International Journal of Structural Stability and Dynamics

The dynamic behaviors of large-scale hoop truss antennas (HTAs) are significantly influenced by the nonlinear torque transmission properties of flexible hinges. Due to the nonlinearity of the hinge, the HTA can be easily excited to exhibit internal resonances that result in the energy exchange between the adjacent two or three modes. This paper focuses on the 3:1 internal resonant responses of an articulated HTA induced by the nonlinearity of the hinge. The analytical modes are obtained by using the global mode method (GMM) and are validated by finite element method (FEM). Then the partial differential equations (PDEs) of planar motions are discretized into ordinary differential equations (ODEs) by Galerkin’s technique. The multiple time scale method is employed to obtain the four-dimensional modulation equations of the HTA with primary and 3:1 internal resonance. By using the Newton–Raphson iteration and the pseudo arclength continuation, frequency–response and force–response curves are obtained to investigate the theoretical steady-state vibrations of the HTA. Moreover, the influence of the cubic spring stiffness, damping, and external excitation amplitude on the system’s nonlinear dynamic behaviors are investigated. The numerical simulation reveals that the articulated multi-beam hoop structure exhibits typical nonlinear phenomena such as hardening-spring type characteristic, jumps, bi-stability, and double peaks. The research findings contribute to the reliable structural design and vibration control of the articulated hoop truss antenna.

The wind field environment in mountainous zones is complex. If the wind field characteristics are regarded as stationary and Gaussian, the inaccurate response results of the structure will be obtained. In this paper, a fatigue evaluation method of steel truss suspension bridge members under non-stationary and non-Gaussian buffeting is proposed. This approach can solve the fatigue evaluation problem of steel truss suspension bridge members under mountain wind. Firstly, the normal wind speed (stationary and Gaussian) is obtained by the harmonic wave synthesis method. The wind speed considering non-stationary characteristics is obtained by adopting time-varying power spectrum. Secondly, through non-linear translation, the wind speed considering non-stationary characteristics is transformed into wind speed considering both non-Gaussian and non-stationary characteristics. Finally, combined with the Palmgren–Miner rule, the effects of three different buffeting responses on fatigue damage of suspension bridge members are studied. They are traditional buffeting response, buffeting response considering non-stationary characteristics and buffeting response considering both non-stationary and non-Gaussian characteristics. The results indicate that the fatigue damage of the main cable of the suspension bridge is the biggest at the mid-span. Under the same wind speed, considering two characteristics, the component fatigue damage will further increase.

Although seismic isolation is a well-accepted design strategy for bridges to provide structural earthquake resistance, for bridges with massive piers, it may unexpectedly pose an abnormal influence on the seismic response of bridges due to the effect of substructure mass. This study investigates the effects of bearing friction and pier mass on the seismic performance of bridges isolated by friction pendulum bearings (FPBs). Nonlinear time history analysis is conducted to demonstrate the variation of the bridge peak responses with different bearing frictional coefficients and pier mass. The inherent influential mechanism of the frictional coefficient of FPBs is also discussed in the current study. The results of the analysis show that for FPB-isolated bridges with massive piers, the peak base shear forces of piers first decrease and then increase with the increase of the bearing frictional coefficient. Such a phenomenon may be attributed to the fact that the inertia force of the massive piers will be altered by the variation of bearing friction. The outcome of this study provides a useful reference for practical engineering that the seismic base force of massive bridge piers calculated under a specified bearing frictional coefficient may be smaller than the actual response and cause reduced safety to bridges.

Advanced automated fiber placement technologies enable variable angle tow sandwich structures possible, which provides an extended flexibility in stiffness tailoring to design lightweight sandwich structures with superior performance. However, complex-shaped openings within this new type of sandwich structures bring great challenges when dealing with vibration problems. In this paper, an isogeometric analysis (IGA) formulation based on a novel high-order sandwich plate theory is developed for the first time to the study of free vibration of variable stiffness sandwich plates with complex-shaped cutouts. The proposed new high-order sandwich plate model is formulated based on the idea of layerwise modeling, that is, the first-order shear deformation theory is employed to characterize the kinematics of the two skins, while the high-order theory based on hierarchic Legendre polynomials is applied to describe the kinematics of the core. The weak-form governing equations for free vibration problems of the perforated sandwich plates are first derived from the virtual work principle, and then the IGA formulation based on the non-uniform rational B-splines (NURBS) is applied to obtain the eigenfrequencies and the corresponding eigenmodes. The novelty of this work lies in that the introduction of hierarchic Legendre polynomials enables the kinematics of the core to be enriched to any desired expansion order, which shows great superiority over its traditional counterpart such as extended high-order sandwich panel theory (EHSAPT). On the other hand, the developed IGA procedure based on the novel high-order sandwich plate theory is applicable to a general sandwich plate even with complex-shaped cutouts. The accuracy and effectiveness of the developed IGA procedure are validated by comparing against the results available in the literature and those obtained using ABAQUS. Effects of cutout size, boundary condition and fiber angle on the vibration characteristics of the perforated sandwich plates are discussed in numerical examples. The results presented herein may be beneficial for the design of variable stiffness sandwich plates with complex-shaped cutouts.

This study employed a method of analysis to examine the free oscillation behavior of functionally graded (FG) porous-cracked beams under axial loads and varied boundary conditions. The cracked beam system was composed of interconnecting beam segments kept together by massless rotating springs. Based on the Timoshenko beam theory (TBT) or Euler–Bernoulli theories (EBT), each segment was sectionally flexible. Using a power-law function, mechanical features were expected to gradually change along with the height of the beam. Two different pore distributions, even and uneven, were also explored. Subsequently, Hamilton’s theory was used to derive the equations of kinematic motion for FG-cracked porous beams, and the transfer matrix (TMM) approach was used to get the determinantal equation. A parametric analysis was performed to evaluate how cracks, porosity distribution, slenderness ratio, volume fraction index, boundary conditions, and axial load affect the dynamic characteristics of FG beams. The results revealed that the suggested analytical approach provided several findings that were similar to the existing analytical outcomes in the literature. Moreover, the computer analysis demonstrated that porosity, especially when there were cracks, significantly affected the eigenfrequencies of FG beams. Hence, this study opened the door for possible applications in a variety of engineering settings by offering some crucial insights into the complex dynamics of FG porous-cracked beams.

In this study, a free vibration model of bi-directional functionally graded (BD-FG) annular microplates is established based on the modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT), and the corresponding governing equations are derived from Hamilton’s principle. The annular microplates are assumed to be composed of metal and ceramic materials, and the equivalent material properties are a combination of power-law function and exponential ones. The generalized differential quadrature method (GDQM) is used to obtain the vibration frequencies and mode displacements for the C–C, S–C, C–S, and S–S (S: simply supported; C: clamped) annular microplates. The convergence and validity of the proposed model are verified through selective numerical examples. Further, the effects of gradient index, material length scale parameter, boundary conditions, and geometrical dimensions on the symmetric/asymmetric vibration frequencies of the annular microplate are explored. The modal assurance criterion is applied to estimate the influence of the radial gradient index and material length scale parameter on different-order mode displacements of the annular microplate. The results show that: (1) the vibration frequencies of the annular microplate are sensitive to changes in the geometry and boundary conditions; (2) compared with the axial gradient index, the radial gradient index not only affects the vibration frequencies of the annular microplate, but also impacts the distribution of the highest and lowest points of the vibration mode displacements as well as the vibration mode nodal lines; (3) as the material length scale parameter increases, the vibration frequencies are significantly increased, and the higher-order vibration modes of the annular microplate also change.

This paper presents an advanced numerical model based on Carrera unified formulation (CUF) and isogeometric analysis (IGA), the size-dependent finite element unified formulation model is proposed to investigate the static bending and free vibration of laminated composite nano-plate. The CUF type of trigonometric function with nine degrees of freedom is used to simulate the displacement fields of laminated nano-plate. The size effect of nano-plate structures is included through the Eringen’s nonlocal elastic theory. The size-dependent governing equations for static bending and free vibration of laminated are established based on CUF, IGA and nonlocal theory. The correctness of the presented numerical model is verified by comparison with existing solutions. Furthermore, with the addition of a nonlocal effect, the plate’s stiffness decreases correlating to an increase in nonlocal parameter. Through different calculations, the changes in the static and free vibration responses of laminated composite nano-plate are effected by nonlocal parameter, plate length-to-thickness ratio, and boundary conditions including Young’s modulus ratio.

Beam string structures (BSS) are frequently employed in large-span spatial structures due to their high load-carrying efficiency and elegant appearance. Owing to the neglect of the influence of prestress, the natural frequency of the BSS is often overestimated which could be crucial to the dynamic behavior of BSS. This paper presents an exact matrix stiffness analysis method (MSM) for investigating the relationship between prestress and the natural frequency of the planar BSS. A novel dynamic stiffness matrix of beam–columns considering the natural frequency and axial force is used to develop the MSM. The dynamic analysis of the structural vibration stability of BSS is performed by using the global structural stiffness matrix which is assembled from the element stiffness matrices in the global coordinate system. The proposed MSM with the exact dynamic element stiffness matrix for the dynamic analysis of the BSS is verified by comparing with previous results based on the finite element method. The illustrative examples demonstrate that the prestress in the cable has a negative effect on the natural frequency of the BSS and should be considered in the dynamic analysis. As the axial force increases from zero to the buckling load $P_{cr}$, the natural frequency of the BSS decreases from the maximum vibration frequency to zero. The influence of prestress on the vibration frequencies of BSS is particularly significant when the prestress to balance the loads is large, especially in the case of large dead and live loads (e.g. floor slabs).

Modal identification of bridges based on the responses of moving vehicles, termed as the indirect method, has drawn much attention in recent years. This indirect method has been proven to be capable of identifying bridge frequencies and mode shapes in the feasibility research. However, in the presence of additional factors such as vehicle speed and road surface roughness, it is difficult to identify high-order frequencies and high-resolution mode shapes of the bridge. The authors previously proposed a tractor-double-trailers model and the time–domain subtraction method to obtain the relative displacement of two trailers for bridge modal identification. In this study, the authors develop a methodology to improve the identification performance by combining the EMD technique and the time–frequency analysis method. The EMD technique is applied to separate the multi-source response signals of the trailers to obtain the signal component that contains only the bridge vibration. Then, different time–frequency analysis methods such as the short-time Fourier transform (STFT), Wigner–Ville distribution (WVD), and continuous wavelet transform (CWT) are adopted to construct the high-resolution bridge mode shapes. Numerical studies with one-dimensional and three-dimensional bridge models are conducted to verify the proposed method and investigate the effects of different factors. Finally, a laboratory test is implemented on a scaled bridge to verify the performance of the proposed method. The results show that the proposed method is able to separate the vehicle frequency and bridge frequencies, which facilitates the identification of bridge frequencies from the dynamic response of moving vehicles. Meanwhile, the CWT method performs the best in the identification of modal shapes among the three time–frequency analysis methods.

A smart foam is a vibration absorption structure integrated with piezoelectric material and shows promise for a highly efficient structural vibration reduction both passively and actively. The arrangement of the smart foams on the primary structure is a key issue in practical engineering. In this work, the vibration reduction performances of distributed smart foams attached to a simply supported beam are investigated, and the distribution scheme is optimized. The dynamic equations of the vibration system are established for passive and active vibration reduction, respectively. The frequency responses are analyzed based on a Newmark-$\beta$ method, and the accuracy is verified by a finite element analysis. An optimization method based on the genetic algorithm is proposed for the smart foams’ quantity and locations. The study reveals that, with the same total attached mass (1% of the beam mass), a limited distribution of smart foams achieves a larger vibration reduction ratio than a single smart foam or uniformly distributed smart foams. For the passive reduction mode, the optimal scheme is to arrange four smart foams at the middle of the beam, and a reduction ratio of 38% is achieved. It is related to both the first-order modal shape of the beam and the mass distribution of smart foams. For the active reduction mode, the optimal scheme is to arrange two smart foams separately, and 98% of the vibration is reduced. The optimal location is no longer at the middle of the beam, because the active moment of the piezoelectric beam makes the main contribution, rather than the passive vibration absorption. This research provides an optimization method and instructions for both passive and active vibration reductions of smart foams.

An increase in the nonlinearity of the bridge will lead to a more obvious vehicle–bridge interaction effect and affect the vehicle response and driving comfort as the span increases. This paper establishes a refined finite element model of vehicle–bridge coupling for the 575 m long-span concrete-filled steel tubular arch bridge, Pingnan Third Bridge. Coupling vibration responses under different vehicle speeds, vehicle weights and road conditions of this bridge is analyzed. Then its comfort is assessed according to the comfort criterion. The results show that the vehicle–bridge coupling model has good agreement with the field test. The dynamic response of the bridge within the speed limit has no significant linear relationship with the magnitude of the vehicle speed without considering the pavement class. When the vehicle exceeds the speed limit, the dynamic response increases sharply with the increase in speed. The increase in vehicle weight leads to an increase in the maximum dynamic deflection of the bridge and a decrease in the impact coefficient, but the actual total response of the bridge does not decrease. The worse the road surface condition, the more dramatic the dynamic response of the bridge structure, taking into account the road surface level.

Aiming at rapid and economical damage detection of a large number of simple supported bridges, a new structural damage identification method under moving load based on variational mode decomposition (VMD) and deep learning is proposed. Firstly, a moving vehicle is used as an exciting load to invoke structural damage feature and enhance the signal-to-noise ratio, and the structural vertical acceleration response is extracted by a finite element simulating analysis under various damage cases. In order to simulate the influence of noise and expand the samples, Gaussian white noise is added to the extracted data, and then the response signal is decomposed into a series of intrinsic mode functions (IMFs) using VMD, and the optimal IMF component is selected as the damage sample of the structure. Then, a one-dimensional convolutional neural network (CNN) model is built and trained by the various samples of damage. The vibration response of the practical bridge is processed and inputted by the trained CNN model to identify the location of the damage and degree of the structure. Finally, the effectiveness and anti-noise performance of the proposed method are verified through numerical analysis and a simply supported beam bridge model experiment. The results show that the average identification accuracy of the numerical simulations and experimental is 93.4% and 86.8% with 20% Gaussian white noise, respectively. Sensors at different locations have almost the same identification effect for various cases of damage, so it is possible to identify structural damage only using a small amount of accelerometer.