International Journal of Structural Stability and Dynamics

A semi-analytical procedure is presented to solve the elastoplastic buckling problem of cylindrical shells made of functionally groded materials (FGMs) under combined axial and torsional loads. The elastoplastic properties are assumed to vary smoothly according to the power law distribution rule, introduced in the J2 deformation theory for formulation of the constitutive relation of FGMs in the framework of the Tamura–Tomota–Ozawa (TTO) model, which is a volume fraction-based material model. The critical condition is deduced by the Ritz method. Assuming the uniform prebuckling strain, a biaxial stress state analysis is conducted to determine the analytical position of the elastoplastic interface, which is used in the integration of the elastoplastic internal force and all the material-related structural parameters. Finally, an iterative procedure is adopted to find the exact elastoplastic critical load. Numerical results indicate the effects of the inhomogeneous parameter and the elastoplastic material properties of their constituents on the stability region and plastic flow region of the materials.

The previously formulated model of the gravity-driven collapse of the twin towers of the World Trade Center (WTC) on September 11, 2011 was shown to match all the existing observations, including the video record of the crush-down motion of the top part of tower during the first few seconds, the seismically recorded duration of collapse, the size distribution of particles caused by impact comminution of concrete floor slabs, the loud booms due to near-sonic lateral ejection velocity of air and dust, and precedence of the crush-down collapse mode before the crush-up. Nevertheless, different degrees of ductility, fracturing and end support flexibility of WTC columns could lead to an equally good match of these observations and remained uncertain, due to lack of test data. Recently, Korol and Sivakumaran reported valuable experiments that allow clarifying this uncertainty. They revealed that, under the simplifying assumptions of rigid end supports and unlimited ductility (or no fracturing) of unheated columns, the energy dissipation of the WTC columns would have been at maximum 3.5-times as large as that calculated by the plastic hinge mechanism normally considered for small-deflection buckling. This increase would still allow close match of all the aforementioned observations except for the first two seconds of the video. The proper conclusion from Korol and Sivakumaran’s tests, based on close matching of the video record, is that the fracturing of unheated columns and the flexibility of their end restraints must have significantly reduced the energy dissipation in columns calculated under the assumptions of no fracture and no end restraint flexibility.

The size-dependent dynamic behavior and flexural vibration of rotating micro-rings are investigated in this paper. Using the modified couple stress theory and Hamilton’s principle, the governing equations of motion of the rotating micro-ring are derived. The natural frequencies for both extensional and inextensional micro-rings are obtained in closed form along with the forward and backward traveling waves derived. The results indicate that the natural frequencies of the rotating micro-ring are clearly size dependent, but the size dependency decreases as the speed of rotation of the ring increases, while it decreases when the radius-to-thickness ratio of the ring increases. A comparison between the natural frequencies of the extensional and inextensional micro-rings is performed. Moreover, the effect of the radius-to-thickness ratio of the ring on the behavior of the micro-ring is investigated. Good agreement is found between the natural frequencies obtained and the experimental results reported in the literature.

This paper addresses the nonlinear random vibration of a rectangular von Kármán plate excited by uniformly distributed Gaussian white noise which is fully correlated in space. The state-space-split method and exponential polynomial closure method are jointly utilized to analyze the probabilistic solutions of the plate. The computational efficiency and numerical accuracy of the methodology for analyzing the nonlinear random vibration of the plate are verified by comparing the computational effort and numerical results with those obtained by Monte Carlo simulation and equivalent linearization, respectively. Meanwhile, the convergence of the probabilistic solution in the sense of Galerkin’s approximation is examined by analyzing the plate modeled as single-degree-of-freedom and multi-degree-of-freedom systems. Some phenomena are discussed after numerically studying the behaviors of probabilistic solutions of the deflection at different locations of the plate.

Utilizing a nonlinear creep model, the dynamic behavior of tilting railway vehicles moving over curved tracks with rail irregularities and under earthquakes and wind loads is studied. The car model adopted consists of 28 degrees of freedom, capable of simulating the lateral, vertical, roll and yaw motions for the wheelsets, truck frames and car body. The derailment quotient is investigated to analyze the running safety of a tilting railway vehicle using the linear and nonlinear creep models, while considering the rail irregularities and environmental forces for various tilting angles. Generally, the derailment risk of the tilting railway vehicle is higher than that of non-tilting railway vehicle with or without rail irregularities and environmental forces. The derailment quotients calculated by the linear creep model are underestimated for a tilting railway vehicle. In addition, the derailment quotients evaluated for rough rails and under environmental forces are higher than those obtained for smooth rails with no environmental forces. It is confirmed that rail irregularities and each type of environmental forces have decisive effects on derailment quotients. They are compared and ranked according to their significance.

To protect structures from external explosions, solid protective barriers have been demonstrated by experimental and numerical studies to be able to effectively mitigate blast loads on structures behind them. However, to protect against blast loads, barriers normally need to be designed to have high structural resistance and ductility. This often requires bulky and heavy protective barriers which are not only highly costly but also often not appropriate for application in downtown areas as they are not friendly to city planning or appearance. Fence type blast wall consisting of structural columns was recently proposed and its effectiveness in mitigating blast loads was investigated through numerical simulations. It was found that the wave–fence interaction and interference of waves significantly reduced the wave energy when the blast wave passed through the fence blast wall. To further investigate the effectiveness and applicability of fence type blast wall as a highly potential technology for structural protection in an urban area, field tests have been conducted and results are reported in this paper. Columns with circular and triangular cross-sections were adopted to build fence blast walls. In addition, a masonry wall was also constructed as solid barrier for comparison. Hemispherical TNT explosive weighing 1.0 kg with different stand-off distances was detonated on the ground to generate the blast load. Blast overpressures in free air, behind the fence blast wall and behind the masonry wall were recorded by pressure sensors. The effectiveness of the fence blast wall in reducing blast wave and protecting structures was demonstrated by the test data.

Owing to their superior mechanical and thermal properties, carbon nanotube (CNT) reinforced composite materials have wide range of applications in various technical areas such as aerospace, automobile, chemical, structural and energy. In this paper, the nonlinear axisymmetric dynamic behavior of sandwich spherical and conical shells made up of CNT reinforced facesheets is studied. The shell is subjected to thermal loads and discretized with three-noded axisymmetric curved shell element based on field consistency approach. The in-plane and the rotary inertia effects are included within the transverse shear deformation theory in the element formulation. The present model is validated with the available analytical solutions from the literature. A detailed parametric study is carried out to showcase the effects of the shell geometry, the volume fraction of the CNT, the core-to-face sheet thickness and the environment temperature on the dynamic buckling thermal load of spherical caps.

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

This paper aims at investigating free vibrations and stability of double-walled carbon nanotube (DWCNT)-based spinning nanobearings. The so-called nanobearing consists of two coaxial carbon nanotubes (CNTs) where either of the two CNTs can be a rotor while the other takes the role of stator. Euler–Bernoulli beam model along with the Eringen’s nonlocal theory of elasticity are employed to obtain governing equations of transverse vibrations for the CNTs. The coupling of the two CNTs originates from the van-der-Waals (vdW) forcing present in the interface of the two CNTs. The coupling is taken into account as distributed spring foundation with an equivalent elastic stiffness. Based on the obtained model, effects of small-scale parameter, vdW interaction between CNTs and the diameter ratio of CNTs on the critical spinning speed are investigated. Finally, the stability margins of the nanobearings are determined and some general conclusions are drawn.

A generalized analytical formula is developed to predict buckling of anisotropic laminated composite fixed–fixed thin columns by using the Rayleigh–Ritz displacement field approximation. Based on the generalized constitutive relationship, the effective extensional, coupling and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of the 6$\times$6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness since the coupling and extensional stiffness coefficients drop out of the formulation for this boundary condition when following the standard Rayleigh–Ritz formulation steps. This formula is similar to the Euler buckling formula in which the flexural rigidity is expressed in terms of the flexural stiffness coefficient of laminated composites. Motivated by reducing some of the discrepancy with the finite element results, the pre-buckling solution was substituted into the bifurcation expression to yield an updated formula that includes the coupling and extensional stiffness coefficients. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is then conducted to examine the effect of ply orientation and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and analytical results is discussed for all these cases. In addition, comparisons with an earlier buckling solution for cross-ply laminated columns are made.

The correlations among wind pressures on roof and walls are examined for the cylindrical roof buildings with different rise-span ratios based on wind tunnel data. Wind-induced dynamic response is also analyzed with a parametric study concerning span length, rise-span ratio, stiffness of supporting frames and connection type between roof and supporting frames, where the roof system is a single-layer cylindrical reticular shell. For both roof and supporting frames, the responses induced by vertical wind loads on the roof and by horizontal wind loads on the walls are investigated. The correlation coefficients of these response components are examined. The results showed that the fluctuating wind pressure on the roof is strongly correlated with the wind pressure on the side wall and the leeward wall, but weakly correlated with the wind pressure on the windward wall. The response of roof and supporting frames caused by the wind loads on the roof is much larger than that of wind loads on the walls. On the bases of a comprehensive parameter study and complete quadratic combination (CQC) rule, a practical simplified combination rule is suggested for estimating response of roof and supporting frames. It is given as sum of response component caused by wind load on roof and that of wind load on walls multiplied with a combination factor of $-0.20$.

Noise and vibration from the railway tracks with fractional railpads are studied in this paper. The track system is modeled by a beam on a viscoelastic foundation including the fractional railpads and nonlinear ballast. The nonlinear fractional governing equation is obtained in the time domain by use of the fractional finite element formulation. The Newmark’s method is combined with the Adomian decomposition method (ADM) to solve the nonlinear fractional equation. The acoustical pressure field around the vibrating beam is obtained by the Rayleigh integral approach. The effects of the fractional parameters, load speed and condition on the track responses are investigated. It is found that the dynamic deflection and stress alongside the railways are more influenced by the loading condition, while the acoustical pressure is remarkably influenced by the load speed.

This paper presents an improved method called the consistent multilevel random decrement technique in conjunction with eigensystem realization algorithm (RDT-ERA) for modal parameter identification of linear dynamic systems using the ambient vibration data. The conventional RDT-ERA is briefly revisited first and the problem of triggering level selection in the RDT is thoroughly studied. Due to the use of a single triggering level by the conventional RDT-ERA, an inappropriate triggering level may produce poor random decrement (RD) functions, thereby yielding a poor estimate of modal parameters. In the proposed consistent multilevel RDT-ERA, multiple triggering levels are used and a consistency analysis is proposed to sift out the RD functions that deviate largely from the majority of the RD functions. Then the ERA is applied to the retained RD functions for modal parameter identification. Subsequently, a similar consistency analysis is conducted on the identified modal parameters to sift out the outliers. Finally, the final estimates of the modal parameters are calculated using weighted averaging with the weights set proportional to the number of RD segments extracted from the corresponding triggering levels. The proposed method is featured by the fact that the information from the signal is fully utilized using multiple triggering levels and the outliers are sifted out using consistency analysis, thus making the identified result more accurate and reliable. The effectiveness and accuracy of the method have been demonstrated in the examples using the simulated data and experimental data.

The concept of energy-regenerative damping is adopted in semi-active vortex-induced vibration (VIV) suppression of an elastically supported inclined impenetrable elliptical cylinder modeled as a two degree-of-freedom (DOF) system in laminar cross-flow at low Reynolds numbers (Re = 210). It is based on the intelligent (model free) adaptive fuzzy sliding mode control (AFSMC) strategy in conjunction with switch-based energy regenerating circuit of a tunable electromagnetic (EM) damper. The semi-active damper is linked to the plant model in a multi-field co-simulation framework via MATLAB/Simulink coupled with a user defined function in a CFD package. The AFSM controller initially calculates the desired transverse control force for suppression of the cylinder VIV. Consequently, by smart adjustment of the variable circuit load resistance, the current flow through EM damper circuit is adaptively modulated in such a way that the damping force continually tracks its active counterpart in a semi-active manner. Furthermore, when the damper is operating in the regeneration mode, the mechanical vibration energy that is traditionally dissipated as heat in conventional viscous dampers will be stored as electric charge in a capacitor. Numerical simulations demonstrate that the regenerative semi-active EM-based VIV control system can effectively suppress the cylinder motion while recovering a certain portion of mechanical vibration energy through the cooperative action of two distinct operation modes of the EM damper. Unlike conventional active control systems, the proposed system does not require a large external power supply, and at least part of the required power may be provided by the recovered energy.

In order to provide a better understanding of the dynamic behavior of single-layer reticulated domes subjected to explosive blast loads, a number of analyses are carried out on structures with different standoff distances ($R$), explosive weights ($W$), rise–span ratios ($f∕L)$ and other parameters. An equation for a structural damage factor is proposed to evaluate structural damage quantitatively. The damage states for single-layer reticulated domes are defined based on their structural dynamic performance and corresponding damage factors. Structural reliabilities for different standoff distances are obtained using the Monte-Carlo Analysis. A typical protective measure is bollards which are used to help ensure a minimum standoff distance. To illustrate the cost-effectiveness of such a protective measure, structural damage states and various losses, including direct and indirect economic loss and maimed and fatality loss, are considered for assessing the risk reduction, costs and benefits. It was found that the bollards significantly reduce the likelihood of structural progressive collapse or severe damage, and the optimal standoff distance can be determined.

This paper introduces a mathematical model for optimizing the dynamic performance of thin-walled functionally graded box beams with closed cross-sections. The objective function is to maximize the natural frequencies and place them at their target values to avoid the occurrence of large amplitudes of vibration. The variables considered include fiber volume fraction, fiber orientation angle and ply thickness distributions. Various power-law expressions describing the distribution of the fiber volume fraction have been implemented, where the power exponent was taken as the main optimization variable. The mass of the beam is kept equal to that of a known reference beam. Side constraints are also imposed on the design variables in order to avoid having unacceptable optimal solutions. The mathematical formulation is carried out in dimensionless quantities, enabling the generalization to include models with different cross-sectional types and beam configurations. The optimization problem is solved by invoking the MatLab optimization ToolBox routines, along with structural dynamic analysis and eigenvalue calculation routines. A case study on the optimization of a cantilevered, single-cell spar beam made of carbon/epoxy composite is considered. The results for the basic case of uncoupled bending motion are given. Conspicuous design charts are developed, showing the optimum design trends for the mathematical models implemented in the study. It is concluded that the natural frequencies, even though expressed in implicit functions, are well-behaved, monotonic and can be treated as explicit functions in the design variables. Finally, the developed models can be suitably used in the global optimization of typical composite, functionally graded, thin-walled beam structures.

Some high-speed rotating micro-machines and micro-vibration devices rely on the use of whirling micro-shafts subject to the effect of gravity and magnetic fields. At present, the consequences of the interaction between the elastic deformation of such shafts and the magnetic/gravitational field effects remain unresolved. Focusing on micro-scale whirling shafts with very high torsional rigidity, this study presents a theoretical treatment grounded in the theory of micro-continuum elasticity to examine the ramification of this interaction. The differential transformation method (DTM) is used to obtain extensive numerical results for qualitative assessments of the magnetic-gravitational effects interaction on standing, hanging and horizontally positioned spinning micro-scale shafts. The influence of bearing-support flexibility on the response of the whirling micro-shaft is also considered with rotational and translational springs. The gravitational sag reduces the stability of whirling standing micro-shafts and increases that of the hanging micro-shafts. Further, for all the micro-shafts configurations investigated, the magnetic field is observed to stiffen the response of the shaft and favorably shifts the critical points of vibration of the whirling shafts forward.