International Journal of Structural Stability and Dynamics

A first attempt is made in this paper to explore new analytic shear buckling solution of clamped rectangular thin plates by a two-dimensional generalized finite integral transform method. The problem is classical but challenging due to the mathematical difficulty in handling the complex boundary value problem of the governing higher-order partial differential equation (PDE). Taking the vibrating beam functions as the integral kernels, and imposing the double transform, the problem comes down to solving a system of linear algebraic equations, thereby the analytic solution is obtained in a straightforward way. The present method is confirmed to be highly accurate with fast convergence, which agrees very well with both the finite element method (FEM) and energy method from the literature. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods.

This paper presents an analytical framework for the horizontal dynamic analysis of a large-diameter pipe pile subjected to combined loadings, in which the pipe pile is simulated by the Timoshenko beam theory. The derived solution allows us to evaluate the effects of both the shear deformations and vertical loads on the horizontal dynamic performance of the pipe pile. The proposed solution provides appropriate estimates of complex impedances of large-diameter pipe piles, unlike the earlier solutions based on the Euler–Bernoulli beam theory for describing the pile behavior, which ignores the shear deformation of the pile. The results indicate that the Euler–Bernoulli theory overestimates the pipe pile’s horizontal impedance, while overestimating the effect of vertical loads on its horizontal performance.

Cable-stayed bridges are of the most unique and cost-effective designs in modern bridge engineering. A key feature of these structures is that the cables or stays run directly from the tower to the deck. The nonlinear dynamic behavior of these cables can significantly affect the resilience and safety of the bridge. In this context, a deeper understanding of the bifurcation and chaotic mechanisms of cable vibration is highly desirable. Accordingly, in this study the nonlinear dynamic equation of a planar cable is derived for quantitative and qualitative analysis. The nonlinear system is solved asymptotically, using the conventional perturbation and two-timing scale methods, to study the periodic motion of the cables. The obtained solutions are primarily affected by the control parameters and the initial conditions. The asymptotic solutions are also simulated numerically. It is found that the chaotic behavior of cables is greatly affected by the governing parameters, including the cable dimensions, vibration amplitude, damping effect, and excitation frequency. Finally, seven state variables of the nonlinear system are analyzed to investigate the occurrence of bifurcation.

In this paper, the response of a bounded one-dimensional medium (strip) subjected to a thermal shock is investigated. The strip is made of a linear visco-elastic material, of which the time-dependency of the elastic modulus is described by the simple Kelvin–Voigt model. To obtain the displacement, stress and temperature within the strip, the Lord and Shulman theory of generalized thermo-elasticity containing a single relaxation time is used. Three coupled equations, namely, the equation of motion, the modified Fourier law and the second law of thermodynamics, are established in terms of the displacement, temperature and heat flux. It is worth noting that the second law of thermodynamics is not linearized and is kept in the nonlinear form. The equations derived are first represented in a dimensionless presentation. Then, they are discretized using the well-known generalized differential quadrature. To obtain the response of the strip in time, the Newmark time marching scheme is implemented. It should be mentioned that due to the nonlinear nature of the governing equations, the successive Picard algorithm is used. The results of the present study are compared with those available in the literature for an elastic strip. Besides, numerical results are given for a strip made of Kelvin–Voigt visco-elastic material. The effects of visco-elastic parameter, coupling parameter, thermal relaxation time and nonlinearity are discussed in numerical examples.

This work presents the nonlinear post-buckling behavior of carbon nanotubes (CNTs) reinforced sandwich composite annular spherical (AS) shells supported by elastic foundations in the thermal environment. This paper takes advantage of the sandwich-structured configuration with three layers: two nanocomposite face sheets and an isotropic core to analyze the static problem. Due to the precious properties, CNTs are applied to reinforce nanocomposite face sheets of AS shells. The governing equations of the nonlinear mechanical response of CNTs reinforced sandwich-structured composite (SSC) AS shells are achieved by using the classical shell theory (CST) and taking von Kármán’s geometrical nonlinearity into account. Applying Airy’s stress function and an approximate solution, we propose a form of stress function for CNTs reinforced SSC AS shells. The detailed effects of different types of CNTs’ reinforcement and volume fractions, geometrical parameters, core to face sheet thickness ratio, Winkler and Pasternak elastic foundations on the nonlinear mechanical post-buckling analysis are examined.

The buckling behavior of partially composite layered columns (PCLCs) under axial compressive load is significantly influenced by the slip at the interface of load carrying layers, which brings complexity to the analysis. In this paper, a matrix method based on the Hencky bar-chain model (HBM) is developed for the buckling analysis of PCLCs. The conventional assumption of HBM is modified to consider the interfacial slip properly. Three illustrative problems are presented to show the solving procedure of the HBM-based matrix method. The results are compared to those obtained through analytical formula or finite element method (FEM), and the applicability of the developed method in the buckling analysis of PCLCs with various sectional compositions and boundary conditions is validated. It is proved that the buckling load can be predicted accurately by the developed method. The method is easy to handle, highly adaptable and widely applicable, thus is a promising tool for the buckling analysis of PCLCs.

This paper presents a new integrity assessment and damage localization method for piles based on one-dimensional wave propagation theory by integrating the analytical mode decomposition (AMD), recursive Hilbert transform (RHT) and complex continuous wavelet transform (CCWT) into a single assessment tool. The AMD is first used as a band pass filter to extract the mono-component over a frequency band of interest from the response of a pile head, aimed at attenuating the interference from various noisy signals. Then, the mono-component signal is demodulated into a purely frequency-modulated signal by means of RHT, which greatly reduces the interferences from the amplitude-modulated function. Finally, the CCWT is utilized to process the frequency-modulated signal and to calculate phase angles; the latter are subsequently mapped into the time–frequency domain to localize pile damage. The methodology is verified by a numerical example, in which a concrete pile is modeled by the finite element method considering the soil-pile interaction, and by an experimental case study on an actual pile. The results from the numerical and experimental examples demonstrate that the proposed method improves the efficiency of damage identification when compared with other three methods ($\mathrm{\text{AMD}}+\mathrm{\text{CCWT}}$, $\mathrm{\text{RHT}}+\mathrm{\text{CCWT}}$ and CCWT). In addition, the proposed method enables the localization of damage in full-scale piles situated in soil with an acceptable engineering accuracy by mutual validation with other pile integrity assessment methods, e.g. the ultrasonic emission method.

In this study, the combination of an expansion tube and a deformable rigid tube with axial splitting is developed as a new mechanism for use as an impact energy absorber. The impact absorbing structure consists of two circular tube forming dies, with each die allowing the tube to expand and to split. The latter is used to remove away radially the debris after expansion and splitting, so that the absorption process can continue without being obstructed by the debris itself. This paper presents the experimental and theoretical investigation of the combined expansion tube-axial splitting as an impact energy absorber. The experiment by the laboratory scale impact testing has been done with a variation of the parameters such as pipe thickness ($t)$, angle of splitter ($\alpha )$, comparison of dies upgrading diameter ($D_2)$ and inner pipe diameter ($D_1)$ ($D_2$/$D_1)$. The theoretical investigation is carried out with a literature study related to the mechanics of material and theoretical studies from previous research studies. The final result of this paper, i.e. a new formula proposed to calculate the mean load, is reflective of the study of a combined expansion tube with axial splitting. The difference between the results of analytical calculation and experiments is 10.13%.

In this paper, the buckling response of laminated functionally-graded CNT-reinforced composite (FG-CNTRC) plate structure is predicted under various types of non-uniform edge compression loading. For the finite element (FE) discretization of the plate, a nine degree of freedom (DOFs)-type polynomial-based higher-order shear deformation theory (HSDT) is considered. The application of non-uniform edge load causes the in-plane stress distribution to be non-uniform. Hence, the in-plane stresses need to be evaluated prior to the buckling analysis. These in-plane stresses are calculated using the in-plane stress analysis method by FE approach or the in-plane elasticity approach. The differential equations are obtained by employing the Lagrange equation of motion and solved as a general eigenvalue problem, after the differential equations are converted into homogeneous equations by means of FE procedure. The accuracy and adaptability of the present model are validated by comparing the present result with the available literature. Further, the impact on the buckling response of the laminated FG-CNTRC plate is investigated by various parameters such as span thickness ratio, aspect ratio, various edge constraints, and different types of non-uniform edge load, CNT fiber gradation and temperature dependency material properties.

This paper investigates the seismic performance of bridges installed with a sliding-lead rubber bearing (LRB) isolation system subjected to near-fault earthquakes. A three-span continuous bridge isolated with sliding-LRB system is used as an example. Nonlinear time history analyses are conducted to investigate the sensitivity effects of isolation period, friction coefficient and sliding displacement limit on the bridge responses. The responses of the sliding-LRB system are compared with those of the conventional LRB system. The results show that the base forces of the piers can be reduced by employing proper friction coefficients. However, the residual displacement of the sliding-LRB system may be larger compared with that of the conventional LRB system. To overcome this disadvantage, an improved solution to reduce the residual displacement is proposed with its effectiveness investigated. It was also demonstrated that the residual displacement and peak displacement can be effectively reduced by employing the shape memory alloy devices in the sliding-LRB system without significantly increasing the base forces.

This paper presents a coarse-fine self-learning active mass damper (AMD) for frequency tracking vibration control. Even though the AMD is under unknown disturbance, it can obtain the exact exciting frequency of primary system after several self tries and achieve significant vibration suppression. The frequency tuning algorithm consists of two improved techniques, namely, the variable-gain frequency estimator and variable learning rate $Q(\lambda )$-learning algorithm, both aim to accelerate the convergence speed of frequency estimation. The coarse tuning method helps to tune the AMD’s natural frequency in a relatively wide effective bandwidth using frequency estimator and the fine tuning method can achieve precise tune in a tiny-scale bandwidth. The simulation results demonstrate that this coarse-fine learning AMD can help obtain the exact exciting frequency after several times of self-learning, and the vibration of primary system is dramatically attenuated by tuning the AMD’s natural frequency to match with the exciting frequency. This is the first time for the tuning method of mass damper proposed using machine learning, which can help obtain the exact exciting frequency after several self-tries.

This paper presents a new method for analyzing the dynamic behavior of train–bridge systems with random rail irregularity aimed at its simplicity, efficiency and accuracy. A vertical train–bridge system is considered, in which the bridge is regarded as a series of simply supported beams, and the train is regarded as a multibody system with suspensions. The Karhunen–Loéve expansion (KLE) is used to simulate the stochastic vertical rail irregularities, and the mean and standard deviation of the system response are calculated by the point estimate method (PEM), based on the Gaussian integration and the dimension reduction method. The proposed KLE–PEM method, which combines the key features of the KLE and PEM, is validated by comparing the results obtained with existing ones. The Monte Carlo simulation (MCS) is used to verify the rationality of the results obtained by the KLE–PEM approach. The results show that the KLE–PEM approach can accurately calculate the response of the vertical train–bridge interaction system with random irregularity. This paper further discusses the responses of the train and bridge system with different speeds for the train.

This paper presents a new approach for modeling the slab tracks by using the spline function to derive an element that is capable of describing the vertical motions of the entire slab. The accuracy and advantages of the method are verified through comparison with the finite element method (FEM) by the frequency response analysis for the CRTS-III slab track system. With this, a three-dimensional train–slab track-coupled dynamic (TSTCD) model is developed and solved by a hybrid explicit–implicit time integration method. Finally, the characteristics and feasibility of the developed TSTCD model are demonstrated through two typical case studies together with the comparison made for verifications. The results indicate that the proposed method provides an alternative approach for modeling the slabs, by simplifying the modeling process and decreasing the computational time without losing accuracy, with respect to the FEM. Besides, the modes of the slab appear many dips and peaks above the first resonant frequency, leading to complicated frequency responses of the CRTS-III slab. Moreover, the developed TSTCD model is not only feasible, but also capable of describing the slab vibrations at medium-high frequencies.

The paper presents simple computational algorithms for analyzing the lateral-torsional buckling of prismatic beams with rectangular cross-sections under bending action due to uniform and nonuniform loads by the Adomian decomposition method (ADM) and variational iteration method (VIM). Unlike the numerical techniques that lead to a discretization process, the proposed method allows us to derive the solution in terms of an analytical function for the problem considered. Although the governing equations of the problem appear as a system of two coupled variable coefficient ordinary differential equations, they reduce to a single equation for rectangular beams. The buckling loads for different loading conditions are computed, with the results for the simple beam compared with previous available results by the differential transformation method (DTM), variational iteration method (VIM) and finite element method (FEM) based on coupled governing equations. The results clearly show the efficiency and advantage of the present technique over those based on the coupled governing equations using the DTM and VIM in view of the number of terms required to obtain the convergent solution.

With the rapid development of material science, the original aluminum alloy shield structure of spacecraft has been gradually replaced by sandwiched structure of carbon fiber reinforced resin matrix composite structure with aluminum honeycomb. In order to reveal the damage characteristics induced by debris impacting on shield structure of spacecraft and aiming at the engineering requirements that spacecraft undergo alternately high and low temperature environment during on-orbit operation, CFRPs/aluminum honeycomb core sandwich shield structure is used as the impact object. The damage characteristics of 2A12 aluminum projectile impacting on CFRPs/aluminum honeycomb sandwich structure with different aluminum honeycomb arm lengths at different impact velocities are studied by using the high and low temperature system for the target and the loading system of two-stage light gas gun. The experimental results show that the arm lengths of aluminum honeycomb have little effect on the perforation area of front and rear surfaces of CFRPs/aluminum honeycomb sandwich structure at high temperature, but the impact speed has a great effect on the perforation areas of front and rear surfaces of rear panels. The lower the impact speed is, the smaller the perforation diameter is. The deformation and ablation areas of the front and rear surfaces of the aluminum honeycomb increase with the increasing of the arm length of the aluminum honeycomb. At the same time, the physical quantities mentioned above have similar changes in low temperature environment. The fitting formulas, such as the relationships among perforations of the front and rear surfaces of CFRP and the arm lengths of aluminum honeycomb, and ablation area of aluminum honeycomb and the arm lengths of aluminum honeycomb are given at the given experimental conditions. The micro-morphology and damage characteristics of the panels and aluminum honeycomb are analyzed at the different locations near the impact point at high temperature.