International Journal of Structural Stability and Dynamics

In this paper, the stochastic moment stability and almost-sure stability of a planner gyropendulum system with synchronous motor under the white noises are investigated. By applying the theory of diffusion process, an eigenvalue problem for the moment Lyapunov exponent is formulated. Then, through a perturbation method and a Fourier cosine series expansion, the second-order expansion of the moment Lyapunov exponent is solved, which is just the leading eigenvalue of an infinite matrix. Finally, the convergence and validity of the procedure are numerically verified, and the effects of system and noise parameters on the moment Lyapunov exponent are discussed. It was found that the increase in both the noise intensity and coefficient of the synchronous motor torque will weaken the stability of the gyropendulum system, and when they reach certain values, the system becomes unstable. In addition, according to the relationship between the moment Lyapunov exponent and maximal Lyapunov exponent, the stable thresholds are also given.

This paper presents a new attempt for geometric nonlinear and postbuckling analysis of structures using only elastic stiffness. This can be achieved not without reasons. Aside from a correct updating of the structural geometry in the incremental sense, there are two concerns for iterations: (i) The local strategy is that the element forces recovered in each iteration should not violate the rigid body rule, in order not to induce any fictitious forces. (ii) The global strategy is that the path-tracing scheme should be able to deal with multi critical points, such as limit and snap-back points. Both strategies will be explained via the mechanism of iterations, which seems not new, but can shed some new lights. The results obtained using only the elastic stiffness will be compared with the normal case including the geometric stiffness, with the level of approximation assessed by the general stiffness parameter (GSP). Through the study of a number of trusses, beams and shell structures, it is confirmed that the elastic stiffness alone can be used to solve the nonlinear and postbuckling responses of a wide range of structures, with only an increase in the number of iterations. This paper represents a limit application of the elastic stiffness to nonlinear structural analysis.

In [M. M. Malakiyeh, S. Shojaee and S. Hamzehei-Javaran, Development of a direct time integration method based on Bezier curve and 5th-order Berstein basis function, Comput. Struct. 194 (2108) 15–31] an unconditionally stable implicit time-integration method using the Bezier curve was proposed for solving structural dynamic problems. In this study, a new class of the previous algorithm is presented by using the Bernstein polynomials and the Bezier curve as the interpolation functions for solving the equations of motion with the possibility of using large time steps. The spectral radius, period elongation, amplitude decay and overshooting of the present method are investigated and compared with some other methods. To show the high-performance, robustness and validity of this method, five numerical examples are presented. The theoretical analysis and numerical examples show that the proposed method has low dissipation in the lower modes and high dissipation in the higher modes in comparison with the other methods reported in the literature.

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is $60^{\circ }$ and $0^{\circ }$, respectively.

In this work, the primary and secondary instability region analysis of rotating multi-walled carbon nanotube (MWCNT) reinforced non-uniform hybrid composite plates (CNT-FRP) under uniaxial periodic loads is performed. First-order shear deformation theory has been used to derive the kinetic and potential energy equations of the various configurations of non-uniform composite plates by including the effect of rotary inertia, shear deformation, varying centrifugal stiffness and non-uniformity along the transverse direction of the plate. The governing differential equations of motion are derived in the form of Mathieu–Hill equations using the Hamilton’s principle. The efficacy of the developed finite-element formulation has been verified by comparing the natural frequencies of the rotating composite plates evaluated using the numerical simulation with the experimental results and available literature. This study also investigates the influence of the CNT vol%, CNT aspect ratio, angular rotation of plate and static load on the primary and secondary instability region of various non-uniform configurations of CNT-FRP hybrid composite plates. It was noticed that the primary and secondary regions of parametric instability of CNT-FRP hybrid composite plates shift upward when CNT vol% increases from 0 to 2%. It was further noticed that primary and secondary instability regions of various non-uniform configurations shift to the lower excitation frequency when MWCNT vol% increases beyond the saturation limit. It was observed that the effect of angular rotation and static load is significant on the primary and secondary regions of instability.

This paper presents a three-dimensional finite deformation theory for the geometric nonlinear analysis of both the curved and twisted beams using the meshfree method based on the Timoshenko beam hypothesis. The theory presented is simple, but it is capable of solving the stability, postbuckling, snap-through, and large deformation problems effectively. Clear physical meanings will be revealed in derivation of the three-dimensional finite deformation theory. A meshfree method based on the differential reproducing kernel (DRK) approximation collocation method combined with the Newton–Raphson method is employed to solve the strong forms of the geometrically nonlinear problems. Numerical examples are given to illustrate the validity of the method presented.

Track is a key component in railway transportation systems. They are usually fixed by fasteners and supported by discrete sleepers, which sit on the ballast. A lot of research has been conducted to check the integrity of the rail track itself, like railway level and alignment; however, limited work has been carried out on the damages of railway supports including loosing and missing fasteners and damaged ballast. In this paper, the support–track–vehicle interaction system is analyzed in which the supports and track are modeled as evenly distributed springs and Euler beam, respectively, and the vehicle is simplified as a spring–mass system. It is found the natural frequencies of the interaction system change periodically with respect to the location of the vehicle, whereas the periodicity is broken when the support is damaged. Then, a detection method is proposed to identify the damaged supports by using the vertical acceleration of the traversing inspection vehicle, which acts as both the “exciter” and “message carrier” of the test. It shows good performance on the detection of damaged supports in both numerical and experimental validations. Moreover, it is more practical than other detection methods in real engineering applications because only one single accelerometer is required.

This paper focussed on the large displacement nonlinear free vibration of a toroidal pressure vessel in free space under constrained volume condition. Three states of the toroidal pressure vessel surface comprising the initial unstrained surface, reference surface, and vibrating surface were considered in the energy functional of the toroidal pressure vessel system based on the principle of virtual work. For the reference surface, it was assumed that the toroidal pressure vessel has a circular cross-section and is subjected to uniform internal pressure. Nonlinear numerical solutions were obtained utilizing the FEM and a modified direct iteration technique, and compared with those generated by ABAQUS. More importantly, this study showed that the fundamental nonlinear natural frequency of a toroidal pressure vessel under the constrained volume condition was lower than that of the published results for an inflated toroidal membrane and shell.

For the oblique penetration of a circular pipe target by a prefabricated fragment, the finite element software LS-DYNA was used to build a computational model for the circular pipe considering the penetration by a cylindrical fragment from different directions. The failure characteristics of the pipe were acquired and the critical penetration velocity was calculated. The relationship between the initial velocity and critical angle of ricochet was found. The experiment was then conducted to verify the results obtained, indicating that the simulation results are in good agreement with the experimental ones. It was shown that the main critical failure pattern of a circular pipe is shear perforation or a penetrating crack. The critical penetration velocity is positively correlated with the direction angle $\theta$ and entry angle $\phi$. For entry angles greater than 30^∘, the critical penetration velocity increases with an increase in the direction angle, and this effect is stronger for higher direction angles. The critical angle of ricochet is positively correlated with the initial velocity of the fragment. The critical angle of ricochet tends to approach a constant of 60^∘ as the initial velocity of the fragment increases.

In the literature, modal kinetic energy (MKE) has been commonly utilized for optimal sensor placement strategies. However, there have been very few studies on its application to structural damage detection. This paper introduces a new two-stage structural damage assessment method by combining the modal kinetic energy change ratio (MKECR) and symbiotic organisms search (SOS) algorithm. In the first stage, an efficient damage indicator, named MKECR, is used to locate the potential damaged sites. Meanwhile, for the purpose of comparison with MKECR, three other indices are also used. In the second stage, an SOS-based finite element (FE) model updating strategy is adopted to estimate the damage magnitude of identified sites, while excluding false warnings (if any), where an objective function is proposed using a combination of the flexibility matrix and modal assurance criterion (MAC). The performance of the SOS algorithm is also verified by comparing with four other meta-heuristic algorithms. Finally, three numerical examples of 2D truss and frame structures with various hypothetical damage scenarios are carried out to investigate the capability of the proposed method. The numerical results indicate that the proposed method not only can accurately locate and quantify single- and multi-damage in the structures, but also shows a great saving in computational cost.

The vibration characteristics of piezolaminated plates under coupled electromechanical loading are investigated using the finite element method. Higher order shear deformation theory is adopted to incorporate the effect of shear in the formulation. In the finite element formulation, an isoperimetric eight-nodded rectangular element is employed with linear through-the-thickness electric potential distribution. In the parametric study, the influences of geometry and boundary conditions on the vibration characteristics of piezolaminated plates are evaluated. Numerical results are presented for the frequencies of simply supported, clamped plates fitted with piezoelectric patches at the top and bottom surfaces of the laminate. For this, a model simulating the effect of the electromechanical loading with control potential is developed. Studies are also performed for piezolaminated plates with various thickness-to-span ratios, along with convergence test. The effect of the provision of piezoelectric layers to improve the vibration response of plates is investigated. This analysis reveals that the electro-mechanical coupling can strengthen the plate’s resistance to vibration.

A passive tuned mass damper (TMD) fabricated using the Reid damping, referred to as the Reid-TMD, is proposed. First, the characteristics of the Reid damping model are introduced, followed by the presentation of a passive variable friction damper to achieve this model. Next, the steady-state response of single-degree-of-freedom structures with the Reid-TMD under a harmonic load is solved by the harmonic balance method (HBM), together with an error analysis of the results. Subsequently, the optimization and control effect of the Reid-TMD damping system are analyzed and compared with the traditional viscous damping TMD. The results show that under the action of a harmonic load or seismic load, the vibration suppression effect of the Reid-TMD with the same mass ratio is essentially equivalent to the traditional viscous damping TMD. In addition, the damping control effect increases with the increase in mass ratio. When the mass ratio is less than 0.05, the energy dissipation coefficient is less than 0.5 and the frequency ratio is less than 0.95. For parameters within this range, the steady-state response of the seismic reduction structure with the Reid-TMD is solved by the HBM. If the parameters of the Reid-TMD are outside this range, the error of the HBM becomes large, and recourse should be changed to general numerical methods. The optimum parameters of the Reid-TMD are determined through an optimization analysis for the mass ratio in the range of 0.005–0.1. While using the Reid-TMD for the vibration absorption design, the optimum parameters can be acquired directly by using the established tables. Because the passive variable friction damper has good durability and economy, the application of the Reid-TMD is beneficial to shock absorption technology.

In this paper, a new computationally efficient algorithm is developed for online and real-time identification of time, location, and severity of abrupt changes in structural stiffness as well as the unknown inputs such as earthquake signal. The proposed algorithm consists of three stages and is based on self-adaptive recursive least-square (RLS) and curvature-change approaches. In stage 1 (intact structure), a simple compact RLS is hired to estimate the unknown parameters and input of the structure such as stiffness and earthquake. Once the damage has occurred, its time and location are identified in stage 2, using two robust damage indices which are based on the structural jerk response and the error between measured and estimated responses of structure from RLS. Finally, the damage severity as well as the unknown excitations are identified in the third stage (damaged structure), using a self-adaptive multiple-forgetting-factor RLS. The method is validated through numerical and experimental case studies including linear and nonlinear buildings, a truss structure, and a three-story steel frame with different excitations and damage scenarios. Results show that the proposed algorithm can effectively identify the time-varying structural stiffness as well as unknown excitations with high computational efficiency, even when the measured data is contaminated with different levels of noise. In addition, as no optimization method is used here, it can be applied to real-time applications with computational efficiency.

Mode shapes estimated from the vehicle responses are normally used to detect bridge damage efficiently for their high spatial resolution. However, an updated baseline finite element model (FEM) is normally required to quantify damages for such an approach. A two-stage damage detection procedure is presented for bridges by utilizing the mode shape estimated from a moving vehicle. Damage locations are first determined through a damage localization index (DLI) defined by regional mode shape curvature (RMSC). Then the relationship between the damage extents and the RMSC changes is investigated by FEM simulation. Finally, an equation set to quantify the single and multiple damages is deduced by combining the RMSCs and the relationship between the damage extents and the RMSC changes established by an un-updated FEM. Numerical and experimental examples are carried out to verify the validity and efficiency of the two-stage method. The results revealed that it can localize and quantify damages with satisfactory precision by using the response measured from one sensor only.

High and slender towers may experience excessive vibrations caused by both wind and seismic loads. To avoid excessive vibrations in towers, tuned mass dampers (TMDs) are often used as passive control devices due to their low cost. The TMDs can absorb part of the energy of vibration transmitted from the main structure. These devices need to be finely tuned in order to work as efficient dampers; otherwise, they can adversely amplify structural vibrations. This paper presents the optimal parameters of a pendulum TMD (PTMD) to control the vibrations of slender towers subjected to an external random force. The tower is modeled as a single-degree-of-freedom (SDOF) mass–spring system via an assumed-mode procedure with a pendulum attached. A genetic algorithm (GA) toolbox developed by the authors is used to find the optimal parameters of the PTMD, such as the support flexural stiffness/damping, the mass ratio and the pendulum length. The chosen fitness function searches for a minimization of the maximum frequency peaks. The results are compared with a sensibility map that contains the information of the maximum amplitude as a function of the pendulum length and the mass ratio between the pendulum and the tower. The optimal parameters can be expressed as a power-law function of the supporting flexural stiffness. In addition, a parametric analysis and a time-history verification are performed for several combinations of mass ratio and pendulum length.

This paper aims to investigate the structural behavior of digitally fabricated thin-walled timber sections with edge connectivity provided by integral mechanical press-fit joints. Experimental, numerical, and analytical investigations have been developed to accurately characterize the press-fit section behavior and their failure modes. Plywood fiber orientation, material thickness, and connection tightness are considered as potential factors that may affect the performance of the press-fit jointing system. Experimental testing of square hollow sections (SHSs) under uniaxial compressive loading showed failure of sections through both conventional crushing and novel pop-off bifurcation failures. Pop-off buckling behaviors were shown to be governed by the integral joint transverse stiffness and its magnitude relative to a critical edge stiffness value. Columns with joint transverse stiffness value less than the critical edge stiffness value exhibited pop-off failures. These joint stiffness values were obtained from testing of unloaded joints and were used to obtain accurate predictions of column failure modes. Joint stiffness values for loaded joints were then predicted with an interpolation model mapping axial strain to a tighter connection tolerance and these were used to obtain accurate estimations for column failure load in most of the tested column types. Comparative investigations showed thin-walled sections with integral joints only to be capable of matching the compressive capacities of glued sections, for instances where crushing governed. Similarly, the weight-specific compressive capacity of timber sections was found to be comparable to thin-walled steel sections when crushing governs.