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This paper explores the nonlinear dynamic responses and bifurcations of the truncated sandwich simply supported porous conical shell with varying thickness under 1:1 internal resonance. Two skins with carbon fiber and a core with porous aluminum foam, which has an exponentially variable thickness along the generator and various porosity distribution types along the core thickness, make up the sandwich shell structure with varying stiffness. The porous shell structure is affected by a combination of the in-plane load, transverse excitation, thermal stress and aerodynamic force, which is formulated by employing first-order piston theory with a modified term for curvature. By way of FSDT, von-Karman geometrical formulations, Hamilton’s principle and Galerkin procedure, the nonlinear dynamic formulations in ordinary differential form for the variable stiffness porous sandwich shell structure are identified. The averaged equations in polar and Cartesian coordinate forms for the sandwich structure under the combined circumstance of 1:1 internal resonance, first-order main resonance and 1/2 subharmonic resonance are determined by multiple-scale technique. The frequency-amplitude and force–amplitude characteristic curves, phase portraits, time history and bifurcation diagrams are exhibited by numerical simulation. The impacts of the damping coefficient, detuning parameters, temperature increment, transverse and in-plane excitations on the nonlinear dynamics and bifurcation behaviors of variable thickness sandwich porous conical shell are demonstrated.

Linear static response structural optimization has been developed fairly well by using the finite element method for linear static analysis. However, development is extremely slow for structural optimization where a non linear static analysis technique is required. Optimization methods using equivalent static loads (ESLs) have been proposed to solve various structural optimization disciplines. The disciplines include linear dynamic response optimization, structural optimization for multi-body dynamic systems, structural optimization for flexible multi-body dynamic systems, nonlinear static response optimization and nonlinear dynamic response optimization. The ESL is defined as the static load that generates the same displacement field by an analysis which is not linear static. An analysis that is not linear static is carried out to evaluate the displacement field. ESLs are evaluated from the displacement field, linear static response optimization is performed by using the ESLs, and the design is updated. This process proceeds in a cyclic manner. A variety of problems have been solved by the ESLs methods. In this paper, the methods are completely overviewed. Various case studies are demonstrated and future research of the methods is discussed.

Irregular wear is one of the main reasons leading to the failure of mechanical equipment and mechanical parts. The coupling between irregular wear and system dynamic behavior has an important influence on the performance of the mechanism. A modeling and calculation method for planar multi-link mechanism considering multiple wearing clearances is proposed. Taking 2 DOFs nine bars mechanism as research object, iterative wear prediction process based on Archard model is applied to calculate wear characteristics, wear prediction process is combined with multi-body system dynamics to obtain dynamic model considering wearing clearance of revolute pair, and its dynamic response is analyzed. The nonlinear characteristics are analyzed qualitatively and quantitatively by phase diagram, Poincare map, and Largest Lyapunov exponent. At the same time, experimental platform of 2 DOFs nine bars mechanism is built to analyze influence of wearing clearance on response of mechanism. Correctness of theoretical model is verified by experimental results.

This study investigates the dynamic responses of gear systems while considering the morphology of worn gear tooth surfaces after different working times. Specifically, the anisotropic three-dimensional micro-morphology of the rough tooth surface model is established based on the W-B fractal theory. The non-uniform wear of the rough tooth surface under different rotational speeds and working hours is quantified according to Archard’s theory. The time-varying meshing stiffness (TVMS) and backlash are calculated with the wear values and then serve as internal excitation input parameters of the dynamic model. The dynamic responses are solved with the variable step Runge-Kutta algorithm. The results show that with increasing gear rotational speed and durations, the depth of tooth surface wear increases gradually, leading to a decrease in TVMS and an increase in backlash. The gear transmission system, considering the micro-morphology of the tooth surface, exhibits diverse dynamic response characteristics as speeds vary. With prolonged working hours, the system’s dynamic response transitions from periodic motion to chaotic motion, manifesting as chaotic vibrations, which are detrimental to steady operation. Transmission systems in chaotic motion can be transformed into stable periodic motion by adjusting the torque or rotational speed of the gears. The findings can provide theoretical guidance for selecting suitable operating conditions for gears subject to different wear degrees.

Western China is a typical high-intensity seismic zone, where seismic and geological disasters are frequent. The tunnel portal slope is prone to earthquake damage, which has become the key and difficult point in engineering construction. To deeply explore the dynamic response characteristics and instability mechanism of high-steep slopes at tunnel portal under frequent earthquakes, a large-scale shaking table test was designed. This experiment mainly simulates the geological environment of a high-intensity earthquake area by applying microseismic waves several times. The test results show that the amplification coefficient of peak ground acceleration (PGA) at different stages decreases with increasing earthquake intensity and finally presents a 50% attenuation. The vertical wave has a greater effect on the dynamic response of the slope, mainly affecting the magnifying effect during the relative elevation of 0.3–0.7. The horizontal wave has a stronger amplification effect on the slope crest region. The nonconsistency of the acceleration amplification factor (MPGA) and the dynamic change characteristics of the ∆MPGA can well identify the three stages of slope failure: the elastic stage (0–2 m/s2), elastoplastic stage (2–5 m/s2), and plastic failure stage (≥ 5 m/s2). The seismic failure modes of the slope can be summarized as follows: tensile fracture is formed first at the crest and waist of the slope, shear failure occurs between the slope waist and tunnel, forming a sliding body gradually, and the slope toe uplifts and finally forms collapse failure. This work can provide a reference for the design of seismic technology for tunnel portal slopes in high-intensity areas.HighlightsTo deeply explore the dynamic response characteristics and instability mechanism of the high steep slope at the tunnel portal under frequent earthquakes, a large scale shaking table test was designed, focusing on modelling the geological environment of high intensity seismic region. The roc k mass degradation effect of complex geological slopes in high seismic regions is simulated by applying microseismic wave forms near the study area for many times.By analyzing the peak ground acceleration and its amplification coefficient, the dynamic response characteristics and instability characteristics of the slope are systematically studied. Waves in different directions have different control effects on slope failure, and complex wave field superposition exists between the slope and tunnel syste m. Meanwhile, the acceleration amplification effect at different locations can assist in identifying slope damage areas.The dynamic failure modes of steep bedding slope with tunnel structures are as follows: tensile fracture shear failure sliding failure of upper slope, collapse failure of slope toe area. The formation and penetration of fissure mainly focus on the weak interlayers of slope surface. In addition, the interlayers are prone to shear failure area, which leads to shear slip of the slope under the seismic force, while the slope toe is prone to collapse failure due to the extrusion action.

Loess tablelands are widely distributed in the center of the Loess Plateau. The percentage of the Loess Plateau area that experiences seismic intensities greater than or equal to level VII is 54.21%. Because of the gravity of the loess slope and a large number of vertical pores, the fissures are mostly developed in the Loess Plateau. The fissures can easily cause slope instability subjected to earthquakes. Considering the structural characteristics of loess tableland slopes and earthquakes, a shaking-table test on slope models with and without fissures is conducted to study the dynamic response characteristics and the law of deformation and instability of the slopes under seismic action. The results indicate that the amplification factors of peak ground acceleration (PGA) in the vicinity of the fissures in the loess slope are significantly higher than those in the non-fissure slope, which reaches a maximum value of 3.6 at the shoulder of slope (measuring point A15). Dynamic earth pressures have stress concentration in the middle and upper part (0.7 times slope height) near the fissure, which affects the variation law of slope earth pressure. The failure mode of the fissure slope is as follows: fissure development, fissure expansion, soil collapse at the slope shoulder, shear failure at high-position on the slope, shear failure at low-position on the slope, and formation of new fissures at the edge of the tableland.

Owing to the superior transient and steady-state performance of the fractional-order proportional-integral-derivative (FOPID) controller over its conventional counterpart, this paper exploited its application in an automatic voltage regulator (AVR) system. Since the FOPID controller contains two more control parameters (µ and λ ) as compared to the conventional PID controller, its tuning process was comparatively more complex. Thus, the intelligence of one of the most recently developed metaheuristic algorithms, called the salp swarm optimization algorithm (SSA), was utilized to select the optimized parameters of the FOPID controller in order to achieve the optimal dynamic response and enhanced stability of the studied AVR system. To validate the effectiveness of the proposed method, its performance was compared with that of the recently used tuning methods for the same system configuration and operating conditions. Furthermore, a stability analysis was carried out using pole-zero and bode stability criteria. Finally, in order to check the robustness of the developed system against the system parameter variations, a robustness analysis of the developed system was undertaken. The results show that the proposed SSA-based FOPID tuning method for the AVR system outperformed its conventional counterparts in terms of dynamic response and stability measures.

A set of benchmark, medium scale, shaking table tests on corroded reinforced concrete (RC) columns is conducted with the aim of investigating the effects of corrosion damage on the nonlinear dynamic behaviour of RC bridge piers. The experimental programme consists of an uncorroded control specimen and two corroded RC column specimens, with identical structural details. An accelerated corrosion procedure is used to corrode the RC columns. The uncorroded and corroded specimens are subjected to far-field long duration ground motion excitations. The two corroded columns had 51% and 65% average mass loss ratios. The testing sequence includes slight, extensive, and complete damage levels, followed by an aftershock to examine the cascade effect on the nonlinear dynamic response of the proposed RC columns. The experimental results show that corrosion changes the failure mode of the RC columns, and has a significant negative impact on the residual strength (about 50% mass loss results in about 80% strength reduction) and drift capacity of RC columns.

In the computation of dynamic response sensitivity for rotor-bearing systems using the multicomplex variable derivation method, the presence of nonlinearity, particularly “fractional power” nonlinearity, in the forces generated at the supports may introduce rounding errors, potentially destabilizing the sensitivity calculation results. To address this issue, this paper proposes an enhanced method for sensitivity calculation using multicomplex variable derivation method. The approach leverages De Moivre’s theorem to conduct recursive operations on multicomplex numbers, thereby circumventing the rounding errors associated with the “fractional power” nonlinearity. This method facilitates the simultaneous calculation of sensitivity for each order and hybrid sensitivity. Subsequently, the viability of the proposed method is substantiated through a nonlinear single disk rotor system and a simulated gas generator rotor system. The results demonstrate that the proposed method maintains high accuracy and stability in dynamic response sensitivity computations even in the presence of “fractional power” nonlinearity.

We demonstrate a passive all-chalcogenide all-optical perceptron scheme. The network’s nonlinear activation function (NLAF) relies on the nonlinear response of Ge Sb Te to femtosecond laser pulses. We measured the sub-picosecond time-resolved optical constants of Ge Sb Te at a wavelength of 1500 nm and used them to design a high-speed Ge Sb Te -tuned microring resonator all-optical NLAF. The NLAF had a sigmoidal response when subjected to different laser fluence excitation and had a dynamic range of −9.7 dB. The perceptron’s waveguide material was AlN because it allowed efficient heat dissipation during laser switching. A two-temperature analysis revealed that the operating speed of the NLAF is ns. The percepton’s nonvolatile weights were set using low-loss Sb -tuned Mach Zehnder interferometers (MZIs). A three-layer deep neural network model was used to test the feasibility of the network scheme and a maximum training accuracy of 94.5% was obtained. We conclude that combining Sb -programmed MZI weights with the nonlinear response of Ge Sb Te to femtosecond pulses is sufficient to perform energy-efficient all-optical neural classifications at rates greater than 1 GHz.