International Journal of Structural Stability and Dynamics

A simple mass–spring system with an attached hanging column is investigated. The problem is formulated and the frequencies obtained with an efficient initial value method. Under forced vibration, the amplitude of the mass may be greatly reduced by adding a hanging column. The possibility of using such a hanging column as a dynamic vibration absorber is shown for the first time.

This paper presents an idea for modeling the road surface roughness in a vehicle–bridge interaction (VBI) system, by simulating it equivalently as two external forces each acting on the two subsystems of vehicle and bridge. Such an idea can be easily included in general-purpose commercial finite element (FE) software like ABAQUS and ANSYS. Compared with frequently used coupled and uncoupled FE models, the present approach is more convenient, since it does not require any self-developed FE codes. The other advantage is that it does not require very small elements in the FE modeling, as is the case with conventional approaches for simulating the irregularity in the profile of road surface roughness, which may be computationally inefficient.

In this study, the impact damage resistance of carbon/basalt hybrid fiber reinforced polymer pipes was experimentally investigated under low velocity impact loading. The composite pipes, composed of thin plastic liner of HDPE wrapped with eight layers of plies at constant winding angle of [$\pm$55${}^{\circ }$/90${}_2^{\circ }$/$\pm$55${}^{\circ }$/90${}_2^{\circ }$], were fabricated through filament winding technique. Eight pipe configurations with different stacking sequence and fiber content proportion were studied. Specimens cut from the original pipes were tested in a drop weight impact machine under two levels of impact energies, 50J and 100J, in order to predict the impact response and induced damage resistance of the pipe. The damage of the tested pipes was assessed based on the force-displacement, force-time histories, the energy absorption mechanism, as well as the micrographs captured by scanning electron microscope (SEM) for the specimens. The results indicate that the impact resistance behavior was highly affected by the stacking sequence of the layers and partly affected by the fiber content ratio. Positioning the basalt fiber on the impacted side enhances the energy absorption mechanism for both levels of imposed energies, while improving the impact resistance. The addition of 50% basalt fiber can slightly increase the impact resistance compared to the addition of 25% basalt fiber. However, specimens with 25% basalt fiber showed lower peak force, lower damage area and lower energy absorption.

A new type of high performance steel (HPS), designated WGJ steel, with high strength as well as improved fire and corrosion resistance, was recently developed by Wuhan Iron and Steel (Group) Company. This paper investigated the lateral-torsional buckling behavior of beams fabricated of WGJ steel through experimental and numerical analysis. Welded I-section beams were tested under concentrated loads, which indicated that lateral-torsional buckling was the dominant failure mode. A finite element model was established and validated by the experimental results. Parametric analyses were conducted to further understand the effect of steel strength on the lateral-torsional buckling capacity of steel beams. The numerical results were compared with design values obtained from the clauses in Eurocode 3 and GB50017. It is found that the design equations in GB50017 give less safe margins for the overall stability design of welded I-section beams fabricated of WGJ high performance steel, whereas Eurocode 3 appears to be more conservative in all conditions.

An improved vehicle-track coupled dynamics model that takes into account the differential ballast settlement is presented in this paper. Central to this formulation is an iterative method for acquiring the mapping relationship between the ballast settlement and the deflection of rail and sleepers. The proposed method is validated by comparing the results obtained with those of the finite element method (FEM) and the equilibrium state calculated for the track with the ballast settlement. Using the proposed method and dynamic model, numerical analyses have been performed for the static deflection of the rail and sleepers and for the dynamic response of the vehicle-track coupled system. The results indicate that the upper track structure will settle along with the ballast bed, and sleepers are likely to become unsupported when the settlement amplitude is large or when the settlement wavelength is small. The contact between the sleeper and the ballast bed changes dynamically when the vehicle passes through the settlement area. The ballast settlement has a significant effect on the deformation of the track and sleepers, thereby deteriorating the running safety and ride comfort of the vehicle.

This paper presents a comparison of two static nondestructive methods used to assess compressive loads in columns of steel space frames. The first method requires knowledge of the flexural rigidity of the column under investigation, whereas the second method requires knowledge of the column’s buckling load. In each method, short-term displacements are measured at given cross-sections along the member under examination, which is subjected to an additional transverse load. The two methods were verified in this study through experimental and numerical tests on a column of a small-scale space frame prototype with generic connections and end conditions. Estimations of compressive forces were generally reliable when second-order effects were accurately considered. In conclusion, the two methods can be successfully used to test steel space frames in a laboratory or under real conditions.

With the rising speed of high-speed trains, the aerodynamic loads become more significant and their influences on the hunting stability of railway vehicles deserve to be considered. Such an effect cannot be properly considered by the conventional model of hunting stability analysis. To this end, the linear hunting stability of high-speed railway vehicles running on tangent tracks is studied. A model considering the steady aerodynamic loads due to the joint action of the airflow facing the moving train and the crosswind, is proposed for the hunting stability analysis of a railway vehicle with 17 degrees of freedom (DOF). The key factors considered include: variations of the wheel–rail normal forces, creep coefficients, gravitational stiffness and angular stiffness due to the actions of the aerodynamic load, which affects the characteristics of hunting stability. Using the computer program developed, numerical calculations were carried out for studying the behavior of the linear hunting stability of vehicles under steady aerodynamic loads. The results show that the aerodynamic loads have an obvious effect on the linear critical speeds and instability modes. The linear critical speed decreases monotonously as the crosswind velocity increases, and the influences of pitch moment and lift force on the linear critical speed are larger than the other components of the aerodynamic loads.

The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.

Incidents of pedestrian-induced large lateral vibrations of footbridges reveal the occurrence of an instability-type phenomenon in pedestrian-induced vibration. However, the mechanism involved has yet to be clearly explained. In this work, a novel model for predicting the lateral vibration of footbridges is proposed. Under an algebraic framework of nonlinear stochastic vibration, the narrow-band vibration caused by the pedestrian intra-subject randomness and the phase lag between the footbridge motion and the pedestrian load are considered. The critical condition that triggers the large lateral vibration of the footbridge is identified using the stochastic averaging method and the concept of stability based on the Lyapunov exponent. The validity of the proposed method is confirmed through case studies of three bridges. Through a parametric analysis, the effects of several crucial parameters on the stability/instability of vibration are discussed. Finally, conclusions are drawn regarding insights that can be useful to the future designs of footbridges.

Based on the theory of double-beam dynamic stiffness, a dynamic equilibrium equation for an inclined beam segment was established for the analysis of the dynamic characteristics of a double-layer sheathing cable system. The closed-form transverse dynamic stiffness matrix of the system considering the bending stiffness, inclination angle, boundary condition, and the sag of the beam was obtained simultaneously. The distribution rule of its elements and determinant, defined as dynamic stiffness coefficients and the characteristic function separately, were analyzed in the space and frequency domain. By using a numerical case study, the vibration characteristics of the double-beam system were investigated. It shows that in a given frequency range, the modal frequencies of the double-beam system are affected by both beams, and the beam with smaller stiffness contributes more to the system frequency. The contributions of each single beam to the system frequencies may be further determined by the distribution rule obtained. Based on these results, a method was proposed for quick evaluation of the contribution of each single beam to the modal frequency of the system. This will help to identify the frequency and cable force of double-layer sheathing cables.

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

This paper presents a closed form solution for the vibration and acoustic problem of orthotropic plates under a thermal environment. Hamilton’s principle is utilized to derive the governing equation of motion for the orthotropic plate with thermal loads, which is then solved by the method of separation of variables. The frequency equations and mode functions obtained for the orthotropic heated plates with at least two adjacent edges clamped are much simpler than those by the conventional methods. Several numerical examples are carried out for the modal, dynamic and acoustic analysis of orthotropic heated plates with different combinations of thermal loads and boundary conditions. The results of the parametric study for the orthotropic plate with different thermal loads are discussed in detail. The validity of the present formulation is confirmed by comparing the results obtained with the numerical ones. Due to its accuracy, efficiency and versatility, the present method offers an efficient tool for the structural and acoustic analysis of the orthotropic plate under the thermal environment.

Cyclic bending of tubes leads to progressive ovalization of the tube cross-section, and persistent cycling causes catastrophic buckling of the tube. This paper presents the response and stability of SUS304 stainless steel tubes with local sharp-notched depths of 0.2, 0.4, 0.6, 0.8, and 1.0mm and notch directions of 0${}^{\circ }$, 30${}^{\circ }$, 60${}^{\circ }$, and 90${}^{\circ }$ under cyclic bending. The experimental results reveal that the moment–curvature relationship first exhibits cyclic hardening and then a steady loop after a few cycles. Because the notches are small and localized, notch depth and direction show minimal influence on the moment–curvature relationship. In contrast, the ovalization–curvature relationship demonstrates an increasing and ratcheting pattern along with the bending cycle, whereas notch depth and direction show a strong influence on this relationship. Finite-element analysis via ANSYS is used to simulate the moment–curvature and ovalization–curvature relationships, and an empirical model is proposed to simulate the relationship between the controlled curvature and number of cycles required to ignite buckling. The experimental and analytical data agree well with each other.

This paper presents the stability analysis of a perforated plate with sector geometry made of composite materials. The sector of concern is a compound of graphite-epoxy and glass-epoxy with identical ply thickness but different fiber angles for each layer. The mechanical load conditions considered include uniform axial, circumferential, and biaxial pressure, while the thermal loading is specified to be uniform temperature increase over the whole sector. The existence of one or two circular holes has increased the complexity of analysis. To obtain solutions of high accuracy, the three-dimensional elasticity theory relations have been employed. Using the finite element method along with the stability condition of Trefftz, the buckling equation of the structure is derived. Green nonlinear strain-displacement relations are used to form the geometrical stiffness matrix. Unlike the finite element method used by other researches, a novel curved 3D B-Splined element is used to more accurately trace the displacement and stress variations of the structure. This element can be used in solution domains with geometric discontinuities, such as perforated plates and also meshed in the thickness direction. Moreover, instead of using the common von Karman assumptions, the most general form of the strain tensors in the curvilinear coordinates is adopted. The buckling load is obtained by extremizing the second variations of the total potential energy. The finite element formulation is coded in the MATLAB software. The effects of various parameters such as sector dimensions, dimensions of the hole, mechanical load directions, and fiber angles of each layer on the thermomechanical buckling is investigated.

In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.