International Journal of Structural Stability and Dynamics

Pole assignment is one of the central problems in most control systems designs. In relation to low-authority active flexible structural systems where robustness is difficult to achieve primarily due to many closely-spaced low-frequency lightly damped modes, pole-placement techniques are commonly used to design constant gain collocated controllers that will ensure that the transient phenomenon of the structure dies down sufficiently fast. In this paper, the active control of flexible structures is presented for collocated control design using a modified pole-placement approach that reduces the control efforts significantly. The effectiveness of employing the proposed approach is demonstrated using tensegrity structures.

The paper presents the results of numerical analyses of elasto-plastic buckling of steel reinforcing bars. Bars with different geometrical parameters made of steel with various mechanical characteristics were analyzed. The commercial program COSMOS/M based on the finite element method was used. It follows from the results that slenderness is not the only parameter that affects the elasto-plastic buckling of reinforcing bars. Such parameters as the length of the plastic plateau, ultimate stress and the plastic hardening module play an important role as well.

The free vibration of functionally graded (FG) beams with various boundary conditions resting on a two-parameter elastic foundation in the thermal environment is studied using the third-order shear deformation beam theory. The material properties are temperature-dependent and vary continuously through the thickness direction of the beam, based on a power-law distribution in terms of the volume fraction of the material constituents. In order to discretize the governing equations, the differential quadrature method (DQM) in conjunction with the Hamilton’s principle is adopted. The convergence of the method is demonstrated. In order to validate the results, comparisons are made with solutions available for the isotropic and FG beams. Through a comprehensive parametric study, the effect of various parameters involved on the FG beam was studied. It is concluded that the uniform temperature rise has more significant effect on the frequency parameters than the nonuniform case.

The simulation of progressive collapse of a power transmission tower-line system subjected to extremely strong earthquakes is studied in this paper. A three-dimensional finite element model is established for the coupled system that combines three towers and four span lines based on a practical project. The birth to death technique is adopted to simulate the progressive collapse of the system by using the user subroutine VUMAT in ABAQUS. The simulation of progressive collapse of the transmission tower-line system under either single-component or multi-component earthquake excitations is conducted. The collapse path, fracture position and collapse resistant capacity of the transmission tower are investigated. The result shows that the effect of multi-component seismic excitations should be taken into account in simulation of progressive collapse of the transmission tower, since the behavior of towers under multi-component excitations is different from that of single-component excitations. In addition, incremental dynamic analysis (IDA) is carried out to verify the results obtained herein. The present result should prove useful to the seismic design of power transmission towers.

The main purpose of this paper is to examine the influence of time delay associated with a semi-active variable viscous (SAVV) damper on the response of seismically excited linear and nonlinear structures. The maximum time delay is estimated on the basis of stability criteria, which consist of analyses of structural modal properties. Numerical computation of the critical time delay is performed by using dichotomic approach, which is based on multiple solving of the eigenvalue problem. Simulation results indicate that variable dampers can be effective in reducing the seismic response of structures, and that time-delay effects are important factors in control design of seismically excited structures. Furthermore, simulation results show degradation of performance whenever the actual delay exceeds the calculated critical time delay, which shows the accuracy and reliability of the proposed approach.

The aim of this paper is to investigate the free vibration of hybrid composite moving beams embedded with shape memory alloy (SMA) fibers. The nonlinear equations of motion are derived based on the Euler–Bernoulli beam theory in conjunction with the von Karman type of nonlinearity in strain–displacement relations via the extended Hamilton principle. Also, the recovery stress induced by the SMA fibers is computed by applying the one-dimensional Brinson model and Reuss scheme. Then, an analytical approach in used to solve the nonlinear equation of motion for the simply supported shape memory alloy hybrid composite (SMAHC) moving beams. Based on the analytical solution, several parametric studies are presented to show the effects of various parameters such as volume fraction, pre-strain in the SMA fibers, temperature rise and velocity on the fundamental frequency of the SMAHC moving beams. Due to the lack of similar results in the specialized literature on the subject of interest, this paper is likely to fill a gap in the state of the art of the related research.

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic, generalized thermo-viscoelastic diffusion material with voids under the influence of magnetic field. The formulation is applied to the generalized thermoelasticity theory under the Lord–Shulman and the classical dynamical coupled theories. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by the Lord–Shulman and the coupled theories in the presence and absence of the magnetic field and diffusion.

The paper presents the application of the differential transformation method (DTM) to the stability analysis of nonuniformly loaded beams under bending. The main advantage of the method is the possibility to obtain the semi-analytical solution for the critical loads of the beam undergoing lateral-torsional buckling. To determine the critical load, the system of two coupled ordinary differential equations with variable coefficients and parameters have to be solved. Numerical analyses were carried out for three different types of load functions: (i) Uniformly distributed load, (ii) linearly varying load and (iii) sinusoidally distributed load. The results were compared with the solutions computed by the finite element method (FEM) and those obtained by the authors using the variational iterative method (VIM). In each case, it was found that the difference with reference to the existing one does not exceed 3%, which testifies the effectiveness of the DTM used. Nevertheless, it should be emphasized that the number of terms of the approximation series used is fairly large and therefore the calculation of higher critical loads can be very time-consuming.

The mechanical behavior and buckling failure of sharp-notched 6061-T6 aluminum alloy tubes with different notch depths subjected to cyclic bending are experimentally and theoretically investigated. The experimental moment–curvature relationship exhibits an almost steady loop from the beginning of the first cycle. However, the ovalization–curvature relationship exhibits a symmetrical, increasing, and ratcheting behavior as the number of cycles increases. The six groups of tubes tested have different notch depths, from which two different trends can be observed from the relationship between the controlled curvature and the number of cycles required to ignite buckling. Finite element software ANSYS is used to simulate the moment–curvature and ovalization–curvature relationships. Additionally, a theoretical model is proposed for simulation of the controlled curvature-number of cycles concerning the initiation of buckling. Simulation results are compared with experimental test data, which shows generally good agreement.

The motivation of this study is to meet the requirement of cutout reinforcements in aerospace industry by using the design flexibility of curvilinearly stiffened panels. The reason is that the load path and tension field caused by curvilinear stiffeners can increase the load-carrying capacity of stiffened panels. The inherent superiority of such structures was examined in detail by comparison with those having straight stiffeners. Due to the large computational burden caused by post-buckling analysis, the optimum design of curvilinearly stiffened panels with single cutout was obtained based on surrogate model. On this basis, variable symmetrization and reduction methods were developed for different design cases, aimed at reducing the number of dependent variables in the optimization. Illustrative examples show the superiority of curvilinearly stiffened panels for cutout reinforcement, and demonstrate the effectiveness of the proposed optimization framework.

The wave-passage effect of earthquake loadings on long-span structures is studied through use of a multiply-supported single-degree-of-freedom (SDOF) system excited by traveling seismic ground motions. The absolute acceleration response of the SDOF system is represented in the analytical form in the time domain. The frequency-domain analysis results indicate that the wave-passage effect may reduce the absolute acceleration response and the earthquake loading acting on the multiply-supported SDOF system. Further, for different velocities of wave-passage, the response spectra are calculated to represent the reduction of the maximum earthquake loading on the long-span system caused by the wave-passage effect. The computation results of the response spectra indicate that the reduction of the maximum earthquake loading is fluctuant, but has a general tendency to decrease with the increase in the apparent wave velocity and the structural natural period.

When studying the vibration of a bridge–vehicle coupled system, most researchers mainly focus on the vertical vibration of bridges under moving vehicular loads, while the lateral and longitudinal vibrations of the bridges and the stochastic characteristics of the traffic flows are neglected. However, for long-span suspension bridges, neglecting the bridge’s three-dimensional (3D) vibrations under stochastic traffic flows can cause considerable inaccuracy in predicting the dynamic performance. This study is mainly focused on establishing a new methodology fully considering a suspension bridge’s vertical, lateral, and longitudinal vibrations induced by stochastic traffic flows under varied road roughness conditions. A new full-scale vehicle model with 18 degrees of freedom (DOFs) was developed to predict the longitudinal and lateral vibrations of the vehicle. An improved Cellular Automaton (CA) model considering the influence of the next-nearest vehicle was introduced. The bridge and vehicles in traffic flow coupled equations are established by combining the equations of motion of both the bridge and vehicles using the displacement relationship and interaction force relationship at the patch contacts. The numerical simulations show that the proposed method can rationally simulate the 3D vibrations of the suspension bridge under stochastic traffic flows.

The classical nonuniqueness problem exists due to uncertainty in the finite element (FE) calibration field. Namely, multiple models with different intrinsic parameters may all fit the observed data well, thus the selected single “best” model probably is not the truly best model to reflect the structural intrinsic property. A probability-based method using a population of FE models, not the single “best” method, is proposed to deal with the nonuniqueness problem. In this method, the Markov Chain Monte Carlo (MCMC) technique is first performed to sample the key structural parameters representing the main sources of uncertainty. Then a FE model population is generated using the samples, and the posterior probability of each model is evaluated by calculating the correlation between the simulation results and measurements through the Bayesian theorem. Finally, all the FE models from the stochastic sampling with their posterior probabilities are used for structural identification (St-Id) and performance evaluation. The advantage of the proposed method is that it not only identifies the magnitudes of structural parameters, but also generates their probability distributions for subsequent probability-based reliability analysis and risk evaluation. The feature provided by the stochastic sampling and statistical techniques makes the proposed method suitable for dealing with uncertainty. The example of the Phase I IASC-ASCE benchmark structure investigated demonstrates the effectiveness of the proposed method for probability-based structural health monitoring.

This paper compares three finite element models for determining the buckling and post-buckling performance of infinite length thin walled composite and metal stiffened panels — such as for modeling theoretical aircraft upper wing skin panels — namely single bay, double half-bay and quad half-bay models. The quad half-bay model is shown to be the ideal model as all wavelengths of buckling are permitted. This model gives an accurate estimate of postbuckling behavior that can include advanced behavior such as mode jumping or collapse while the single bay and double half-bay models are more restrictive and do not allow for accurate mode jumping to take place. Sample panels are analyzed for buckling performance using the computer program VICONOPT, which assumes an infinite length structure based on exact strip theory. This analysis is then compared to results from the quad half-bay FEM model, using the Abaqus solver, where the two models are in good agreement for the initial buckling performance for both the metal and composite panels. Buckling prediction for the quad half-bay model is within $0.5\%$ for the critical buckling mode, and within $3\%$ of all compared modes; and postbuckling performance compares well with the results of previous investigation of the same sample panel geometry.