International Journal of Structural Stability and Dynamics

The paper addresses the problem of asymmetric buckling of geometrically imperfect circular plates undergoing large axisymmetric deflections under thermal loading. The plate edge is assumed to be immovable in the radial direction and elastically restrained against bending rotation. The plate material is graded in the thickness direction and dependence of the material properties on temperature is taken into account. The governing equations are derived using the von Karman nonlinear plate theory and the concept of physically neutral surface. It is shown that, when subjected to increasing temperature, the plate initially bends into a figure of revolution and then buckles into asymmetric mode with local circumferential waves. To determine the critical temperature rise, a nonlinear eigenvalue problem is formulated by linearizing the governing equations about the axisymmetric state of equilibrium and solved using power-series expansions. The effect of temperature-dependent material properties, rotational spring stiffness and initial geometric imperfection on the critical temperature rise and buckling mode shapes is studied.

The main objective of this paper is to validate a finite-element (FE) modeling protocol to simulate thin-walled members for static and dynamic analyses. Arbitrary-shaped cross-sections, including open, closed, and multicellular sections can be efficiently modeled for further advanced study. The framework is thoroughly validated and verified using the existing analytical and closed-form solutions, as well as experimental results available in literature. This work is motivated by the higher accuracy of the shell FE-based modeling to capture the local and global complex behaviors of thin-walled members with asymmetric sections. Higher computational expenses, however, are required for such sophisticated shell finite element models (SFEM). Accordingly, a framework hosted in MATLAB and implementing the python scripting technique in ABAQUS, is developed, which includes eigen buckling, static nonlinear, modal frequency and dynamic time-history analyses. For a more modeling convenience, various parameters are incorporated such as imperfections, residual stresses, material definitions, element choice, meshing control, and boundary conditions. Several examples are provided to illustrate the application of the proposed framework, and to prove the robustness and accuracy of the generated FE models. This paper concludes with the efficiency of implementing SFEMs for simulating thin-walled members; thereby, establishing a more accurate and advanced structural analysis.

The effects of different percentages of multiwall carbon nanotube (MWCNT) on natural frequencies of polymer composite plates of varying edge-to-thickness ratio, aspect ratio and boundary conditions at ambient temperature are investigated experimentally and numerically. Conventional hand lay-up technique is used to prepare the MWCNT polymer composite plates with different percentages of carbon nanotubes (CNTs) mixed to the polymer. The elastic properties are determined experimentally by conducting uniaxial tensile test in the universal testing machine INSTRON 8862 as per ASTM D-3039. A set of experiments were conducted for the natural frequencies of vibration of MWCNT composite plates using the Bruel and Kjaer Fast Fourier Transform (FFT) analyzer with pulse platform. Detailed parametric studies are carried out to determine the effect of weight fraction of CNTs, aspect ratios, edge-to-thickness ratios and boundary conditions on the natural frequency of composite plates. Numerical solutions were obtained by the commercial finite element method (FEM) package ABAQUS. A simulation model is developed using the same geometrical and material properties determined experimentally from which the frequency responses are obtained. The simulation results are found to be consistent with the experimental ones. The results obtained showed an increase in elastic properties and natural frequencies up to 0.3 wt.% of MWCNT and decrease thereafter for all cases due to agglomeration of CNT in the polymer matrix. The morphology and dispersion of the CNTs in composites at micro level are investigated by using scanning electron microscopy (SEM) to further corroborate the behavior of specimens.

An eigen-based theory for structure-dependent integration methods is constructed and it can provide the fundamental basis for the successful development of this type of integration methods. It is proved that a structure-dependent integration method can simultaneously combine unconditional stability and explicit formulation since it is proposed to accurately integrate low-frequency modes while no instability is guaranteed for high-frequency modes. In general, it is promising for solving inertial problems, where the total response is dominated by low-frequency modes. In addition, it can be explicitly and implicitly implemented for time integration although an explicit implementation is of practical significance since it can save many computational efforts due to the combination of unconditional stability and explicit formulation. A typical procedure to develop structure-dependent integration methods is constructed. In general, a coupled equation of motion for a multiple degree of freedom system can be decomposed into a set of uncoupled modal equations of motion by means of an eigen-decomposition technique. Next, an eigen-dependent integration method is developed to solve each modal equation of motion. Consequently, all the eigen-dependent integration methods are combined to form a structure-dependent integration method by employing a reverse procedure of the eigen-decomposition technique.

The size-dependent free vibration of microbeams submerged in fluid is presented in this paper based on the modified couple stress theory. Two different cross-section shapes of microbeams are considered, i.e. the circular cross-section and rectangular cross-section. This nonclassical microbeam model is introduced for capturing the size effect of microstructures. In this fluid and structure coupled system, the effect of hydrodynamic loading on microbeams can be expressed by the added mass method. By using Hamilton’s principle and differential quadrature (DQ) method, we can derive governing equations of microbeams in fluid, and then rewrite them in the discretized form. The frequencies and mode shapes for microbeams are determined by proposing an iterative method. Numerical examples are given to show the effect of fluid depth, fluid density, length scale parameter, slenderness ratio, boundary condition and cross-section shape on the vibration characteristics.

This study provides an overview on the effect of porosity on free vibrations and more importantly aeroelastic stability margins of cylindrical shells. A general formulation for cylindrical shells is first developed including the effects of shear deformation and rotary inertia along with Sander’s rigid body rotation modification. Two porosity distributions of even and uneven are considered for functionally graded shells. The most general form of power-law model which is known as four-parameter power-law is utilized to provide a clear understanding for the qualification of functionally graded material. A Ritz-based solution algorithm being capable of representing all combinations of symmetric and asymmetric boundary conditions by a penalty method is also introduced. In addition to the capability of satisfying all boundary conditions, the presented solution method is very fast in terms of convergence and computational effort. Various parametric studies are provided and practical results are reported.

This paper presents an analytical investigation on dynamic buckling of cylindrical shells with general thickness variations under exponentially increasing external pressure over the time. Different from the previous studies in literatures, the shell thickness varies arbitrarily and is common in actual engineering, which leads to failure of the existing methods. A new analytical method is first developed to solve the fourth-order governing partial differential equations with variable coefficients for the shell subjected to varying external pressure. Then the asymptotic formulae for dynamic buckling loads considering general thickness variations are derived and expressed by geometry sizes of the shell and thickness variation functions. To validate the presented results, two specific non-axisymmetric thickness cases are discussed in detail. The critical dynamic buckling loads show a great agreement with the previous ones by other researchers for simple and axial thickness variation situation. Finally, example calculations and parametric discussion are performed, and influences of thickness variation types, speed of external pressure and the power exponent of time on the critical dynamic buckling loads are discussed.

This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.

This paper aims at shedding new light on the elastic post-buckling behavior and strength (elastoplastic collapse) of steel channel section beams undergoing lateral-torsional (LT) buckling. This new insight is acquired using a two-node geometrically exact beam finite element developed by the author, which can handle large displacements, including torsion-related warping, Wagner effects, plasticity, residual stresses and arbitrary initial configurations (namely geometrical imperfections). Several cross-sections and loading/support conditions are analyzed. The results obtained show that the LT buckling behavior of channels is asymmetric, meaning that the direction of the geometric imperfection can influence significantly the strength of the beams. Moreover, it is demonstrated that the loading and support conditions play a major role, leading to a significant scatter of results which hinder the definition of a single buckling curve for design purposes. Nevertheless, in all cases considered, the buckling strengths obtained fall significantly above those predicted by the current version of Eurocode 3.

Principal component analysis (PCA) is a classical dimensionally reduction method having been widely applied in structural health monitoring (SHM) systems. However, it usually works as a “black-box” in most applications, i.e. the outputs of PCA only make sense statistically without physical meaning. This problem causes the difficulty to estimate the stability of the current PCA-based SHM methods, due to the unclear physical essence in engineering. This paper aims to propose a physical interpretation of PCA when it is applied to the response data from a multi-freedom system under ambient excitation. Both non-damping and damping cases are analyzed theoretically and verified by both numerical and laboratory experiments. The results indicate there is a close connection between the outputs of PCA and dynamical parameters: PCA can reveal information about the mode shape and modal participation of the structure. This work gives a theoretical foundation of the current PCA-based SHM method under ambient excitation, leading to the possibility of further advancement.

In this paper, the axial buckling of boron nitride nanotubes (BNNTs) is investigated by considering the effects of surface and electric field. To achieve this purpose, the surface elasticity theory is exploited and the results are compared with the molecular dynamic simulation in order to validate the accuracy of the applied theory. In the molecular dynamics simulation, the potential between boron and nitride atoms is considered as Tersoff type. The Timoshenko beam theory is adopted to model BNNT. Moreover, two types of zigzag and armchair BNNTs are considered. In this study, the effects of surface, electric field, length, and thickness of BNNT on the critical buckling load are investigated. According to the results, the critical load of zigzag BNNT depends on the electric field. However, the electric field would not affect the critical load of the armchair BNNT. It should be noted that the surface residual tension and surface Lamé’s constants of BNNT have considerable impact on the critical load of BNNT. For lower values of electric field and smaller dimensions of BNNT, the critical load would be more dependent on the surface effect regarding the results. Furthermore, as an efficient non-classical continuum mechanic approach, the surface elasticity theory can fill the potential gap between the classical continuum mechanic and molecular dynamics simulation.

Civil structures suffer deterioration either for years of service, deficiency due to environmental factors or damages caused by factors such as earthquakes, winds, impact loads, and cyclical loads. When a structure ages, it is necessary to know its state of health and make a decision of maintenance or replacement. When a structure such as a bridge or building is subjected to destructive environmental forces, determining its state of health becomes a priority since its recovery is urgently required to function normally. Structural Health Monitoring (SHM) is a technology that aims to prevent the collapse of structures and loss of human life through early diagnosis of the health status of a structure. There are a large number of damage detection methods that can be classified into (1) non-destructive testing methods, (2) dynamic characteristics-based damage detection methods, (3) dynamic response-based, (4) multi-scale damage detection method and (5) damage detection methods with consideration of uncertainties. In this work, it is implemented synchrosqueezed wavelet transform (SWT), which can be classified as a methods based on the dynamic response. To validate the robustness of the method it is identified first, the natural frequencies of the Benchmark Phase I without damage, which consists of a steel structure of 4-story $2\times 2$ bay 3D steel frame structure subjected to ambient vibrations. Subsequently, some damage patterns are validated according to IASC-ASCE SHM Task Group. The results obtained in the identification of natural frequencies are compared with those reported in literature. SWT was efficient, presenting a minimum error of 0.12$\%$ and a maximum of 3.06$\%$ in the identification of natural frequencies about the AISCE-ASCE group model. SWT overcomes some other damage detection methods, which are deficient in the identification of closely spaced frequencies, commonly present in many civil structures due to symmetric geometry or similar physical properties in different directions.

The paper presents a solution to the dynamic response of three-layered, annular plates that are thermo-mechanically loaded. Time-dependent forces are considered to act on the facings of the plate. The thermal loading is defined by a flat, axisymmetric temperature field whose profile is expressed by the stationary or increase in time temperature differences between the plate edges. The cases of the plates loaded only thermally or mechanically have been examined. The problem has been solved analytically and numerically using the approximation methods: orthogonalization and finite difference. The selected reactions of an exemplar plate have been compared with the results obtained for the plate analyzed by the finite element method (FEM). The critical temperature differences and critical loads and corresponding dynamic buckling modes have been analyzed in detail. The numerous results presented for the dynamic responses have an important and practical meaning in the design process of plate structures subjected to complex thermo-mechanical loads.

Passive damping systems are energy dissipating devices that are used in building constructions to reduce excessive vibration caused by wind or earthquakes.

Recently, the use of inerters, devices using the inertia of the rotating mass, as a passive damping system has become more and more popular. Inerter, regardless of the construction, generates a resistance force that is proportional to the relative acceleration at the terminal ends of the device.

The purpose of this study is to evaluate the effectiveness of the viscoelastic (VE) dampers in combination with the inerter. For the derived equations of motion of structures with VE dampers and inerters, the Laplace transformation is applied, which leads to a nonlinear eigenproblem. The solution to the eigenproblem is obtained using the continuation method, also known as the homotopy or as the path following method.

It was found that for some cases of inerter connection with ve damper, there are some additional solutions in relation to the degrees of freedom of the structure. Furthermore, the dynamic characteristics of the structure associated with the above-mentioned additional eigenvalue are strongly dependent on the equivalent inerter mass.

Damping efficiency is tested by determining changes in the system’s dynamic characteristics: natural frequencies, non-dimensional damping ratios and displacement transfer functions. The presented approach allows determining the appropriate parameters of the inerter and VE damper and their appropriate location on the structures that correspond to the most effective damping. The obtained numerical results confirm the effectiveness of the proposed approach.

This paper presents a modified variational method for free and forced vibration analysis of coupled beam systems resting on various viscoelastic foundations. Non-uniform as well as uniform curved and straight Timoshenko beam components are considered in the coupled beam system. Using proper coordinate transformations, interactions among the beam components of the coupled beam system are accommodated by combining Lagrange multiplier method and least-square weighted residual method. Interface potential energy for various boundary conditions including the elastic ones is simultaneously formulated. Thus, the proposed method allows flexible choice of the admissible functions, regardless of the boundary conditions. Based on the proposed energy method, Winkler, Pasternak or even variable foundations distributed in a parabolic or sinusoidal manner can be easily introduced into the coupled beam systems. Two kinds of damping, namely the proportional and viscous damping, are also employed to model the energy dissipation of the viscoelastic foundations. Corresponding finite element (FE) simulations are performed where possible and good agreement is observed. Thus, great efficiency and accuracy of the present approach are demonstrated for free, steady-state and transient vibration of the coupled beam systems. The influences of the parameters of the variable viscoelastic foundations on the dynamic properties of the coupled beam system are also examined.

Support-induced membrane action can enhance the resistance, while altering the failure pattern, of reinforced concrete (RC) members under static/dynamic loadings. Nevertheless, the membrane effect on the load-response is regarded as a safety factor in current design guides, hence, a thorough understanding of the resistance capability of RC members in the presence of membrane actions is considered essential. To quantitatively depict the membrane behavior and its influence on the blast-resistance and failure pattern of Hybrid Fiber Reinforced-Lightweight Aggregate Concrete (HFR-LWC) beams, a specially built end-constraint clamp is developed to provide membrane actions on the structural component subjected to the blast load simultaneously. A series of field tests are conducted to investigate the dynamic behaviors of the HFR-LWC beams under close-range detonations. Overpressure-time histories of shock waves induced by the close-range explosive charge are captured. Then the deflection-responses and failure modes of the HFR-LWC beams are further investigated. The responses of the clamped HFR-LWC beam under blast loadings can be well simulated, and the blast-resistances of the beam-type members with membrane action are evaluated reasonably. The results show that membrane action is beneficial for the bridging effects of hybrid fibers and the interlocking effects of coarse aggregate, thereby giving rise to the ductile failures of HFR-LWC beam. The maximum deflections of the clamped HFR-LWC beam decrease by about 60% compared with simply-supported HFR-LWC beam in this paper, illustrating that the blast-resistance may be seriously underestimated if the membrane effects are ignored in structural design.