International Journal of Structural Stability and Dynamics

The stressed-skin effect refers to the enhancement of skin stiffness on structural stiffness and the ultimate load. Accurately quantifying the magnitude of the stressed-skin effect is of great significance for the safety and economic benefits of structures. In existing research, the skin panels are usually modeled by shell elements rigidly connected to the members, which may have lower computational efficiency and are not consistent with actual construction practices. For the triangular skin panels in aluminum alloy single-layer spherical reticulated shells, this paper proposed a simplified calculation model based on multiple non-linear springs. This model can greatly reduce the number of elements and its reliability has been successfully validated. Through parametric analysis, it was observed that the skin stiffness is primarily determined by the thickness of the skin panels and the connection stiffness between the skin panels and the members. The simplified model was applied to the models of aluminum alloy single-layer spherical reticulated shells to explore the effects of skin stiffness and initial geometric imperfection on the ultimate load of the shells. The results show that considering skin stiffness can increase the ultimate load by 10–20%, while the adverse effects of initial geometric imperfection can be weakened. Based on extensive numerical results, the formula for the ultimate load of the aluminum alloy single-layer spherical reticulated shells was modified to consider the stressed-skin effect.

A dynamic model of a vibration system with two degrees of freedom and multiple rigid constraints is constructed, the dynamics constraints of the segmented smooth vibration system under the multi-body impact coupling condition are given. Based on the cell mapping principle, a two-parameter co-simulation is carried out with two important parameters of excitation frequency and constraint gap as control variables. The model types and distribution rules of the periodic motion of the system response on the $(\omega ,\delta )$-whole two-parameter plane are obtained. The correlation between the dynamic response of the system and the model parameters is analyzed, and the evolution and bifurcation characteristics of fundamental periodic vibrations in the low-frequency small-gap parameter domain of the two-degree-of-freedom multi-rigid constrained vibration system are discussed. The diversity and regularity of subharmonic shock vibrations in the translational domain of the lingual domain are found.

Base isolation proves to be an effective vibration control strategy for buildings. However, the base-isolation floor (BIF) may undergo substantial displacements. To improve the seismic performance of base-isolation system, this paper proposes a multi-performance economical optimization procedure (MPEOP) for exploring the optimal parameters of base isolation system with tuned inerter negative stiffness damper (BIS-TINSD) subjected to non-stationary seismic excitation. The simplified analysis model for BIS-TINSD is developed, followed by the formulation of the state-space representation. The non-stationary seismic excitation is represented as a stationary Gaussian process with a time-modulating function based on the Clough–Penzien spectrum, and combining the equations of motion with seismic excitation results in the augmented state-space representation of structure-damper-excitation, followed by the formulation of differential Lyapunov equation. The multi-objective performance economical index is proposed, in which the performance optimization objective is defined as a weighted combination of base isolation floor displacement and superstructure acceleration, and the economic optimization objective is set as the support stiffness. The Pareto optimal fronts (POF) are adopted to deal with optimal objectives. The examination of optimal design parameters is extended under real earthquake records. The results demonstrate the effectiveness of the MPEOP, and indicate the advantages of the BIS-TINSD compared with the inerter amplify damper (IAD) and negative stiffness inerter damper (NSID).

This paper investigates the nonlinear dynamics of FG-FCMPs with initial imperfections. Based on the MCST, the nonlinear equations of motion and the corresponding boundary conditions are established by applying Hamilton’s principle, the Euler–Bernoulli beam theory, and von-Kármán geometric nonlinearity. To describe the initial geometric imperfection of the FG-FCMP, the first-order vibrational mode is employed. Subsequently, in cases of primary parametric resonance, 1:2 subharmonic resonance for the first-order mode, as well as primary resonance for the second-order mode, Galerkin’s method, and the multiple scale method are utilized to analyze the amplitude–frequency responses of the imperfect FG-FCMP. The numerical simulations test the influence of flow velocity, micro-scale parameter, geometrical imperfections, and external loads on the nonlinear characteristics of a coupled system with two DOFs. It is found that, as the increase of flow velocity, micro-scale effect, and external load, the amplitude of the first two modes can be increased. The hardening characteristics are converted into the softening characteristics due to the imperfect effect. Furthermore, numerical results provide a more comprehensive understanding of the nonlinear dynamics of FCMPs for both periodic and chaotic motions.

As the supporting structure of the wind turbine, the tower is important for the safety of the wind turbine. The accurate estimation of tower response is critical for the wind turbine tower design. In the preliminary design, lots of calculations are necessary to determine design parameters. The traditional time domain calculation suffers its low efficiency and hinders the design progress. To overcome this difficulty, the frequency domain analysis should be developed, especially for the large wind turbine which may be significantly affected by the aerodynamic damping. In this study, a semi-analytical formula for the variance of the tower base bending moment is developed from the frequency domain analysis at parked condition. First, based on the quasi-steady theory and the three-component (mean, background and resonant components) method commonly used in the wind-resistant design of structure, the analytical formula of the variance for the tower base bending moment is presented considering the three components of the wind velocity. Second, the analytical formula is corrected based on the comparison with the calculation result by FAST. In the correction, the empirical aerodynamic damping is adopted. Finally, the applicability of the developed semi-analytical formula is verified by 5MW, 10MW and 15MW wind turbines.

This paper analyzes the beam under isolated and uniform loads, extending this calculation towards the structural type of the continuous beam, by means of a single expression of the elastic curve. A general expression of the bending is proposed, deduced by integrating the different differential equations of the elastica, associated to each section between discontinuities produced by the loads. In this paper, support reactions are incorporated into the load system. Therefore, the continuous beam is understood as a bar made up of sections aligned between discontinuities. With this, the isostatic beam, the hyperstatic beam and the continuous beam can be treated by means of the same integrated expression of the displacement, also called the Macaulay method. Equivalent notations are provided to the expression of bending for the cases of traction–compression and torsion, obtained through the same reasoning and sequence of operations. The formulation of elastic type and the associated operations shown allow us to cover the analysis of the generic structural form, which we can define as the beam of any number of spans, or continuous beam of $n$ spans. The load system is also generalized, being able to contemplate loads of a different nature and form of distribution, both static and mobile. The examples that have been developed always provide analytical results of solicitation and deformation. They intend to explain the systematic path followed from the approach of the structural problem to its mathematical modelling, and the resolution procedure developed to obtain useful values for the structural verification. In these examples, an increasing degree of complexity and generalization has been followed. The expressions obtained are validated by comparing them with those that are usual in the structural literature for the same or similar problems.

In recent decades, carbon fiber, glass fiber, polyester and Kevlar fiber have been utilized to replace the steel shims in conventional steel-reinforced elastomeric isolators (SREIs). This study chose nylon fabrics owing to their extreme low cost, low elastic modulus and good adhesion to rubber, and nine nylon fabric-reinforced elastomeric isolators (N-FREIs) were manufactured with different design parameters. Compression and compression shear tests were, respectively, conducted to investigate the mechanical properties together with their influential factors of the N-FREIs. Results show that the vertical load-carrying capacity of the isolator is high enough to sustain a compressive stress of 10MPa without visible damage. The compressive stiffness of N-FREI is much smaller than that of SREI, and the vertical damping ratio under cyclic compression reaches up to 7%. In the compression shear tests, the shear stiffness of the isolator first decreases and then increases as the shear strain increases within 300%, and the equivalent damping ratio varies between 9% and 14% for different sizes of the isolator. Additionally, due to the flexibility and extensibility of the low modulus nylon fabric, both vertical and horizontal stiffness decrease a bit with an increase in the number of fabric layers. Finally, a formula for calculating the horizontal stiffness of N-FREI is proposed, it provides a comprehensive mathematical model to predict the behavior of the N-FREI under horizontal shear conditions.

Considering the importance of wind turbine tower, its vibration under multi-hazard action consisting of vortex-induced load and seismic load needs to be controlled, especially as the height of the wind turbine tower increases, it increases the risk of its higher-order vibration. To address this issue, theoretical equations for vortex-induced load based on the governing equation of particle damping system are put forward, the vibration control of a 1/20 scale wind turbine model is studied, and the experimental and numerical analyses are conducted. Many studies have shown that wind turbine tower equipped with tuned mass damper (TMD) can result in an RMS response reduction ratio ranging from 20% to 40%. Compared to TMD, particle tuned mass damper (PTMD) has better vibration control effect under single seismic load, and still achieves good vibration control ability with a maximum RMS (root–mean–square) reduction ratio of 35.55% under multi-hazard action. Furthermore, MPTMD (multiple particle tuned mass damper) is proposed for controlling higher-order vibration mode, achieving a maximum RMS reduction ratio of 65.93%. Combining the spectrum diagram result, the ability to control higher-order mode vibration of MPTMD is confirmed.

The nonlinear dynamic responses of the corrugated sandwich plate under mechanical-thermal loads are studied and analyzed. Based on hyperbolic parabola shear deformation plate theory (HPSDT), the partial differential equation of the sandwich plate with the corrugated core is established. Using the Galerkin truncation method, the nonlinear motion equation is derived. By the solution, the response of the corrugation plate with simply supported four edges at different temperatures is obtained and validated. Then the transient responses of the corrugated sandwich plate under different impact loads are analyzed, and the effects of the base materials, the corrugation types and the structural parameters of the corrugated plate on the transient responses are discussed in detail. The research provides a reference for improving the impact resistance of the sandwich plate in practical application.

Previous vibration-based damage detection studies mostly focus on developing a more sensitive optimization function to promote the effectiveness of damage identification. However, a few studies have conducted comparative analyses on the detection performance of different optimization functions. In the study, changes in the frequency and mode shape are applied as the inputs to different optimization functions for damage identification. Three optimization functions are established using the frequency residuals, the combinations of frequency and mode shape residuals, and the modal flexibility residuals, respectively. Considering the sparsity of damage element distribution, an iterative reweighted $l_{1/2}$ $(\mathrm{\text{IR}}{l}_{1/2})$ regularization is added as a norm penalty to the optimization function. A numerical model and an experimental example are applied to assess the performance of distinct optimization functions. The results show that the increase in modal data number cannot significantly improve the detection accuracy when the number meets the basic requirements for identifying damage. The detection error of the optimization function established by combining the frequency and mode shape residuals is 6.65% and 5.18% using the first four and fourteen-order noisy modal data, respectively. Furthermore, the optimization function constructed using the modal flexibility residuals requires more less modal data to identify damage than the other two functions.

To design walk-fast and energy-efficient robots, there has been lots of work in the last decade examining the locomotion dynamics of a passive biped. As the walking environment or system parameter changes, an energy use efficient robot may become inefficient. A possible approach to increase the energy efficiency is through the ability to harvest the energy used during the locomotion. The paper’s main goal is to investigate the relations between walking speed, the locomotion energy consumption of a passive biped, and the ability to retrieve the lost energy as locomotion energy efficiency varies. Piezoelectric bimorphs were attached to the feet of the biped to harvest energy via exploiting the acceleration excitations induced vibrations at the instant foot lift and heel strike. It is found that as a foot-to-hip mass ratio increases, the stable periodic-1 (P1) walking gait becomes slower and more energy costing. Also it means more available energy to harvest, although the retrieved energy is much smaller compared to the locomotive energy. Once the foot-to-hip mass ratio passes the periodic doubling (PD) point, P1 walking gaits will become limped P2 walking gaits, and the high energy cost situation alleviates, which also means less available energy to harvest. On the other hand, if the foot-to-hip mass ratio is fixed and the slope angle increases, the walking will experience sequences of PD bifurcations, and the walking gaits go through P1, P2, P4, P8, and chaotic walking. As the walking gaits change, the average walking efficiency, average locomotion energy consumption, and average harvested energy grow as the slope becomes deeper.

Nonlinear energy sinks (NESs) are critically important for structural vibration suppression. They can absorb vibrational energy across a broad frequency spectrum, possess strong robustness, and have a relatively small mass. This study addresses the vibration suppression in a piecewise linear stiffness NES system under random excitation. Initially, a theoretical model of the piecewise linear stiffness NES system is developed. The piecewise linear stiffness function is approximated using Legendre polynomial approximation. Following this, the steady-state Fokker–Planck–Kolmogorov (FPK) equation of the system is formulated via the Generalized Harmonic Function Method. The FPK equation is solved using the fourth-order central difference method, and the effectiveness of this approach is validated by comparing the FDM results with numerical simulations. Lastly, the influence of varying system parameters on the stability of the piecewise linear stiffness NES system is analyzed.