International Journal of Structural Stability and Dynamics

The critical pressure is determined for a trapezoidal vault with rigid members and semi-rigid joints. For maximal volume enclosed per boundary length, it is found that the critical pressure is highest when the vault symmetrical, with top three pieces 39.64% of the base length. The upper two joints should also be heavily strengthened.

The present study focusses on buckling and post-buckling of graphene-reinforced laminated composite plates subjected to uniaxial and biaxial loadings. Poly-methyl-methacrylate (PMMA) is used for matrix. Depending on the type of graphene distribution in each layer, three patterns are considered for the plate cross-section. Graphene sheets are considered in both perfect and defective forms. Kinematics of the plate is modeled using the first shear deformation theory and for large deformation, von Karman nonlinearity is considered. Mechanical properties of each layer are evaluated using the molecular dynamics simulation. Besides, Halpin–Tsai and rule of mixtures are calibrated for graphene PMMA composite. Stability equations are solved based on the incremental-iterative type of Ritz method. In order to validate the solution procedure, comparison studies are conducted on isotropic plates. Numerical results are presented for four different types of boundary conditions. It is shown that, for all types of boundary condition, X-pattern provides higher buckling load. Furthermore, it is found that plates reinforced by defective graphene sheets with 5% vacancy provide lower buckling and post-buckling resistance with respect to those reinforced by pristine graphene.

This paper investigates the rocking behavior of two free-standing columns capped with a freely supported superstructure in an effort to explain the seismic stability of Tang-Song timber frames subjected to pulse-type excitations. The geometric characteristics of the column determine the acceleration amplitude needed to create uplift of the rocking frame, which also affect the loss of energy during impact along with the mass ratio of the superstructure to the column. Two distinct rocking modes are analyzed according to whether the frame can be limited by the tenon-mortise joint. The expression that yields the minimum acceleration required to overturn the frame is derived within the limits of the linear approximation of the governing equation of motion. Different safety and overturning regions plotted on the stability diagrams indicates that the partially joint limitation may weaken the seismic behavior. The entirely limited frame will rock within the fixed amplitude caused by the joint gap and never topple down. Probability analysis results of the entirely limited frame suggest that a great majority of this type of traditional timber structures have excellent seismic capacity to resist the horizontal excitation.

This paper presents the moving element method (MEM) for dynamic analyses of functionally graded (FG) plates resting on Pasternak foundation under moving harmonic load. The Mindlin plate theory is used to model the FG plates. Macroscopic material properties of FG plates are assumed to continuously vary across the thickness direction by a simple power-law distribution. The governing equation of the FG plate is formulated in a coordinate system which moves along with the applied load. In addition, the method simply treats the moving load as “stationary” at the discretized node of plate to completely eliminate the update procedure of force vector due to the change of contact point with elements. To verify the accuracy of the computational paradigm, static and free vibration analyses of FG plates are examined first. Dynamic analyses of FG plates subjected to a moving harmonic load are then conducted to investigate the effects of various parameters such as volume fraction exponent, Young’ modulus, load velocity, foundation damping coefficient and load acceleration/deceleration on dynamic responses of the plate.

As a classic bridge type, cable-stayed bridge is widely used because of its superior spanning capacity. Based on the mechanical characteristics of stay cable supporting deck, we propose a novel mechanical model aiming to evaluate the vertical bending stiffness of a floating cable-stayed bridge, namely, multi-beam model with discrete springs. First, a single-tower cable-stayed bridge is modeled as a triple-beam model with discrete springs in order to introduce the novel method easily. In this model, the stay cables are simplified as springs without mass and the single tower is regarded as an Euler–Bernoulli beam with consideration of the effect of axial force. At the same time, the bridge deck has been cut into two Euler–Bernoulli beams at the intersection of a deck and a tower. Then equations governing vibrations of the beam and tower are derived according to Hamilton’s principle for dynamic problems in elastic body under equilibrium state. The program is established by transfer matrix method to solve the eigenvalues of the system along with its boundary and matching conditions. Thus, the vertical bending stiffness of the floating cable-stayed bridge can be evaluated based on the frequency. In addition, the influences of the cables’ material, location, stiffness and number on vertical bending stiffness are analyzed in detail when the steel cables are replaced with CFRP cables. Lastly, the same method is directly extended to modeling the floating multi-tower cable-stayed bridge. The results, which are validated by commercial finite element software, demonstrate that the proposed mechanical model and method are both valuable and significant not only in theoretical research and calculation but also in design of engineering.

Exact solutions for the torsional bifurcation buckling of functionally graded (FG) multilayer graphene platelet reinforced composite (GPLRC) cylindrical shells are obtained. Five types of graphene platelets (GPLs) distributions are considered, and a slope factor is introduced to adjust the distribution profile of the GPLs. Within the framework of Donnell’s shell theory and with the aid symplectic mathematics, a set of lower-order Hamiltonian canonical equations are established and solved analytically. Consequently, the critical buckling loads and corresponding buckling mode shapes of the GPLRC shells are obtained. The effects of various factors, including the geometric parameters, boundary conditions and material properties on the torsional buckling behaviors are investigated and discussed in detail.

An unusual amplitude growth of the steady-state response for structures with high natural frequencies was found in explicit or semi-explicit structure-dependent integration algorithms with unconditional stability, second-order accuracy and no overshoot. This paper proposes a general formulation for eliminating such an unusual amplitude growth, by incorporating the load-dependent term into the displacement recursive formula without changing the numerical properties of the integration algorithm. Compared with the existing formulation using the local truncation error for eliminating the unusual amplitude growth, the proposed formulation has the advantages of less symbolic operations, while naturally including the existing formulation. In addition, it is observed that the coefficients of the load-dependent term are proportional to the limit values of the displacement coefficients in the displacement recursive formula as the natural frequency of the system tends to infinity. Then, the general formulation of the load-dependent term is tested for 15 structure-dependent integration algorithms to verify its correctness. Finally, numerical examples of linear and nonlinear multiple-degrees-of-freedom systems illustrate that the general formulation can remove effectively and conveniently the unusual amplitude growth for dynamic response analyses.

In this paper, the dynamic stress and radial/lateral vibration of circular/annular discs made of fractional-order viscoelastic materials under nonuniform mechanical loads are investigated for the first time, utilizing the exact 3D theory of elasticity, rather than the plate theories. The governing equations of motion of the disc are derived based on the Kelvin–Voigt fractional viscoelastic model. To solve these equations, the spatial partial and the time ordinary derivatives are replaced by adequate central, backward or forward finite difference expressions. Then the resulting Caputo-type time-dependent system of the coupled integro-differential governing equations of the fractional-order is solved by a novel numerical procedure. Namely, a time-marching procedure is employed to extract the time histories of the responses, in the space-time domain for various time and spatial distributions. Finally, comprehensive sensitivity analyses and various 3D plots are presented and discussed. In this regard, effects of the fractional-order of the constitutive law, viscoelastic parameters, material rigidity, distribution and time variation patterns of the nonuniform distributed transverse loads, and boundary conditions on the distributions of the displacement and stress components are investigated.

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

According to Eurocode 3, the design of plated structures may be carried out using three different approaches: effective width method, reduced stress method, and finite element analysis (FEA). For the particular case of elements under compression, the effective width method makes use of the plate buckling slenderness to obtain the corresponding effective cross-sectional area. Since the effective width method was developed for uniform web and flange panels, Eurocode 3, and most design codes, has no specific provisions for the particular case of nonrectangular panels, stating that they may conservatively be treated as rectangular panels with this larger width. With the final objective of improving design rules for tapered members, this paper first presents finite element (FE) numerical results for the elastic buckling coefficient of trapezoidal plates under compression. Four cases are considered which correspond to different boundary conditions usually present in webs and flanges of steel profiles and rectangular hollow sections. Numerical results are used to propose approximate closed-form expressions that can be used to compute local buckling loads for trapezoidal plates in a direct way. Additionally, ultimate strength is obtained for a number of compressed trapezoidal plates using nonlinear geometric and material FEA with equivalent geometric imperfections. Contrary to the philosophy of Eurocode 3, results show that there is no clear correlation between buckling loads and ultimate strength.

This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

China Railway Track System II (CRTS II) slab ballastless track structure is one of commonly adopted track systems on the high-speed railway bridge, which has been found seismically vulnerable under strong earthquakes. To investigate the earthquake-induced damage mechanism of the CRTS II slab ballastless track structure, a nonlinear numerical model of typical 7-span simply supported bridge–track system was established by the finite element software OpenSees and well calibrated by the test data and relative literatures. The nonlinear time history analysis was employed to calculate seismic responses of bridge and track parts under a suite of 10 seismic records. Results demonstrate that the sliding layer in the track structure is the most damage-prone component, especially at the bridge-subgrade transition section, and the shear alveolar may also sustain earthquake-induced fail. By analyzing the seismic damage mechanism of the track structure, this paper reveals that the nonuniform displacement responses of the girders and friction plate at the bridge-subgrade transition section are main factors that result in the extensive damage of the sliding layer and failure of the shear alveolar. However, the damage of these two components are beneficial to reduce the seismic responses of other components in the track structure and protect them from being damaged. From the perspective of engineering safety, the sliding layer and shear alveolar should be rigorously designed because the residual displacement of the sliding layer increases along with the maximum displacement and the failure of the shear alveolar may make the whole track structure failed.

This paper studies the nonlinear dynamic responses of graphene-reinforced composite (GRC) beams in a thermal environment. It is assumed that a laminated beam rests on a Pasternak foundation with viscosity and consists of GRC layers with various volume fractions of graphene reinforcement to construct a functionally graded (FG) pattern along the transverse direction of the beam. An extended Halpin–Tsai model which is calibrated against the results from molecular dynamics (MD) simulations is used to evaluate the material properties of GRC layers. The mechanical model of the beam is on the establishment of a third-order shear deformation beam theory and includes the von-Kármán nonlinearity effect. The model also considers the foundation support and the temperature variation. The two-step perturbation technique is first applied to solve the beam motion equations and to derive the nonlinear dynamic load–deflection equation of the beam. Then a Runge–Kutta numerical method is applied and the solutions for this nonlinear equation are obtained. The influence of FG patterns, visco-elastic foundation, ambient temperature and applied load on transient response behaviors of simply supported FG-GRC laminated beams is revealed and examined in detail.

This paper deals with the simultaneous identification of road roughness and vehicle parameters, considering the effect of vehicle–structure interaction. The proposed technique avoids the use of bridge response data (which has practical implementation difficulties along with the high chances of corruption with environmental noises) and utilizes the vehicle response data (which is relatively easier to record). Further, vehicle calibration is not needed as the roughness is estimated simultaneously. The identification is carried out by the coupling of an unbiased minimum variance estimator with an optimization scheme. This study considers a quarter-car vehicle model and a half-car vehicle model, instrumented to measure the vehicle vibration data. The unbiased minimum variance estimator (MVE) allows a linear temporal evolution of the state variables, incorporating the roughness as an unknown input term such that the need for linearization is avoided, unlike the traditional nonlinear filters. The optimization scheme helps in choosing a set of optimal solutions for the vehicle parameters as designed in the coupled scheme. The best split of the available measurement data to be used in the two schemes (MVE and optimization scheme) is discussed. The effect of different objective functions is also studied. The proposed technique is successful in terms of simultaneously estimating the vehicle parameters, roughness profile and vehicle responses (states) accurately.

The identification of a breathing crack is a highly challenging inverse problem in structural health monitoring. A novel output-only diagnostic technique for breathing cracks is proposed in this paper based on the singular value decomposition (SVD). A new damage index based on the singular values of the harmonic time history response, related to the Fourier spectrum amplitude of the superharmonics, is presented for breathing crack localization. The robustness and effectiveness of the proposed SVD-based approach are verified through both numerical and experimental studies.

The investigation of hyperelastic responses of soft materials and structures is essential for understanding of the mechanical behaviors and for the design of soft systems. In this paper, by considering both the material and geometrical nonlinearities, a new neo-Hookean model for the hyperelastic beam is developed with focus on its nonlinear free vibration with large strain deformations. The neo-Hookean model is employed to capture the large strain deformation of the hyperelastic beam. The governing equations of the hyperelastic beam are derived by using Hamilton’s principle. To avoid expensive calculations for solving the nonlinear governing equations, a simplified Taylor-series expansion model is proposed. The effects of two key system parameters, i.e. the initial displacement amplitude and the slenderness ratio, on the nonlinear free vibrations of the hyperelastic beam are numerically analyzed. The bifurcation diagrams, displacement time traces, phase portraits and power spectral diagrams are presented for the nonlinear free vibrations of the hyperelastic beam. For small initial displacement amplitudes, it is found that the hyperelastic beam will undergo limit cycle oscillations, depending on the initial amplitude employed. For initial displacement amplitudes large enough, interestingly, the free vibration of the hyperelastic beam will become quasi-periodic or chaotic, which were rarely reported for the free vibration of linearly elastic beams. Also observed is the traveling wave feature of oscillating shapes of the hyperelastic beam, indicating that higher-order modes of the beam are excited even for free vibrations. All these new features in the nonlinear free vibrations of hyperelastic beams indicate that the material and geometric nonlinearities play a great role in the dynamic analysis of hyperelastic beams.

This paper presents a novel fatigue crack monitoring method for steel specimens based on the smoothness priors method (SPM) and Tsallis entropy (TE) of strain measurements. The aim of the study is to detect initiation of a crack in steel specimens and subsequently to monitor its propagation under the fatigue load, based on real-time strain measurements. The nonlinear dynamic response of the structure was exploited since it degrades due to the initiation and subsequent propagation of the crack under the external dynamic excitation. The proposed method was experimentally validated. Here, the SPM is applied to decomposing the structural strain response into a nearly-stationary (NS) component and a low frequency aperiodic trend (LFAT) component. Features associated with crack initiation can be extracted from the NS component. The LFAT component, on the other hand, can be used to identify crack propagation. To tackle the singularity of the structural responses associated with a crack, the TE of the NS component was used in detection and monitoring of the crack in the steel specimen. Two other techniques, namely, acoustic emission (AE) sensor and crack opening displacement (COD) gauge were used for the purpose of calibration and comparison. The results show remarkable resemblance in terms of crack initiation and propagation identification exhibited by all three types of sensors, highlighting the potential of the proposed method for real-time detection and subsequent monitoring of crack propagation in steel structures.