International Journal of Structural Stability and Dynamics

The unique solution for the fully stressed hanging string with a bottom load is found. For a given length of string, the problem depends on two parameters, representing the ratio of string density to maximum stress, and the ratio of bottom mass to maximum stress. The cross-sectional area of the string decays exponentially downward. Vibration frequencies are found from the exact characteristic equation. Results from analytic perturbation formulas compare well with those of numerical solution.

Two factors are critical to the effectiveness of the vehicle scanning method for bridge frequencies. One is the frequency of the test vehicle itself. This can be eliminated by using the vehicle–bridge contact point response calculated from the vehicle response. The other is the surface roughness of the bridge, which can be removed by using the residual response of two connected vehicles. In this paper, it is demonstrated for the first time that both vehicle’s frequency and surface roughness can be simultaneously eliminated using the contact residue of two connected vehicles. Theoretically, a formulation is presented for both the contact response and residues. In the numerical study, the contact response is demonstrated to outperform the vehicle response as more bridge frequencies can be identified, while the contact residue is verified to work well for various surface roughnesses, vehicle spacings, and bridge damping ratios. For damped bridges with rough surfaces, the contact residue enables us to extract the first three bridge frequencies.

This research aims to analyze the thermal buckling and post-buckling of carbon nanotube (CNT) reinforced composite beams. It is assumed that the beam is rested on a nonlinear elastic foundation which contains the Winkler spring, shear layer, and nonlinear spring. Distribution of CNTs across the thickness may be non-uniform which results in a functionally graded media. The elastic properties of the beam are evaluated using the refined rule of mixtures which contains efficiency parameters. Temperature dependency of the constituents is also taken into account. Using three different beam models, namely, first-order, third-order, and sinusoidal theories, the governing equations for the composite beam are established. Three different types of edge supports are considered which are pinned–pinned, clamped–clamped, and clamped–roller. With the aid of the two-step perturbation technique, closed-form expressions are extracted to obtain the elevated temperature as a function of the post-buckling deflection in the beam. Results of this study are compared with the available data in the literature. After that, new results are given to discuss the effects of important factors such as foundation parameters, geometrical characteristics, boundary conditions, the CNT volume fraction, and CNT pattern. It is shown that the critical buckling temperature of pinned–pinned and clamped–roller beams is the same while their post-buckling responses are totally different.

This study focuses on developing and implementing Mamdani hybrid fuzzy logic inference system (FIS) for transverse crack detection and fault diagnosis in a woven fiber laminated glass/epoxy composite beam using different vibration modes of natural frequencies. The shifting of vibration is attributed to the implication of cracks. These vibration signatures are fuzzified through hybrid fuzzy sets (triangular, trapezoidal, Gaussian) and scaled to crack location and depth using the fuzzy rules and defuzzification process. The vibration signatures are recorded using ABAQUS finite element (FE) simulation software for a fixed beam and are fed as input parameters to the developed FIS for computing the desired outputs. The realization for crack depth and position is experimentally verified through a Fast Fourier Transform (FFT) analyzer. The experimental results with simulated data show that fuzzy logic application detects crack positions and depth accurately at different levels. It is concluded that the hybrid FIS bears a close resemblance to the experimental analysis and also stands out as an effective method for crack detection in LCB over other standalone methods. The current method can be used as a cost-effective non-destructive technique for health monitoring and fault diagnosis of composite beam structures in any practical field.

A closed-loop controlled system usually consists of the main structure, sensors, and actuators. In this paper, asymptotic stability of trivial solutions of a controlled nonlinear stochastic system considering the dynamics of sensors and actuators is investigated. Considering the inherent and intentional nonlinearities and random loadings, the coupled dynamic equations of the controlled system with sensors and actuators are given, which are further formulated by a controlled, randomly excited, dissipated Hamiltonian system. The Hamiltonian of the controlled system is introduced, and, based on the stochastic averaging method, the original high-dimensional system is reduced to a one-dimensional averaged system. The analytical expression of Lyapunov exponent of the averaged system is derived, which gives the approximately necessary and sufficient condition of the asymptotic stability of trivial solutions of the original high-dimensional system. The validation of the proposed method is demonstrated by a four-degree-of-freedom controlled system under pure stochastically parametric excitations in detail. A comparative analysis, which is related to the stochastic asymptotic stability of the system with and without considering the dynamics of sensors and actuators, is carried out to investigate the effect of their dynamics on the motion of the controlled system. Results show that ignoring the dynamics of sensors and actuators will get a shrink stable region of the controlled system.

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method.

Previous studies show that Kalman filter (KF)-based dynamic response reconstruction of a structure has distinct advantages in the aspects of combining the system model with limited measurement information and dealing with system model errors and measurement Gaussian noises. However, because the recursive KF aims to achieve a least-squares estimate of state vector by minimizing a quadratic criterion, observation outliers could dramatically deteriorate the estimator’s performance and considerably reduce the response reconstruction accuracy. This study addresses the KF-based online response reconstruction of a structure in the presence of observation outliers. The outlier-robust Kalman filter (OKF), in which the outlier is discerned and reweighted iteratively to achieve the generalized maximum likelihood (ML) estimate, is used instead of KF for online dynamic response reconstruction. The influences of process noise and outlier duration to response reconstruction are investigated in the numerical study of a simple 5-story frame structure. The experimental work on a simply-supported overhanging steel beam is conducted to testify the effectiveness of the proposed method. The results demonstrate that compared with the KF-based response reconstruction, the proposed OKF-based method is capable of dealing with the observation outliers and producing more accurate response construction in presence of observation outliers.

Hopf bifurcation, as the most representative dynamic bifurcation, is closely related to the stability of many engineering structures. In this work, the stochastic Hopf bifurcation (SHB) of a controlled quasi-integrable Hamiltonian system (H.S.) of multi-degree-of-freedom (MDOF) is investigated, where the system is subjected to wide-band noise and controlled by a Fractional-order Proportional-Derivative (FOPD) controller with time delay. By decoupling FOPD control force and simplifying it without time delay, the averaged Itô differential equations of the approximated system are derived with the technique of stochastic averaging. Then, the average bifurcation parameter expression of system is obtained, which can determine the criterion of the SHB deduced by the FOPD control force. Last, an illustration of coupled Rayleigh oscillators is given to demonstrate the validity of the procedure. The influences of time delay, noise intensities and fractional order on the system SHB are discussed.

Deployable mechanisms have notable applications in mechanical engineering, civil engineering, and space technology. Although often ignored, deployable linkage mechanism exhibits additional flexibility beyond rigid folding owing to the deformation of nonrigid components. The actual behavior of flexible deployable linkage usually involves the dynamic effect and geometric nonlinearity. Using the finite particle method (FPM), this study investigated the nonlinear responses of flexible deployable linkage mechanisms. As a particle method, the FPM is displacement based, explicit, and can avoid iterations to solve nonlinear equilibrium equations. It can be used for nonlinear analyses of structures with rigid body motion and infinitesimal mechanisms, and to determine the internal force and structural deformation. To investigate the nonrigid Bennett linkage and Bricard linkage, formulations of a three-dimensional beam element and revolute hinge element were derived for FPM analysis. Agreement between analytical solutions and numerical simulations demonstrated the efficiency of the proposed approach for nonlinear motion analysis of nonrigid mechanisms. The FPM results revealed that mechanism flexibility can cause deviation from rigid compatibility paths, and the internal force and deformation of mechanisms should be considered when designing nonrigid mechanisms.

In this study, the instability regions of a honeycomb sandwich plate are investigated for different end conditions under periodic in-plane loading. The core layer of the sandwich plate is made of carbon nanotube (CNT)/glass fiber-reinforced honeycomb and the face layers of CNT/glass fiber- reinforced laminated composite. The governing equations are derived using classical laminated plate theory (CLPT) and solved numerically by using finite element formulation. The effectiveness of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies with those available in the literature. The effects of CNT wt.% on the core material, CNT wt.% on the skin material, ply orientation and various end conditions on the variation of natural frequencies, loss factors and instability regions are studied. Finally, some inferences for the effects of CNT reinforcement on the honeycomb sandwich plate subjected to the periodic in-plane loads are discussed.

This study presents a new approach for obtaining a set of tri-directional time histories compatible with target design spectra by modifying real recorded earthquake ground motions. The influence matrix method (IMM) based on eigenfunction expansion is improved for typical design response spectra with different shapes and employed in order to achieve accurate matching with the target design spectra. By applying the Gram–Schmidt orthogonalization in each iteration of the IMM procedure, the correlation coefficient between any two components can be guaranteed to be strictly zero. Hence, the generated three components in the orthogonal directions are statistically independent. The generated time histories satisfy the requirements of current codes and standards. Two examples are presented to illustrate the procedure and the superiority of the proposed method, with the maximum relative error between the generated time histories and target design spectra being less than 0.2% in [0.6, 100] Hz, and the code requirements being satisfied strictly.

This paper reports for the first time the experimental investigation on the free vibration characteristics of angle-ply laminated composite stiffened plates along with the numerical investigation. The natural frequencies of these plates are computed experimentally using an FFT analyzer and numerically by employing the finite element method with combination of isoparametric nine nodded plate and three nodded beam elements. Angle-ply laminated stiffened plates are fabricated using woven glass fiber fabrics and epoxy by hand layup technique. The effects of various support conditions; number, orientation and types of stiffeners; aspect ratios of plates and different fiber orientations on the fundamental frequencies of the angle-ply laminated stiffened plates are investigated. These parameters significantly influence the natural frequencies. It is found that there is a very good agreement observed between the fundamental frequencies obtained from both experimental and numerical investigation. Mode shapes are also presented for angle-ply laminated square stiffened plates with three different support conditions to justify the trend of increasing/decreasing of the modal frequency with the addition of stiffeners. It is observed that the enhancement of the frequencies of the angle-ply plates due to addition of stiffeners is influenced significantly by the position of stiffeners and consequently mode shapes. As the research on the free vibration behavior of angle-ply stiffened plates with experimental analysis is very rare, this study can be considered as the benchmark for future research.

In the applications of supplemental dampers for seismic hazard mitigation, the supporting braces for the dampers are considered an important component for ensuring an efficient energy dissipation in the structure. Despite their importance, studies on the effects of the brace stiffness and the velocity exponent in the case of nonlinear viscous dampers are rather limited. In this paper, a numerical time-stepping method is developed for computing the seismic response of the structure with supporting braces and nonlinear viscous dampers. Using the proposed method, effects of the parameters of the nonlinear damper-brace systems are investigated, using first a single-story structure, followed by multi-story buildings. Results indicated that the design parameters for the dampers and supporting braces may be combined in numerous ways to satisfy a given set of structural performance objectives, but the brace stiffness can be minimized to achieve design efficiency in the range of velocity exponent commonly used for seismic applications of nonlinear viscous dampers. Results also indicated that for a set brace stiffness, if the dampers are optimally designed, the velocity exponent has an insignificant effect on the structural seismic performance objectives considered in this paper.

This study considers a thermoelastic micro-elongated solid which is being heated by a laser pulse in order to investigate the corresponding impact of thermal loading and magnetic field. A laser beam that is non-Gaussian in nature is used to heat the surface of the bounded plane with a pulse duration $0.0001$ps. The dual-phase-lag (DPL) model is considered to develop a better understanding of the problem. Also, the problems are solved using normal mode analysis as well as it helps in attaining the appropriate expressions for micro-rotation, components of displacement, the force stress, couple stress, concentration field, the temperature distribution the scalar micro-elongated function, and the micro-stress. The results obtained from the thermal variations are validated by comparing them to Coupled Theory (CT) of thermo-elasticity, Lord and Shulman (L–S) theory, and the DPL model. The graphical illustration of these comparisons has been presented as it helps in exploring the impacts of the laser pulse at two different times and the magnetic field parameter. The investigation also helped deduce some specific cases of interest.

There are three kinds of isolators commonly used in storage tank, friction pendulum bearing (FPB), laminated rubber bearing (LRB), and variable curvature friction pendulum bearing (VCFPB), respectively. Real-time hybrid simulation is conducted in this paper to compare the seismic performance of the storage tank isolated by the above three types of bearings. The storage tank is used as the physical substructure for experimental testing, and the isolators are adopted as the numerical substructure for numerical simulation. The isolation performance is estimated by the following perspectives: deformation of the isolator, shear force, overturning moment, and input energy. Test results show that the deformation of LRB is the largest, which can be twice that of FPB, and that larger deformation will enlarge the seismic energy input into the storage tank. Moreover, the low-frequency components of shear force and overturning moment are amplified by LRB. In contrast, the FPB and VCFPB have a good performance on all frequency bands. Particularly, the softening mechanism enables VCFPB to have better seismic performance and have a reduction rate of about twice that of LRB.

Based on the aerostatic and self-excited aerodynamic force models, a computational approach of three-dimensional (3D) refined flutter analysis for long-span bridges under skew winds is established, in which the structural nonlinearity, aerostatic effect and full-mode coupling effect, etc., are fully considered, and the computational procedure ($N$ flutter-sw) is developed accordingly. By taking the Runyang Suspension Bridge over the Yangtze river as an example, under the wind attack with initial angles of 0^∘ and $\pm 3^{\circ }$ and yaw angles between 0^∘ and 25^∘, the flutter stability of the bridge in completion under skew winds is analyzed, and the influences of skew wind and aerostatic effect on the flutter stability of suspension bridges are assessed. The results show that the aerostatic effect has a significant influence on the flutter stability of long-span suspension bridge, and it may worsen its flutter stability, with an average decrease of 6.0%. However, it does not change the evolution of flutter stability of suspension bridge with increasing wind yaw angle. The critical flutter wind speed fluctuates with the increase of wind yaw angle, and it reaches the lowest value mostly under the skew wind, with an average reduction of 8.0%. The combined influence of the aerostatic effect and skew wind further reduces the flutter critical wind speed by 11.5% on average, and therefore, the aerostatic effect, skew wind effect and their adverse influences need to be comprehensively considered in the flutter analysis of long-span suspension bridges.