International Journal of Structural Stability and Dynamics

A simplified method is presented for evaluating the dynamic properties of structures considering the effects of soil–pile–structure interaction (SPSI). A substructure method is used to establish the model of the soil–pile–structure system which is characterized by several dimensionless parameters. The shear-type structure is modeled as a generalized single-degree-of-freedom system using the virtual displacement principle, and the impedance functions of the floating pile-foundation are formulated by the thin-layer method. A number of coupled systems are analyzed and the results are used as the statistical base to obtain the mathematical relations between the dimensionless parameters and the dynamic properties. The dynamic properties solved by the equations are compared with those of the field experiment, shaking-table test and other analytical methods. The results indicated that the proposed equations are of high accuracy and can be used to obtain the dynamic properties of piles directly without performing complex analysis.

In this paper, a new modified harmonic balance method is presented for the nonlinear aeroelastic analysis of two degree-of-freedom airfoils. Using this method, the nonlinear problem is first translated into a minimization problem, and the Particle Swarm Optimization which has high calculation efficiency is adopted to solve the problem. The proposed method is used to solve the nonlinear aeroelastic behavior of supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Three examples of nonlinear aeroelasticity with significantly different coefficients are prepared, in which the frequencies and amplitudes of the limit cycles are obtained. The results show that the present current method is computationally more efficient.

One of the important problems in time-controlled switched dynamical systems is to find a stabilizing time sequence if there is any. The problem is challenging for switched systems with all unstable modes. Two fundamental approaches are introduced, which are classified as the fast switching method and the method of converting state-controlled signals. Five schemes are delineated and validated in the numerical study based on the two approaches. The effects of switching frequency and duty ratio on the dynamical system performance are analyzed, from which important implications have been drawn for use in practical system design. The proposed methods shall also provide intuition into understanding the mechanism of how to maintain a dynamical system’s stability when all of its modes are unstable.

This paper analyzes the dynamic response of space and plane trusses with geometrical and material nonlinear behaviors using different time integration algorithms, considering an alternative Finite Element Method (FEM) formulation called positional FEM. Each algorithm is distinguished from each other by its specific form of position, velocity, acceleration and equilibrium equation concerning the stability, consistency, accuracy and efficiency of solution. Particularly, the impact problems against rigid walls are analyzed considering Null-Penetration Condition. This formulation is based on the minimum potential energy theorem written according to the nodal positions, instead of the structural displacements. It has the advantage of simplicity when compared with the classical counterparts, since it does not necessarily reply on the corotational axes. Moreover, the performance of each temporal integration algorithm is evaluated by numerical simulations.

This paper deals with the free vibration response of MDOF mass-spring systems with time-variable mass and constant stiffness. To show the necessity of this study, a review on the related published articles is presented. After formulating the governing initial value problem which is a coupled system of differential equations with variable coefficients, the differential transform method (DTM) is employed to obtain an analytical solution. The proposed solutions are verified against exact results available in the literature. It is demonstrated that the effect of time-variable mass is equivalent to viscous damping. This viscous damping can be positive or negative depending on the sign of the mass change rate. This role is thoroughly investigated via numerical examples.

The resolution of structural finite element model (FEM) determines the computation cost and accuracy in dynamic analysis. This study proposes a novel wavelet finite element model (WFEM), which facilitates adaptive mesh refinement, for the dynamic analysis and damage detection of beam structures subjected to a moving load (ML). The multi-scale equations of motion for the beam under the ML are derived using the second-generation cubic Hermite multi-wavelets as the shape functions. Then an adaptive-scale analysis strategy is established, in which the scales of the wavelet beam elements are dynamically changed according to the ML position. The performance of the multi-scale WFEM is examined in both dynamic analysis and damage detection problems. It is demonstrated that the multi-scale WFEM with a similar number of degrees of freedom can achieve much higher accuracy than the traditional FEM. In particular, the multi-scale WFEM enables the detection of sub-element damage with a progressive model updating process. The advantage in computation efficiency and accuracy makes the proposed method a promising tool for multi-scale dynamic analysis or damage detection of structures.

This paper addresses the compressive local buckling behavior of an infinitely long laminated composite plate resting on a tensionless elastic foundation (Winkler foundation). The analytical solution to the contact buckling coefficient of a laminated composite plate is derived using a one-dimensional analytical method. Numerical examples are considered to investigate the influence of the ply angle and foundation stiffness on the contact buckling coefficients of laminated composite plates under uniaxial compression. The lateral boundary conditions including clamped and simply-supported edges are treated. Finally, finite element (FE) analysis is conducted to provide an independent check on the analytical solutions.

The paper proposes a self-sustained single-degree-of-freedom oscillator to accurately generate the longitudinal contact force between a pedestrian’s feet and the supporting flat rigid surface. The model is motivated from the self-sustained nature of pedestrian walking, i.e. a pedestrian produces the required internal energy to maintain a repetitive body motion. It is derived by adding two nonlinear terms to the conventional Rayleigh oscillator to yield odd as well as even harmonics, as observed in experimentally recorded longitudinal force data. For the dynamic analysis of the oscillator, two methods are adopted: the energy balance method and the Lindstedt–Poincare perturbation technique. Moreover, the least-squares identification procedure is used to identify values of the oscillator parameters from the force records of 12 different pedestrians walking on an instrumented treadmill at 10 walking speeds. The results generated by the proposed oscillator agree well with the experimental data.

The so-called “plastic buckling paradox” originates from the fact that the Prandtl–Reuss’ flow theory of plasticity overestimates the plastic buckling load of plates and shells, whereas Hencky’s deformation theory of plasticity provides results that are more accurate. However, it has been shown that this problem can be overcome by introducing certain initial imperfection in accurate finite element (FE) simulations based on the flow theory of plasticity.^– The present study goes deeper into the problem and reveals that in the case of short cylinders under combined loading, which have long been the object of extensive research in the elastic range, a different modeling of the material behavior can also trigger a mode jumping from the initial imperfection, which may even reverse the reported predictions by the flow and deformation theories of plasticity. This fact must be taken in maximum consideration when performing nonlinear FE analyses for estimating the plastic buckling of thin and moderately thin short cylindrical shells.

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

In this paper, the reliability of stochastic dynamical systems under Gaussian white noise excitations with fractional order proportional–inegral–derivative (FOPID) controller is estimated. First, the FOPID controller is approximated by a set of combination of displacement and velocity based on the generalized van der Pol transformation. Then, the stochastic averaging method of energy envelope is applied to obtain a diffusive differential equation, from which the Backward Kolmogorov equation, governing the conditional reliability function, and the Generalized Pontryagin equation, governing the statistical moments of first-passage time, are derived from the averaged equation and solved numerically. Finally, in the two examples, the critical parameters in the FOPID controller are shown to be capable of improving the reliability of the stochastic dynamical system apparently, and all numerical results are verified to be efficient and correct by the Monte Carlo simulation.

The dynamic behavior of singly and doubly curved panels of the rectangular planar form subjected to different types of loadings is presented. The mathematical formulation is based on the higher order shear deformation theory, and the principle of virtual work is used to derive the equations of motion. The fast converging finite double Chebyshev series and Houbolt time-marching scheme are used for evaluating the dynamic response of the panel. The effect of the magnitude and duration of pulse loadings on the transverse central displacement and bending moment responses is evaluated for different parameters. The accuracy of the present solution methodology is established by the convergence study of non-dimensional central deflection and central moments and comparison of the present results with those available in the literature. Some new results are presented for the hyperboloid panels.

Stability and dynamic modeling of the floating wind turbine (FWT) is a crucial challenge in designing of the type of structures. In this paper, the tension leg platform (TLP) type FWT is modeled as a multibody system considering the flexibility between the nacelle and tower. The flexibility of the FWT is modeled as a torsional spring and damper. It has 6 degrees of freedom (DOFs) related to the large-amplitude translation and rotation of the tower and 4 DOFs related to the relative rotation between the rotor-nacelle assembly and the tower. First, the nonlinear equations of motion are derived by the theory of momentum cloud based on the conservation of momentum. Then, the equations of motion are solved and the system is simulated in MATLAB. Moreover, the effect of flexibility between the nacelle and tower is investigated via the dynamic response. The stability of the system in three different environmental conditions is studied. Finally, the spring and damping coefficients for the system response to get near to instability are determined, by which the critical region is defined. The simulation results demonstrate the importance of the flexibility between the nacelle and tower on the overall behavior of the system and its stability.

This study investigates the dynamic response of a 5MW offshore wind turbine with monopile foundation subjected to wind and wave actions under parked condition. It includes dynamic interaction between the monopile and the underlying soil subjected to stochastic wind and wave loading. The offshore wind turbine tower has been modeled using the finite element software ANSYS 14 as a line structure and it comprises a rotor blade system, a nacelle, and a flexible tower under parked condition. The mass of the rotor, blade, and nacelle are lumped at the top of the tower for simplicity. Stochastic wind and wave loadings are simulated using the Kaimal spectrum and the Pierson–Moskowitz spectrum correlating wind and wave forces, respectively. The soil–structure interaction (SSI) effect at the foundation level is taken into consideration by including rotational as well as lateral spring constants derived from Wolf’s double cone model for embedded foundations. The results are studied in the frequency domain for both wind and wave loadings in the form of power spectral density functions, which show that the response of the structure depends not only on the external forces but also on the soil–structure interaction effect. Under very soft soil conditions, the displacement response is amplified to a very high value under wind loading when compared with that under wave loading at lower frequencies. Incorporation of soil–structure interaction also modified the peak value of displacement and its subsequent frequency when compared with that for the fixed base structure which does not consider soil–structure interaction.

For seismic isolated buildings, the isolators should be able to control peak deformation and have good restoring ability to return the building to its original position. Shape memory alloys (SMAs) are known for their properties of energy dissipation and deformation recovery, which make them appealing for use in isolation systems. To this end, the feasibility of SMA-based damping devices for use in an isolation system of low-rise frame buildings is studied in this paper. Numerical analyses were conducted and compared for buildings installed with SMA-based bearings (SMABs) and lead-rubber bearings (LRBs). A two-mass isolated frame building installed with these bearings was subjected to earthquakes corresponding to multilevel seismic hazards. The results show that the SMABs offer comparable seismic hazard mitigation efficacy to that of the LRBs while successfully restoring the building to the rest position after the earthquake. Furthermore, adding the energy dissipation capacity and properly using the strain hardening behavior of the SMAs are favorable for controlling isolation deformation while protecting the superstructure. The strain hardening behavior of the SMABs is beneficial for controlling deformation at the isolator level, which can still maintain isolation efficacy.

In this study, numerical simulations are conducted with a verified model to develop damage threshold curves for structural insulated panels (SIPs) with OSB skins strengthened by basalt fiber cloth subjected to windborne debris impact. Numerical models of the SIP with OSB skins strengthened by basalt fibre cloth at the front or back side are developed by using LS-DYNA. The accuracy of the numerical model is verified by comparing numerical results with laboratory testing data. Using the verified numerical model, intensive simulations are conducted to examine the influence of various parameters, including thickness of basalt fiber, location of basalt fiber layer, bonding strength between the basalt fiber cloth and the OSB skin, on the dynamic responses of the SIP. The debris penetration or fracture of the strengthened SIP that creates an opening is defined as failure of the panel in this study. Empirical formulae are derived on the basis of the numerical results to predict the thresholds of penetration velocity and projectile mass that lead to failure of the SIP. The empirical formulae can be straightforwardly used to assess the performance of the SIP with OSB skins strengthened by basalt fiber cloth subjected to windborne debris impact.