International Journal of Structural Stability and Dynamics

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis.

The interaction between underground pipelines and soils is crucial to the design and maintenance of underground pipeline network systems. In this paper, the dynamic stiffness matrix in the frequency-domain of the buried pipeline is obtained by the improved scaled boundary finite element method (SBFEM) coupled with the finite element method (FEM) at the interface between the far and near fields. A new coordinate transformation together with a scaled line is introduced in the improved SBFEM. Combined with the mixed variable algorithm, the time-domain solution of the buried pipeline under dynamic loads is then obtained. The accuracy of the proposed algorithm was verified by numerical examples. A parametric study is performed to assess the influence of the anisotropic characteristics of the layered soils on the dynamic response of the pipeline, the result of which provides a reliable basis for engineering practice. The results show that these parameters have a significant impact on the pipeline. The understanding of this impact can contribute to the design, construction, and maintenance of the corresponding engineering projects.

The in-plane vibrations of regular polygonal rings composed of rigid segments joined by torsional springs are studied for the first time. The nonlinear dynamical difference equations are formulated and solved by perturbation about the equilibrium state. As the number of segments increase, the frequencies, if aptly normalized, converge to the classical vibration frequencies of a continuous elastic ring. The vibration mode shapes are illustrated. The tiling of many identical polygons is discussed. Possible applications include the vibrations of space structures and graphene sheets.

This paper proposes an implicit and unconditionally stable two-sub-step composite time integration method with controllable numerical dissipation for general dynamics called the two-sub-step generalized central difference (TGCD) method. The proposed method is established by performing the generalized central difference scheme in two sub-steps as the nondissipative and dissipative parts to ensure amplitude accuracy and controllable damping, respectively. It is accurate to the second order, with the amount of numerical dissipation controlled exactly by the spectral radius ${\rho }_{\infty }$. In addition, the related parameters of the proposed method are determined by optimizing the amplitude and phase accuracy of the free vibration of a single degree-of-freedom system. Several representative linear and nonlinear numerical examples are analyzed to demonstrate the advantages of the proposed method in terms of accuracy, stability and efficiency, especially its stability in solving nonlinear problems.

Latticed shells and domes usually consist of hundreds, sometimes thousands, beam elements connected by rigid or semi-rigid joints. These connecting elements result, generally, very sophisticated, made with different materials and constituted by disparate connection systems. Recently, the stiffness connections were studied, numerically and experimentally, as one of the most important factors influencing significantly the structural response of space structures and domes. Very often, in the design process, the joints are assumed to be hinged or clamped. This assumption may result significantly far from the actual condition of in-service structure and components, leading to not understanding or not being able to prevent sudden catastrophic collapses (buckling, snap-through). Thus, the inclusion of joint stiffness reduction in the numerical model is necessary, more and more also due to the types of external loads, such as overloads that occur during the life of the structure or, especially, seismic solicitations. In this paper, the stability of an existent timber dome has been studied increasing the yieldingness of the connecting nodes according to an original approach. In addition, sensitivity of this kind of structure to the amplitude and the geometrical imperfections shape have been also considered. Numerical analyses have been conducted with local displacement controls, to take into account the geometric nonlinearity effects. Results evidenced that the dome is affected by instability interaction for particular slenderness and stiffness reduction of the connections.

Nanoporous materials and structures have attracted widespread attention due to their excellent mechanical properties. Based on the surface elasticity, the effective Young’s moduli are derived for four typical nanoporous structures with periodic unit cells. When the cross-sectional size reduces to nanoscale, the effective Young’s modulus is revealed to be strongly size-dependent. Both the effects of residual surface stress and effective-surface Young’s modulus are examined. The results indicate that negative effective Young’s modulus can be achieved when the residual surface stress is less than zero. The influences of the cross-sectional shape on the relationship between the overall deformation and applied loads are examined. The relative density also plays an important role to the mechanical characteristics not only at macroscales, but also at nanoscales.

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

Tuned liquid dampers (TLDs) have many advantages in controlling building vibrations, among which multi-tuned liquid dampers (MTLDs) appear to have better stability and effectiveness. However, the tank wall was assumed to be rigid in the past by ignoring the fluid-structure interaction (FSI) at the interface, resulting in simplified calculation for the design of the TLDs. Moreover, the fluid in the tank was considered to be separate from the structure. This paper presents two numerical methods to control the responses of the frame under the dynamic loadings: (1) the lumped mass method for quickly designing the TLDs, and (2) the finite volume method/finite element method (FVM/FEM) for analyzing the fluid and solid domains of the TLDs in a single computational 3D model. In addition, the multi-field interaction between the structure-fluid-tank walls is considered by solving the coupling equations at the interfaces. A steel frame is fitted with an MTLD and tested experimentally on a shaking table to investigate its dynamic response. Numerical results are verified with the experimental ones, which show good agreement.

In this study, we propose a novel and effective computational approach for free and forced vibration analyses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement under various loads. To this end, the outstanding features of isogeometric analysis (IGA) are first combined with the four-variable refined plate theory (RPT). The non-uniform rational B-splines (NURBS) are adopted to obtain the $C^1$-continuity essential to the RPT model. The various distributions of internal pores as well as GPLs with uniform or non-uniform properties along the plate’s thickness are investigated. The effective elastic properties of the material models are obtained by the Halpin–Tsai micromechanics model for Young’s modulus, the rule of mixture for Poisson’s ratio and mass density. The Newmark’s time integration scheme is implemented to obtain the solutions of the forced vibration problems. Numerical examples are carried out to investigate the effects of various key parameters such as porosity coefficient, GPL weight fraction, porosity distribution, as well as GPL dispersion pattern, on the behaviors of the plate structure.

Time-varying parameter identification is essential for structural health monitoring and performance evaluation. In this paper, a combined method based on the variational mode decomposition and generalized Morse wavelet is proposed to identify the structural time-varying parameters. Based on the sparse property of structural response signals in wavelet domain, a fast iterative shrinkage-thresholding algorithm is adopted to reduce the noise. Then the de-noised signal is decomposed into multi- modes by the variational mode decomposition, and the generalized Morse wavelet is performed to identify the instantaneous frequency. To validate the proposed method, a numerical example including different frequency variations is studied. Experimental validations of a moving vehicle across a bridge and a time-varying cable system considering two patterns of cable tension variations in the laboratory are carried out to investigate the capability of the proposed approach. It is confirmed that the proposed approach can effectively perform the signal decomposition, while identifying the instantaneous frequencies of the time-varying systems accurately.

The Refined Zigzag Theory (RZT) is a structural theory developed for the analysis of composite multilayer and sandwich beams. However, the accuracy of RZT for buckling analysis of sandwich beams has not been experimentally investigated, and for RZT and Timoshenko Beam Theory (TBT) the effect of the degree of heterogeneity on their accuracy requires further study. The aim of this work was to validate the use of the RZT for predicting the critical buckling loads of sandwich beams, even with highly heterogeneous material properties, and to assess the use of the TBT for the same application. Buckling experiments were conducted on five foam-core sandwich beams, which varied in geometry and included highly heterogeneous configurations. For each beam, two finite element (FE) models were analyzed using RZT- and TBT-beam FEs. The comparison between the numerical and the experimental results highlighted a major capability of RZT to correctly predict the critical buckling load for all the beams considered. The dependence of the TBT results on the beam characteristics was further investigated through a parametric analysis, which showed the dominant effect to be a close to linear relationship between the TBT error and the beam face-to-core thickness ratio. The work demonstrated the outstanding accuracy of the RZT predictions, including the superior capabilities with respect to TBT, and has application for rapid and accurate analysis of industrial structures.

This paper aims to improve the accuracy of time integration algorithms (TIAs) for long-term simulation of structural dynamics. To this end, a new method of reducing the period elongation (numerical dispersion) was proposed by utilizing the mass scaling matrix. Firstly, the period elongation of explicit Gui-$s$ algorithm as a representative was analyzed, and the strategy of enhancing the algorithm accuracy was investigated. Subsequently, the period elongation was reduced by introducing a parameter to change the mass matrix, which is weighted by the original mass matrix and stiffness matrix. The bisection method is utilized to determine the parameter according to the formulation of period elongation. Since just the mass matrix of original algorithm is changed slightly, the convergence rate of original TIA remains unchanged and the proposed mass scaling method imposes little influence on the stability condition of original algorithm. Moreover, this method has few modifications to the computer program of TIA and is easy to implement. Finally, both linear and nonlinear long-term dynamic response analyses for multiple-degree-of-freedom systems indicated that the proposed mass scaling method is effective and convenient to reduce the period elongation for several typical TIAs.

In this paper, the lateral torsional buckling (LTB) behavior of multi-layered long-span laminated glass (LG) beams is investigated through full-scale model test and numerical simulation. In the test program, the LG beams consisting of up to four glass plies and spanning 5000mm are constructed and tested. The load-displacement curves and development of strain in glass plies are recorded, based on which the deformation and stress state of buckled LG beams are analyzed, and the strength checking criterion is provided. The test results are also used to determine the shape and amplitude of initial imperfection through statistical analysis and to validate a numerical model based on the finite element method (FEM). Parametric analysis based on the FEM model is then conducted to investigate influential factors on the LTB resistance of LG beams, among which the influence of shape and amplitude of initial imperfection is emphasized. For the LTB design of LG beams, the applicability of existing formula to determine the critical buckling moment through effective stiffnesses is evaluated for multi-layered LG beams with the test and numerical results. Finally, the design buckling curves adopting the Ayrton–Perry formula (APF) are proposed and validated for LG beams categorized with glass type and load duration.

With the development of high-speed railways, the double-line mode of ballastless tracks is being adopted increasingly worldwide. In some sections where subgrades need to be laid, this type of line mode is also applied above the subgrade, thus forming double-line track-subgrade structure. In this structure, the subgrade on one side of the double-line is subjected to the eccentric pressure of the load when the unidirectional train is running (the most common operating condition in actual operation). When the subgrade contains embankment layer, the complexity of the problem is increased. Therefore, a 1:4 scale test model of the double-line ballastless track-subgrade system was constructed in this paper in order to study the dynamic responses of the double-line track-subgrade structure with embankment layer under the unidirectional high-speed train loads. By considering the similarity of shear wave velocities, a new uniform dynamic similarity method was adopted to design the track, subgrade and foundation models. The effects of a series of sine waves with 1–30Hz excitation frequency and three kinds of loading modes on the speed, soil stress and acceleration response of the track and subgrade were systematically investigated. The relationship between the effective composite values of velocity beneath the track and the depth was finally obtained. The results show that the dynamic stress attenuation of the subgrade bottom layer under larger axle loads are relatively faster. It is found that the dynamic stress attenuation of the subgrade bottom layer is relatively fast under the high-frequency uniform excitation of large axial heavy load.

This paper studies experimentally the nonlinear aeroelastic and flutter behavior of a cantilever plate wing with an external store. The wing model that is constructed from plexiglass sheet is designed and tested in a closed-circuit subsonic wind tunnel. To deal with the structural nonlinearities of the model, various analysis tools such as time history plots, phase-plane projections and Fast Fourier Transform (FFT) have been used for detecting the critical and post-critical behaviors of the structure. The results show that flutter takes place by the coupling between the torsional and bending modes. A good correlation between the present experiments and previous numerical results is obtained. The nonlinear aeroelastic response and flutter boundary are investigated for different sweep angles. The flutter velocity and amplitudes of limit cycle oscillations (LCOs) increase rapidly with increasing sweep angle. The nonlinear response of the wing with an external store is also investigated, with the effect of store location on the nonlinear flutter boundary evaluated.