface roughness. Specifically, (1) the crack zone in the concrete bridge is modeled by a damage function with three parameters, i.e. the length of damaged zone, the magnitude of the damage, and the variation of Young’s modulus of the material; (2) a cellular automation (CA) based traffic flow model is adopted, which can capture the basic features of the probabilistic traffic flows using realistic traffic rules; (3) a three-dimensional (3D) vehicle model and a single vehicle model are each used to simulate the vehicles in the traffic flow for computational efficiency; and (4) the bridge and vehicle coupled equations are established by combining those for the bridge and vehicles using the displacement and interaction force relationship at the contact patches. The experimental and numerical investigations are conducted to validate the proposed modeling methodology. As an illustration, a prototype concrete bridge structure with partial damage is studied. Finally, parametric studies are conducted to study the effects of damage cracks, stochastic traffic flows, and surface roughness on the dynamic displacement, impact factor, impact force, and dynamic load coefficient of the bridge.

A pattern recognition-based damage detection method using a brand-new damage index (DI) obtained from the frequency response function (FRF) data is proposed in this paper. One major issue of using the FRF data is the large size of input variables. The proposed method reduces the dimension of the initial FRF data and transforms it into new damage indices by applying a data reduction technique called the two-dimensional principal component analysis (2D-PCA). The proposed damage indices can be used as the unique patterns. After introducing the damage indices, a dataset of damage scenarios and related patterns is composed. Pattern recognition techniques such as the artificial neural networks and look-up-table (LUT) method are employed to find the most similar known DI to the unknown DI obtained for the damaged structure. As the result of this procedure, the actual damage location and severity can be determined. In this paper, the 2D-PCA and LUT method for damage detection is introduced for the first time. The damage identification of a truss bridge and a two-story frame structure is performed for verification of the proposed method, considering all single damage cases as well as many multiple damage scenarios. In addition, the robustness of the proposed algorithm to measurement noise was investigated by polluting the FRF data with 5%, 10%, 15% and 20% noises.

This paper deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented.

Dynamic wind loads on tall buildings can be decomposed into three components, i.e. two translational components and one torsional component. When one component reaches its maximum, the other two components have low probability to take their maximum values. It is common to use combination coefficients for estimating the mean extremes of linearly combined wind loads. The traditional design practice for determining wind load combinations relies partly on some approximate combination rules and lacks a systematic and reliable method. Based on the high frequency force balance (HFFB) testing results, wind loads can be acquired in terms of time history data, which provides necessary information for the more rigorous determination of combination coefficients by probabilistic methods. In this paper, a 3D copula-based approach is proposed for determining the combination coefficients for three stochastic wind loads associated with a specific exceedance probability and a set of 3D realizable equivalent static wind loads (ESWLs) on tall buildings. Using the measured base moment and torque data by the HFFB wind tunnel test, a case study is presented to illustrate the effectiveness of the proposed framework to determine the dynamic wind load combinations and associated 3D realizable ESWLs on a full-scale 60-story building.

This paper studies the viscously damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously damped free vibration frequencies and corresponding damped mode shapes are calculated and plotted, aside from the undamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the natural frequencies and the corresponding mode shapes of longitudinal and torsional bars, especially for the fundamental frequency.

The objective of this paper is to investigate the dynamic instability of deepwater top-tensioned risers (TTRs), when subjected to the fluctuating axial tension originated from the heave motion of a surface floating platform as the instability source. Based on a rigorous derivation on the governing equation, a reduced model of the lateral displacement of a TTR is achieved by an ordinary differential equation with periodic coefficients. To identify the instability range of practical amplitudes and frequencies of the excitation, a newly proposed extended precise integration method (EPIM) is employed to generate the Floquet transition matrix (FTM). EPIM possesses high precision and efficiency due to the doubling algorithm and the increment-storing technique. The instability charts of TTRs in several typical depths are numerically obtained using EPIM. The effects of factors such as the top tension ratio, the stiffness of the heave compensators, damping constant, and internal flow velocity on the instability region are analyzed. In addition, because the nonlinear hydrodynamic damping will lead the TTR’s lateral vibration to reach a steady state, the instability response is thereby simulated by EPIM. Three response scenarios are discussed with examples. As the heave amplitude increases, the parametric resonance of the TTR is first triggered, then the transition stage appears, and ultimately the local dynamic buckling occurs. The bending stress analysis shows that the local dynamic buckling is the worst scenario for structural safety.