International Journal of Structural Stability and Dynamics

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

Steady-state and transient acoustic radiation characteristics of clamped-free annular plate with tuned mass damper (TMD) device is studied. Galerkin’s procedure is employed to obtain the transverse vibration of the annular disk. Based on the Rayleigh integral approach, acoustic pressure radiation is obtained and subsequently the modal sound power and modal radiation efficiency are obtained. A new formulation for the transient acoustic pressure in Laplace domain is presented for the first time in this paper. Durbin’s numerical Laplace transform inversion scheme is employed to obtain the response spectrum. The optimum parameters of vibration absorbers are proposed for suppressing the dynamic vibration and acoustic pressure. A parametric study is carried out and the effects of vibration absorber characteristics are investigated using the analytical procedure. Limiting cases are considered and good agreements with the finite element solution, as well as with those available in the literature, are achieved.

In this study, a finite element method (FEM) based on the size dependent nonlocal integral elasticity theory is implemented for buckling analysis of nanoscaled beams with various boundary conditions. The method is based on the principle of total potential energy. The variations of buckling load with respect to the scaling effect parameter and to the length-to-thickness ratio are investigated. Furthermore, the effect of attenuation function type on the buckling load is examined. The results are compared with the corresponding solutions of governing stability equations which are derived in the context of nonlocal differential elasticity theory. It is found that the small scale coefficient has a noticeable effect on the buckling load of nanobeams.

System identification refers to the process of building or improving mathematical models of dynamical systems from the observed experimental input–output data. In the area of civil engineering, the estimation of the integrity of a structure under dynamic loadings and during service condition has become a challenge for the engineering community. Therefore, there has been a great deal of attention paid to online and real-time structural identification, especially when input–output measurement data are contaminated by high-level noise. Among real-time identification methods, one of the most successful and widely used algorithms for estimation of system states and parameters is the Kalman filter and its various nonlinear extensions such as extended Kalman filter (EKF), Iterated EKF (IEKF), the recently developed unscented Kalman filter (UKF) and Iterated UKF (IUKF). In this paper, an investigation has been carried out on the aforementioned techniques for their effectiveness and efficiencies through a highly nonlinear single degree of freedom (SDOF) structure as well as a two-storey linear structure. Although IEKF is an improved version of EKF, results show that IUKF generally produces better results in terms of structural parameters and state estimation than UKF and IEKF. Also IUKF is more robust to noise levels compared to the other approaches.

The stability of a nonuniform column subjected to a tip force and axially distributed loading is investigated based on the Timoshenko beam theory. An emphasis is placed on buckling of a standing column with varying cross-section and variable material properties under self-weight and tip force. Four kinds of columns with different taper ratios are analyzed. A new initial value method is suggested to determine critical tip force and axial loading at buckling. The effectiveness of the method is confirmed by comparing our results with those for Euler–Bernoulli columns for the case of sufficiently large shear rigidity. The effects of shear rigidity, taper ratio, and gravity loading on the buckling loads of a heavy standing or hanging column are examined.

A damage detection and estimation method is proposed for structural health monitoring using incomplete modal data and least squares support vector machine (LS-SVM). To accommodate the use of incomplete modal data, the iterated improved reduction system (IIRS) method has been used to condense the mass and stiffness matrices of the structure. The first two incomplete mode shapes and natural frequencies of a damaged structure are used as input data to the LS-SVM. The coupled simulated annealing (CSA) and standard simplex method using 10-fold cross-validation techniques are adopted to determine the optimal tuning parameters in the LS-SVM model. Three illustrative examples with and without noise in modal data are prepared to evaluate the performance of the proposed method. The results indicated that this method can be reliably used to identify the damages of structures with good accuracy.

This paper presents the analysis of flutter and nonlinear dynamics of an orthotropic composite laminated rectangular plate subjected to aerodynamic pressures and transverse excitation. The first-order linear piston theory is employed to model the air pressures. Based on Reddy’s third-order shear deformation plate theory and von Karman-type equation for the geometric nonlinearity, the nonlinear governing equations of motion are derived for the composite laminated rectangular plate by applying the Hamilton’s principle. The Galerkin method is utilized to discretize the partial differential governing equations to a set of nonlinear ordinary differential equations. The critical Mach number for occurrence of the flutter of the composite laminated plate is investigated by solving the eigenvalues problem. The relationship between the limit cycle oscillation and the critical Mach number is analyzed based on the nonlinear equations. The numerical simulation is conducted to study the influences of the transverse excitation on the nonlinear dynamics of the composited laminated plate. The numerical results, which include bifurcation diagram, phase plots and waveforms, demonstrate that there exist the bifurcation and chaotic motions of the composited laminated plate subjected to the aerodynamic pressures and the transverse excitation.

This paper discusses the necessity of considering the concurrent effects of uniform temperature and earthquake loadings in the design of cable-stayed bridges. This load combination is not foreseen in current design standards such as AASHTO and Eurocode. Three-dimensional finite element models of cable-stayed bridges are employed for nonlinear time history analyses. A load combination is proposed that adds uniform temperature loading to the existing extreme event load combination. The proposed combination is compared with existing extreme event load combination and the changes in forces and displacements are noted. A parametric study is then conducted by varying a number of properties of the cable-stayed bridges such as, span length, shape of the pylon, the deck/pylon connection and the actual temperature load. Pylon reactions and the deck axial forces are found to be more vulnerable to concurrent loadings for cable-stayed bridges of longer spans.

The seismic response of a stiff single-story and a flexible multi-story building isolated with triple friction pendulum bearing (TFPB) are investigated under the pulse-like (near-fault, NF-Pulse) and (NF-No Pulse) NF nonpulse ground motions. By varying the geometric parameters, such as the effective spherical surface radius, or by specifying different friction coefficients for each surface, one can adjust the behavior of the bearing. Consequently, the stiffness and damping ratio of the system can be optimized for multiple performance objectives under multiple levels of hazard. The seismic responses are evaluated under different isolation parameters for the displacement of isolation and the superstructure demand functions of the system, including the base shear, maximum inter-story drift and top floor absolute acceleration of the isolated structure. First, the seismic response of twenty TFPBs with different stiffnesses and damping ratios are investigated under NF motions. A comparison of results suggested that the displacement of the TFPB under the NF-Pulse motion is about twice that of the NF-No Pulse motions. The best performance of the system is found when the TFPB works in its third stage of motion. Next, from the sensitivity analysis, the effect of each parameter of the TFPB on the seismic response of system is investigated and the trends for optimal parameters of TFPB are presented. The criterion selected for optimality is to minimize the performance function that considers all seismic responses simultaneously. The optimum ranges for the related parameters are: (a) 0.02–0.04 for the coefficient of friction of the inner surface; (b) 0.06–0.14 and 0.04–0.12 for the bottom concave plate under the NF-Pulse and NF-No Pulse, respectively; (c) 0.06–0.18 and 0.06–0.16 for the top concave plate under the NF-Pulse and NF-No Pulse, respectively; (d) 200–500 mm for the radius of curvature of the inner surface; and (e) 2500–4500 mm for the outer surface.

Approximate numerical solutions are obtained for the vibration response of a functionally graded (FG) micro-scale beam entrapped within an axially-directed magnetic field using the differential transformation method (DTM). Idealized as a one-dimensional (1D) continuum with a noticeable microstructural effect and a thickness-directed material gradient, the microbeam’s behavior is studied under a range of nonclassical boundary conditions. The immanent microstructural effect of the micro-scale beam is accounted for through the modified couple stress theory (MCST), while the microscopic inhomogeneity is smoothened with the classical rule of mixture. The study demonstrates the robustness and flexibility of the DTM in providing benchmark results pertaining to the free vibration behavior of the FG microbeams under the following boundary conditions: (a) Clamped-tip mass; (b) clamped-elastic support (transverse spring); (c) pinned-elastic support (transverse spring); (d) clamped-tip mass-elastic support (transverse spring); (e) clamped-elastically supported (rotational and transverse springs); and (f) fully elastically restrained (transverse and rotational springs on both boundaries). The analyses revealed the possibility of using functional gradation to adjust the shrinking of the resonant frequency to zero (rigid-body motion) as the mass ratio tends to infinity. The magnetic field is noted to have a negligibly minimal influence when the gradient index is lower, but a notably dominant effect when it is higher.

In the present paper, the vibrational and buckling characteristics of nanotubes with various boundary conditions are investigated considering the coupled effects of nonlocal elasticity and surface effects, including surface elasticity and surface tension. The nonlocal Eringen theory is adopted to consider the effect of small scale size, and the Gurtin–Murdoch model the surface effect. Hamilton’s principle is employed to formulate the governing equation and differential transformation method (DTM) is utilized to obtain the natural frequency and critical buckling load of nanotubes with various boundary conditions. The results obtained match the available ones in the literature. Detailed mathematical derivations are presented and numerical investigations are performed. The emphasis is placed on the effects of several parameters, such as the nonlocal parameter, surface effect, aspect ratio, mode number and beam size, on the normalized natural frequencies and critical buckling loads of the nanotube. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects. Numerical results are presented which may serve as benchmarks for future analysis of nanotubes.

Employing a coupled model for vehicle–track interaction, this paper presented the dynamic analysis of railway track system in the presence of weld irregularities with different geometric profiles in two parallel rails. A 3D model of a standard railway wagon running on a ballasted track system is used to examine the vibrations of the system under track irregularities. Four samples of measured rail profiles at rail welds are considered as the source of dynamic excitations, in which the profiles of parallel rails are unequal. Hence, the individual profiles of left/right rails are imported into the numerical model, taking into account the nonuniform conditions of rail welds in both sides of the railway track. The dynamic responses of the track system caused by irregularities at welds are studied by performing the time-domain vibration analysis. The time histories of the nodal responses under various weld scenarios (measured in an actual railway track site) are recorded. Finally, the peak responses of dynamic forces along the track are determined for left/right rails. The results of dynamic simulations in various weld scenarios are compared and the values of dynamic amplification factors (DAFs) are evaluated. Such findings provide an estimation for the levels of dynamic forces occurring under impact loading conditions of nonuniform rail welds in left/right rails.

For the analysis of dynamic characteristics of fluid-conveying pipes with piecewise linear support, a fluid–structure coupling dynamic model based on the finite element method is proposed. A user-defined pipe element based on Euler–Bernoulli beam is developed for modeling the pipes, considering the dynamic flow conditions. A nonlinear spring element is utilized to model the clamp between the pipe and the base. The dynamic responses of the system are obtained through the direct time integration. The stiffness of the clamp support is investigated by the analytical method and the experimental method, in which it is found that the clamp stiffness is piecewise linear. For different pipe geometries the user-defined element model, analytical model and measurement data are compared. The results show high quality of the element developed in this paper. Finally, the dynamic characteristics of the pipe system with piecewise linear support subjected to base harmonic excitation are calculated and the effects of the system parameters on pipe behaviors have also been studied. As a consequence, the model proposed in this paper can represent the piecewise linear nonlinearity of the clamp support and be used conveniently to investigate the effects of the fluid–structure coupling on the system behaviors.

This paper is concerned with the development of a theoretical model for predicting the dynamics and pull-in instability of magnetically actuated pipes conveying fluid. The equation of motion of the pipe is constructed in the presence of nonlinear magnetic forces. The lateral displacement of the pipe comprises two parts, namely, a static displacement and a perturbation displacement about the static. Based on the finite element method (FEM), the static deflection of the pipe is calculated numerically first. The computed static deflection is then used to solve the equation governing the perturbed displacement. Consequently, the pull-in and flow-induced instabilities can be determined for clamped–clamped or cantilevered boundary conditions. Results show that the flow speed can significantly affects the static deflection of the pipe and hence the pull-in magnetic force. The magnetic force, on the other hand, has a great impact on the dynamics of the pipe system.