International Journal of Structural Stability and Dynamics

Active control systems are always restricted in one form or another. One of the restrictions is the lack of sensors or actuators for control implementation. This restricted control problem in the form of partial sensing and actuation thus poses a challenging problem for active controls, since most of the existing approaches make the implicit assumption that such information is readily available. This paper discusses the possibility of controlling structural vibration using restricted sensing and actuation control methodology. This opens a new avenue that, although counter to the current development in active control system designs through smart materials and smart structures, is readily applicable in practice. A number of fundamental results are derived concerning the active restricted controller properties, while algorithms are presented for the implementation. A case study is also provided, which demonstrates the feasibility of active restricted vibration control solutions.

The systematic running safety assessment of railway bridges presents lots of challenges, one of which is estimating the uncertainty bounds of the structural responses of bridges under vehicle loads with multisource randomness. In this study, a probability safety assessment method is proposed for evaluating the uncertainty bounds of random time-history responses for the stochastic train-bridge coupled system. First, a refined probabilistic model for the train-bridge coupled system (TBS) in heavy haul railway is established with the multi-excitations of random track irregularities, random vehicle loads and stochastic structural parameters. The probability density evolution method (PDEM) is employed to obtain the solution of the time-varying probability transferred between the stochastic excitations and the output of the dynamic responses. Then, to establish a rapid and straightforward approach for the systematic running safety assessment of the TBS, the quantiles of the probability distribution are used to estimate the time-history uncertainty bounds of random responses of interest distributed in real probability functions. Case studies by the field test and numerical simulation are presented to verify and investigate the accuracy and reliability of the proposed method. The results show that the quantiles of the probability distribution proposed are suitable for the systematic running safety assessment of the TBS.

This work focuses on analyzing the dynamical behavior of a mechanical system consisting of a double spatial pendulum in contact with a movable obstacle. The pendulum’s ability to move in space is achieved by the use of special Cardan–Hook joints as the links of the pendulum. The mechanical system is equipped with a special movable obstacle, i.e. a rotating circular plate situated below the pendulum, which limits the space of admissible positions. A significant part of this work is devoted to the modeling of the contact between the pendulum and the obstacle. In this regard, a special class of reduced models is derived with the resultant friction force and moment acting on the finite size of the contact area along with a compliant model of impact based on the Hertz stiffness. Finally, the effective model suitable for fast and realistic numerical simulations is obtained. The contact model is tested numerically and the effect of its parameters on the system bifurcation dynamics is investigated.

Frame structures are widely used in engineering applications, especially in space structures. For special use such as shape and vibration control of such structures, piezoelectric patches are usually placed on the beam surfaces to form active frame structures. To perform shape control or vibration control tasks, modeling methods for the formed active frame structures need to be studied. This paper develops a new distributed model of an active frame structure composed of multilayer piezoelectric beam components. First, the governing equations of a beam, bonded with piezoelectric patches, are developed via the generalized Hamilton principle, by considering the transverse shear strain. Then, the analytical solutions of the governing equations and the generalized element stiffness matrix are derived through the distributed transfer function formulation. Finally, the analytical solution of the entire system is obtained by the technique for assembling element stiffness matrix. In numerical simulations, buckling and vibration of an active frame structure are both studied. In addition, a novel Improved Ant Lion algorithm is proposed for optimal design of the frame structures. The optimization examples confirm that the proposed algorithm is more efficient than other existing popular algorithms such as Genetic Algorithm (GA) and Ant Lion Optimization (ALO) algorithm.

The dynamic response of an offshore pile in saturated soil subjected to lateral harmonic loading is theoretically investigated by considering the dynamic pile-water interaction. The governing equation of water is solved based on the separation of variable method, and the analytical expression of the hydrodynamic force applied on the pile is then obtained. Based on the continuous conditions at the pile-soil interface and pile-water interface, the analytical solution of the dynamic impedance of the offshore pile is derived by using transfer matrix method. To verify this solution, the dynamic impedance obtained for a cylinder in water is compared with that of a partially embedded pile. Based on this solution, the effect of hydrodynamic pressure and other parameters on the dynamic response of offshore piles is investigated. The results show that the analytical model ignoring the hydrodynamic force applied on the pile misestimates the impedance of the pile in the high frequency range.

Excessive floor vibrations due to human activities such as heel-drop and jumping can induce annoyance to occupants and cause a serious serviceability problem. Both field tests and finite element analysis were conducted to study the vibration behavior of the composite slab with precast ribbed panels (CSPRP), a relatively new floor system compared with the cast-in-place reinforced concrete (RC) slab. In addition, both heel-drop and jumping impacts were employed to generate the acceleration response of the floor, from which two important vibration characteristics of natural frequencies and damping ratios are obtained. A comparison of the vibration behavior of CSPRPs with RC slabs indicates that the former exhibits more satisfactory perceptibility in terms of vibration. Appropriate coefficients (i.e. ${\beta }_{\text{fp}}=0.03$ and ${\beta }_{\text{rp}}=0.14$) with the root-mean-square and peak accelerations subjected to heel-drop and jumping excitations are proposed for both CSPRPs and RC slabs. Lastly, an extensive parametric study considering different boundary conditions, floor types, and floor spans was carried out using the finite element method. It is recommended to use CSPRP under 3.3m span in order to keep the fundamental frequency above 3.0Hz.

Wind-driven rain (WDR) and its interactions with structures is an important research subject in wind engineering. As bridge spans are becoming longer and longer, the effects of WDR on long-span bridges should be well understood. Therefore, this paper presents a comprehensive numerical simulation study of WDR on a full-scale long-span bridge under extreme conditions. A validation study shows that the predictions of WDR on a bridge section model agree with experimental results, validating the applicability of the WDR simulation approach based on the Eulerian multiphase model. Furthermore, a detailed numerical simulation of WDR on a long-span bridge, North Bridge of Xiazhang Cross-sea Bridge is conducted. The simulation results indicate that although the loads induced by raindrops on the bridge surfaces are very small as compared to the wind loads, extreme rain intensity may occur on some windward surfaces of the bridge. The adopted numerical methods and rain loading models are validated to be an effective tool for WDR simulation for bridges and the results presented in this paper provide useful information for the water-erosion proof design of future long-span bridges.

Plates are applied to a wide array of structural applications of varying complexity. Each application requires rigorous analysis to determine the viability of the proposed model. One such application involves modeling a larger structure as a collection of smaller flat plates connected at the plate boundaries. Previous research into these types of structures has led to varying levels of accuracy. It has been dependent on the applications and assumptions involved. To improve the accuracy of these types of structures in a more general context, we propose expanding on current models of coupled plates by modeling the plates using Mindlin plate theory. We analyze the vibration of the improved model with general elastic boundary conditions, point supports and coupling conditions using the Fourier series method and finite element software. When the Fourier series method is applied directly, continuity issues arise at the plate coupling boundaries. To resolve these issues, the Fourier series solution of the vibration displacements is amended to include auxiliary functions. This improved coupled plate model is analyzed and numerically simulated for a variety of elastic boundary conditions and coupling conditions. The numerical results are produced using the Fourier series method and a finite element solution to demonstrate the validity of the improved coupled plate model.

This paper proposes a novel method for estimating the evolutionary power spectral density (EPSD) of a nonstationary process based on a single sample. In the proposed method, a sample of a nonstationary process is decomposed into several components with a new binomial fitting decomposition (BFD). The EPSD of each component can be estimated using a newly proposed time-varying standard deviation estimation method and short-time Thomson multiple-window spectrum estimation method. The EPSD of the analyzed nonstationary sample is obtained by combining the EPSDs of all components. Via a comprehensive numerical study, the applicability of the proposed EPSD estimation method (for estimating the EPSD of a nonstationary process) is analyzed and compared with those by the Priestley method and wavelet-based method. The numerical results indicate that the estimated EPSD by the proposed method is more consistent with the corresponding theoretical one than those by the other two methods. Finally, the EPSDs of Storm Ampil, measured atop the Shanghai World Financial Center, are analyzed by the proposed method.

In this paper, a closed-form solution is presented for the free vibration response of a 2-DOF parametric system by a technique with special trigonometric series. The technique extends the concept of modulation feedback to the problem of multiple degrees of freedom (M-DOF) parametric system using an equivalent dynamic system. The characteristic equation is derived by the harmonic balance in a parametric equation with the principal oscillation frequencies computed. The computation of modes and splitting modes is carried out by operation on a mixed matrix. The arbitrary constants in the general solution are determined by the initial conditions. A real-life example of a coupled inverted-pendulum system is provided to illustrate the applicability of the proposed approach. An approaching error is adopted to assess the computational errors both using the proposed technique and the Runge–Kutta algorithm. Of interest is that the time-periodic coefficient results in the changeability of the mode in the 2-DOF parametric system, while exciting the splitting mode in the harmonic combination resonance. The proposed technique is numerically demonstrated to possess not only high approaching accuracy, but is also capable of revealing some new phenomena in the parametric system, such as characteristics of mode and slitting mode, etc. It proves to be useful for future research and engineering applications of parametric systems.

With the increase of the span and height of modern engineering structures, the design length of engineering cables is increasing while the structural form is becoming more complicated, whose dynamic problem has become the key to structural design, performance monitoring and maintenance and vibration control. Therefore, it is necessary to study and develop a unified dynamic analysis theory for complex cable system with high calculation accuracy and efficiency to meet the requirements of exact analysis of engineering structures. In view of this, a unified dynamic analysis method for shallow sagged cable system is proposed in this paper based on the dynamic stiffness method. Since the derivation process is given in analytical form, the calculation accuracy and efficiency are promoted greatly. Full-scale cable test and numerical cases are used to verify the accuracy of the proposed method. Results show that the proposed method is in good agreement with the measured results and can effectively overcome the “root-missing” phenomenon existing in conventional iteration methods when solving the transcendental frequency equation.

This study comprehensively explores the dynamic behavior of a slender slab due to the excitation of pedestrian traffic. Three kinds of excitation models are adopted to describe the vibration of the slab induced by pedestrians. A comparison of the structural responses shows that the bipedal model results in larger vibrations than the mass–spring–damper or pseudo-excitation models. Further research indicates that the pedestrians evidently alter the dynamic properties of the slab by affecting its frequency and damping capacity. The slab tends to be more flexible at a lower frequency as the pedestrian walks across its surface while its damping capacity is improved. In contrast, the slab can increase the frequency, while decreasing the damping of the pedestrian model. Thus, the slab also alters the properties of the pedestrians. In addition, an investigation of the bipedal model parameters indicates that the variations of the leg stiffness, damping, and body mass have distinct effects on the slab characteristics and vibrations. In order to assess the response of the slab to a crowd, a new simplified theory is introduced to describe the dynamic properties of the slab under multi-layout excitations, including human influences resulting from different body properties. The results of this study provide potential ways for understanding the vibratory mechanisms of slender structures such as footbridges, grandstands, or stations under crowd excitations.

This paper concerns with a suspended cable in thermal environments under bi-frequency harmonic excitations, with a focus placed on the effect of temperature changes on one type of simultaneous resonance. First, the nonlinear equation of motion in thermal environments is obtained for the in-plane displacement of the cable. Then, the Galerkin method is employed to reduce the partial differential equation to an ordinary one. Second, based on the discretized form of the governing equation, the method of multiple scales is employed to obtain the second-order approximate solutions, with the stability characteristics determined. Third, numerical results are presented by using the perturbation method, together with numerical integration by the following means: frequency-response curves, time-displacement curves, phase-plane diagrams, and Poincare sections. The direct integration method is utilized to verify the results obtained by the perturbation method, while revealing more nonlinear dynamic behaviors induced by temperature changes. Both the softening and/or hardening behaviors, and the switching between them are observed for the cable in thermal environments. The response amplitude of the cable is very sensitive to temperature changes, but the number of circles in the phase diagrams and the number of cluster points in Poincaré sections is independent of the thermal effects in most cases. Finally, the vibration characteristics of the cable for different thermal expansion coefficients and temperature-dependent Young’s moduli are also investigated.

The identification of parameters of linear or nonlinear systems under unknown inputs and limited outputs is an important but still challenging topic in the context of structural health monitoring. Time-domain analysis methodologies, such as extend Kalman filter (EKF), have been actively studied and shown to be powerful for parameter identification. However, the conventional EKF is not applicable when the input is unknown or unmeasured. In this paper, by introducing a projection matrix in the observation equation, a time-domain EKF-based approach is proposed for the simultaneous identification of structural parameters and the unknown excitations with limited outputs. A revised version of observation equation is presented. The unknown inputs are identified using the least squares estimation based on the limited observations and the estimated structural parameters at the current time step. Particularly, an analytical recursive solution is derived. The accuracy and effectiveness of the proposed approach is first demonstrated via several numerical examples. Then it was validated by the shaking table tests on a five-story building model for the robustness in application to real structures. The results show that the proposed approach can satisfactorily identify the parameters of linear or nonlinear structures under unknown inputs.

The buckling mode is important to determine the critical load of specially orthotropic rectangular plates under axial compression with simply supported boundary. However, in classical laminated plate theory (CLPT), the critical buckling mode can only be obtained by iterative or numerical methods. This paper derives the critical buckling mode mathematically and presents the critical buckling load in closed form. By taking advantage of the derived closed-form solution, it is convenient to investigate the effects of aspect ratio, load ratio, and fiber orientation on the buckling load, and the parameters affecting the buckling mode can be easily obtained. The first-order shear deformation theory (FSDT)-based finite element method is developed to verify the closed-form solution. The bending-torsional coupling effects are analyzed and discussed to assess the approximation of the buckling behavior of specially orthotropic plates to general laminates. The obtained finite element solutions of general laminates are compared with the closed-form solutions of specially orthotropic plates. The accuracy of approximation of the buckling behavior of specially orthotropic plates to the general laminates increases as the bending-torsional coupling coefficients decrease. The closed-form solution can be applied to laminates with small bending-torsional coupling coefficients.

This paper is concerned with the nonlinear vibration and dynamic response of carbon nanotube (CNT) reinforced composite truncated conical shells resting on elastic foundations in a thermal environment. The material properties of shells are assumed to be temperature-dependent and graded in the thickness direction according to various linear functions. The nonlinear equations of motion are expressed in the form of two-component deflection function and solved by the analytical method. Detailed studies for the influences of various types of distribution and volume fractions of CNTs, geometrical parameters, Winkler and Pasternak elastic foundations on the dynamic response and nonlinear vibration of CNT polymer composite truncated conical shells are examined and the comparison study is carried out to verify the accuracy and efficiency of the proposed method.

In this paper, first a complete buckling experiment of the sandwich beams with the foam core is carried out, which includes the manufacturing of specimens and their experimental verification. Second, a refined sinusoidal zig-zag theory (RSZT) is established, which can describe the zig-zag effect during the in-plane compression of sandwich beam and accommodate the transverse shear free surface boundary conditions. Based on the established model combined with Hu–Washizu variational principle, a two-node beam element has been developed to address the buckling problem of the sandwich beams. Thus, the established beam element is able to accommodate interlaminar continuous conditions of transverse shear stress. Several examples have been investigated to validate the accuracy of the established method. The comparative analysis of the results including experimental data, the results acquired from three-dimensional finite element (3D-FEM) and diverse models has been made. Comparative analysis shows that the accurate buckling loads can be acquired from the established model. Nevertheless, other models discarding the continuous conditions of transverse stresses among the adjacent layers largely overestimate the critical loads.

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar$é$ method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.