International Journal of Structural Stability and Dynamics

Structural vibration is a widespread issue occurred in the field of civil engineering. The passive energy dissipation devices are being increasingly popular for protecting structures from external excitations due to their high performance and no need for external energy. They can be divided into displacement-dependent dampers and velocity-dependent dampers, among which the metallic yielding dampers (MYDs) and fluid viscous dampers (FVDs) are the most representative. This paper presents an overview of the MYD and FVD, aiming to reveal their defects and provide suggestions for future development. The basic concept, the mechanical models, the design approaches, and the applications in civil engineering of the two dampers are reviewed. In particular, the obstacles in application and preference in research of these two dampers are summarized, and their merits and drawbacks are further discussed. Emphatically, the strategies for improvement and future development trends are explored.

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ($v_{\mathrm{\text{br}}}$) of the bridge, from which we can determine the sub-resonance speed as ($v_{\mathrm{\text{br}}}∕n{|}_{n=2,3}$). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.

In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.

To investigate the dynamics of the wind–vehicle–bridge (WVB) system in the multi-body dynamics framework, which avoids the large computation cost of programming the motion equation of complex vehicle models and improves the calculation efficiency, an advanced hybrid method is proposed to optimize the WVB system coupling vibration analysis model. The dummy body coupling (DBC) method is integrated to build the connection between the MBS and the FE model, which cannot change the mechanical characteristics of the MBS vehicle model and the bridge FE model. The proposed method makes full use of the high efficiency of the established structure modeling, the powerful wheel–rail analysis function, and vehicle modeling in the multi-body dynamics framework. The complex bridge is modeled by a number of elements to reflect the actual dynamic characteristics of structure, which cannot satisfy the requirement of calculation in the multi-body dynamics framework. Thus, to avoid forming the wheel–rail relationship function, the bridge modeling as a finite element model would be transferred into multi-body dynamics coupling model of the WVB system as a flexible body. The verification of the relationship among the sub-systems of the multi-body model of the WVB system is investigated by analysis of the wind–vehicle, wind–bridge, and vehicle–bridge sub-systems. Finally, a dynamic analysis of the WVB system based on the proposed method is carried out for a double-track railway continuous bridge, in which the effects of different vehicle speeds and the incoming wind directions are studied. The simulation of the WVB system by the hybrid method has a high computational efficiency and strong practicability.

Plate frame structure with holes is a novel candidate to reduce the weight and strengthen the architectural structures to fulfill the requirements of practical engineering applications. The designed periodic hole structure can generate a band gap from the perspective of the frequency spectrum. In this study, a new band gap calculation method was proposed under the basic energy method framework for the analysis of hole periodic structures. Gaussian wavelet function with a good localization characteristic was adopted to overcome the inaccurately assumed displacement filed function due to the introduced hole issue. The entire plate structure was divided into cell elements and an artificial spring model was introduced to satisfy the cell coupling conditions. The coupling constraints were converted into elastic potential energy to be added to the energy functional for the entire system. The dispersion curves obtained by this method are in excellent agreement with the results of the finite element method. It was observed that periodic hole plates lead to the generation of complete and directional flexural wave band gaps. By introducing bi-directionally orthogonal stiffeners, the band gap of periodic hole plates could be significantly lengthened and complete band gaps could be successfully generated. Furthermore, geometrical parametric studies on flexural wave band gaps were analyzed. A wide and complete band gap could be realized by increasing the width of the stiffener to a certain extent, but not fully proportional.

To more realistically describe the psychological feeling of pedestrians walking on the pedestrian, and better evaluate the vibration comfort of pedestrians, this paper adopted Stevens’ law. Based on statistical and psychophysical principles, Stevens’ membership function in discrete and continuous distributions was obtained which established a new annoyance rate model. Moreover, an approximate solution to the annoyance obtained using the fitting curve is proposed. Furthermore, calculating the annoyance curves and the coefficient of variation of human-induced vibration for a pedestrian bridge, to verify the accuracy and reliability of the improved pedestrian bridge annoyance rate, field tests are performed on an actual pedestrian bridge. The results show that Stevens’ annoyance rate model can more accurately describe the uncertainty of subjective responses. The changing regular of the fitting value of the approximate curve is consistent with the measured value. Thus, Stevens’ annoyance rate model can provide a new basis for the evaluation of walking vibration comfort of pedestrian bridges.

After increasing the train speed, the wheel-rail coupling effect is intensified, as is the coupling effect between the train and the surrounding air, which causes the severe vibration of the train. Considering this problem and taking the high-speed train as the object of this study, a method for the coupling of aerodynamics and vehicle dynamics is proposed. Its validity is then demonstrated by the results of field tests and moving model experiments. On this basis, the fluid–structure coupling characteristics of a high-speed train passing through a tunnel are studied, as well as the effects of different coupling methods and track irregularities. The obtained results demonstrate that the interaction between the tail car and the surrounding air is significant. In the tunnel and at its exit, the lift and the car body acceleration significantly change, especially when the coupling of aerodynamics and vehicle dynamics, as well as the vertical and lateral track irregularities, are simultaneously imposed. When the head car travels out of the tunnel, the lift of the middle and tail cars both dramatically will change. It is deduced that the fluid–structure interaction has a significant effect on the swing phenomenon of the tail car. This phenomenon is the result of the combined effects of aerodynamics and track irregularities. The different frequencies of the lateral displacement for each car body, except the frequencies of the car bodies themselves, are mainly determined by vertical track irregularities.

Vibration absorber usually aims to control the vibration in engineering, but few efforts focus on suppressing the low and variable frequency vibration by tuning the natural frequency. To obtain the optimal tooth layer parameters of the electromagnetic vibration absorber in this paper, the working bandwidth and corresponding linearity are reasonably optimized by establishing a nonlinear multiobjective programming function, and the results indicate that the working performances are significantly improved. The simulations illustrate that the optimized vibration absorber is within the effective stroke of the negative stiffness characteristic, and the reduction of its natural frequency can realize an apparent control effect in a wide low-frequency band for variable frequency vibration by adjusting the coil current. The experimental results demonstrate that the natural frequency of the vibration absorber is tuned to a reasonable value by adjusting the current, and a notable vibration suppression effect is achieved under the variable frequency. As the current increases from 0 to 550mA, the natural frequency of the vibration absorber can be tuned from 9Hz further to 7.2Hz for vibration control, and the vibration suppression effect can reach 62.1%.

In this paper, the nonlinear vibration of a flexible rotor supported on squeeze-film dampers (SFDs) with centering springs is analyzed using the incremental harmonic balance (IHB) method, and bifurcation phenomena appeared in the resonance region are investigated. Complex nonlinear phenomena occur in this system due to the interaction of the fluid-film forces and the unbalance forces of the rotor in the SFD. Systems with these complex nonlinearities cannot be solved using the classical IHB methods. To overcome this problem, the classical IHB method and the alternating frequency/time (AFT) method are combined. The processing of linear matrices is performed in the same way as the classical IHB method, and only the processing of nonlinear force matrix caused by fluid–structure interaction is modified (application of transformation matrix). To prove the validity of the proposed method, the results calculated using the proposed method are compared with the results calculated using the Runge–Kutta method and the results presented in reference. Then, frequency response curves according to changes in bearing parameter $B$, gravity parameter $W$, stiffness ratio $K$, mass ratio $\alpha$, and unbalance parameter $U$ are constructed. Stability and bifurcation analyses of the calculated solution are performed using the Floquet theory. The proposed method can be effectively applied to the nonlinear vibration analysis of rotor systems supported on fluid-film bearings.

Perforated cold-formed steel (PCFS) beams are regarded as an economical option for steel construction industry owing to its various advantages. They can provide access for the facilities like electric wires and pipelines to penetrate the web so that extra building space could be saved. However, the web openings might change the web stress distribution as well as reduce the cross-sectional properties, which make the PCFS beams more susceptible to buckling and may have effect on their load-bearing capacity. In this paper, a simplified spring model was proposed based on the use of energy method, to predict the critical moment of lateral-torsional buckling of PCFS channel beams with circular holes in web subject to pure bending. The effect of hole sizes and lateral restraint at the tension flange was examined by using the derived analytical solution. In addition, eigenvalue buckling analysis was conducted by using finite-element package ANSYS to validate the accuracy of the proposed analytical model. The results demonstrated that the proposed analytical solution was reliable and the critical moment predicted can be used for the extension of DSM formulae for the design of PCFS beams when considering the failure caused by lateral-torsional buckling of the beams.

The assessment of the lateral buckling for the unbraced top chord of a truss bridge (a pony truss bridge) requires a finite element analysis of a three-dimensional model of the whole structure or a method of the chord analysis based on the reliable estimation of the lateral restraint for the chord nodes. The latter alternative becomes crucial if rapid assessment is necessary. Majority of the existing analytical methods of assessment of the stability of top chords of pony truss bridges rely on the stiffness of $U$-frames that consist of cross-beams and truss bracing members. The available analytical methods of setting the $U$-frame stiffness seem to neglect the existence of independent cross-beam decks that, together with Warren-trusses, constitute contemporary truss bridges. Such structures are analyzed in the paper. The stiffness of the lateral restraint provided to the truss top chord by the cross-beams, the diagonals and the bottom chord are computed. The influence of the cross-beams is reflected, for the first time, as an equivalent torsional stiffness of the truss bottom chord. The analytical method is applied against the method included in the DIN design code to the pony Warren-truss bridges of various height-to-span ratios and various arrangements of their member cross-sections. Then the Timoshenko and Gere model of a compressed bar is adapted to find the critical load for the top chords of the aforementioned truss bridges. The results are compared to those obtained from the finite element method (FEM) analyses. It is concluded that the analytical method provides lower estimate for the critical load obtained from the FEM analysis provided the smallest values of cross-sectional properties, within the respective groups, are taken as representative for the computations.

Railway transportation, as an important lifeline during earthquake relief and post-disaster reconstruction, has an extremely significant role. The study of track irregularity caused by earthquakes is the basis for ensuring traffic safety after their occurrence. In this paper, a finite element model of a five-span simply supported high-speed railway beam bridge with the China Railway Track System (CRTS) II was established and an experimental verification was performed. Eighty arbitrarily selected seismic waves were extracted from the Pacific Earthquake Engineering Research Center (PEER) strong ground motion database and a nonlinear time-history analysis was performed on the finite element model. The frequency–domain distribution law of earthquake-induced track irregularities was studied. A stable target earthquake-induced track irregularity spectrum model was constructed, and its expression was fitted. According to the results, in the case of transverse earthquakes, the rails experienced noticeable alignment irregularity and cross-level irregularity, while the amplitude of the gauge and vertical irregularity were relatively small. The target irregularity spectrum has a higher amplitude in the low-frequency components. When peak ground acceleration (PGA) was low, earthquake-induced track irregularity was not obvious, but the deteriorating effects of earthquakes on track irregularities increased significantly with increasing PGA.

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown.

The conventional modal strain energy (MSE), as a practical objective function, suffers from the lack of access to the damaged stiffness matrix and uses the intact stiffness matrix of the structure instead. To overcome the aforementioned deficiency of the MSE, this study proposes a reformed elastic strain energy-dissipation criterion called the “augmented modal strain energy” (AMSE) which is composed of relative differences of natural frequency and mode shape. In the AMSE not only the effects of the energy-dissipation criterion as a function of natural frequency but also the equilibria of the elastic strain energy as a function of mode shape are considered. Hereupon, the AMSE is implemented along with the interactive autodidactic school (IAS) optimization algorithm to investigate the effectiveness of the proposed identification method. In this regard, the AMSE is verified by assessing three benchmark truss and frame structures. The obtained results confirm the reliable performance of AMSE in both terms of intensification and diversification. Furthermore, it is observed that despite using noise-polluted modal data, the proposed AMSE not only identifies the damage location accurately, but also anticipates the extent of damage precisely. Consequently, the proposed energy-dissipation-based objective function (AMSE) is suggested, along with the IAS optimization algorithm, as a robust technique for the damage detection of structures.

The aim of this work is to investigate the free vibration and buckling characteristics of sigmoid functionally graded (FG) nanoplate with the influence of porosity. The modified rule of the mixture is utilized to calculate the effective material properties of porous sigmoid functionally graded (P-SFGM) nanoplate. Three schemes of porosity distribution, including uniform, symmetric and nonsymmetric are investigated. The first-order shear deformation theory is utilized to simulate the displacement fields of P-SFGM nanoplate. Eringen’s nonlocal elastic theory and isogeometric analysis (IGA) are used to establish the governing equations for free vibration and buckling analysis of nanoplate structure with small size effect. By using NURBS as a basic function, IGA can fulfill the higher-order derivative requirement of governing equations. The accuracy of the presented solution is verified. By taking the nonlocal parameter into account, the stiffness of the plate is softened. Also, the effects of porosity distribution across the plate’s thickness, porosity parameter, material power index, boundary conditions (BCs) and aspect ratio on the frequency response of P-SFGM nanoplate are presented.

Wind turbines are slender and flexible structures which can undergo large amplitude vibrations when subjected to external loads and, an important way to reduce these excessive vibrations is to apply structural control. In this work, the vibration control of the coupled wind tower–blade system subjected to external lateral loads and rotating blade is studied. To model the tower and blade, the nonlinear Euler–Bernoulli beam theory was applied, and the structural control device considered is a nonlinear inverted tuned mass damper pendulum (ITMDP), located at the top of the tower. The Rayleigh–Ritz method, together with Hamilton’s principle, is applied to obtain a set of coupled nonlinear ordinary differential equations of motion which are in turn solved by the Runge–Kutta method. First, the dynamic instability of the system is studied by considering the variation of the natural frequencies of the tower, as a function of the speed of rotation of the blade and the veering phenomenon is observed. The optimum parameters for the ITMDP are obtained and, a nonlinear dynamic analysis is performed to evaluate the influence of the tuned mass damper (TMD) in the nonlinear regime, by obtaining the time responses, resonance curves, Poincaré maps and basins of attraction. The obtained results show the importance of considering the coupled system and the good performance of the structural control in the dynamic behavior of the system.