International Journal of Structural Stability and Dynamics

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young’s modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson’s ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates.

To overall investigate the mechanical performance of resilient wheels to suppress the vehicle–bridge (especially LSB) coupled vibration, the coupled dynamic characteristics of metro train–LSB considering nonlinear resilient wheels are studied. Firstly, the mechanical property test of rubber of resilient wheel is designed and conducted, the mechanical characteristics of the nonlinear resilient wheel (NLRW) and linear resilient wheel (LRW) are discussed, and the dynamic model of LRW and NLRW are established. Then, based on train–track–bridge dynamic interaction theory, the coupled dynamic models of metro train–LSB considering LRW and NLRW are established, respectively. Adopting the established model, the dynamic influences of NLRW and LRW on the metro train–LSB coupled system are investigated by long-short wave irregularity excitation. The effects of damping characteristics of LRW and NLRW on the metro train–LSB system are discussed from the time–frequency domain. Results show that the wheel–rail vertical force of NLRW is smaller than that of LRW. The acceleration of the web, axle box, bogie, and car body of the NLRW is smaller than that of the LRW. The main frequency of wheel–rail vertical force under the action of NLRW and LRW is about 4 and 22Hz. The main frequencies of the rim and web of the NLRW are about 25Hz, while those of the LRW are about 50 and 25Hz, respectively. The acceleration of the web of the NLRW is significantly smaller than that of the LRW. The main frequency of acceleration of the LSB is about 10Hz, and the acceleration of the LSB under the action of NLRW is significantly less than that of the LRW when the frequency is in the range of 22–62Hz. Vibrations of the metro train and LSB increase with the increase of speed, and the dynamic response of the metro train–LSB system under the action of NLRW is smaller than that of LRW.

An investigation is performed in this paper to analyze the nonlinear thermo-electro-mechanical response of long sandwich cylindrical shells with functionally graded porous (FGP) core and thin piezoelectric actuator layers. The FGP core of the sandwich shell is assumed to be temperature- and microstructure-dependent. It is assumed that the sandwich shell is subjected to uniform lateral pressure loading in a thermo-electrical environment. The equilibrium equations of the shell with infinite length are established with the aid of the virtual displacement principle and von Kármán kinematic assumptions. The governing equations are obtained in terms of displacement components based on the first-order shear deformation model of shallow cylindrical shells and the modified couple stress theory. These nonlinear differential equations are analytically solved for a sandwich shell having both the simply-supported and clamped–clamped edge conditions by employing a two-step perturbation technique. Analytical closed-form solutions are determined as a relationship including the load parameter and the mid-span deflection. The comparison examples are made with the existing results in the literature for a simple functionally graded shell, where good agreement is obtained. It is shown that the nonlinear response of the sandwich shell is highly dependent upon the temperature variation, power law index, porosity coefficient, couple stress parameter, piezoelectric layers, and geometrical parameters of the shell.

This study investigates the effect of variable spindle speed with sinusoidal modulation on chatter vibrations generated in turning of flexible parts. The Euler–Bernoulli beam theory is assumed for mathematical modeling of the slender workpiece that is clamped at the chuck and pinned at the tailstock. The induced force as interaction between tool and workpiece (A2024-T351) during chip formation is calculated using finite element simulation. Numerical-based semi-discretization approach is utilized to seek stability regions and chatter frequencies regarding coupled dynamic model of tool and workpiece, in the form of delay differential equations with time varying delay term. The simulated data are validated and compared with those for a rigid part. The results indicate the efficiency of periodic modulation in improvement of machining stability especially for low spindle speeds. The stability charts for different interaction location and also time history response are studied, extensively. Finally, detection of period-one, flip and secondary Hopf bifurcations for different spindle speeds at instability borders are analyzed and discussed by solving corresponding eigenvalue problem.

This paper develops a modal derivative enhanced Kron’s substructuring method to calculate the structural responses and response sensitivities of geometrically nonlinear systems. The proposed method divides the global structure into substructures, which are then assembled in a dual form. The substructural displacements are approximated around the initial linear equilibrium position by using a quadratic modal manifold governed by a few master modes only. A time-variant reduction basis augmented by the master modal derivatives is derived from the quadratic modal manifold, enabling the geometric nonlinearities to be accurately captured. With the reduction basis, the global system is transformed into a reduced one containing the master modes only. Subsequently, the master modal responses and response sensitivities are solved efficiently from the reduced system. The global structural responses and response sensitivities are finally recovered from the master modal solutions based on the quadratic modal manifold. The effectiveness of the proposed method is demonstrated through its application to a thin plate structure. The reduced system enjoys the merit of Kron’s substructuring method that does not contain the interface degrees of freedom. Besides, the proposed reduced system is formed from the quadratic modal manifold directly. Its size is equal to the number of master modes of the substructures and smaller than that of the conventional method, where its size grows quadratically with the number of master modes.

It is well known that the inertial actuator can be used as the passive vibration absorber if the natural frequency of the inertial actuator is closed to the targeted structural resonance frequency. Typically, the inertial actuator as a passive or semi-active vibration absorber can only control a single structural resonance at a time. In this study, a simple and practical multiple-degree-of-freedom (MDOF) vibration absorber, which is based on a single inertial actuator and a parallel connection of multiple low-pass filters as controller, is proposed to damp multiple structural resonances simultaneously. The control performance of the proposed MDOF vibration absorber is the combined control effects for both passive absorber and active absorber. It means that the multiple-mode structural vibration can be reduced effectively by using a single inertial actuator. Additionally, the proposed controller can be designed by low-cost analogue circuit and allows directly using acceleration feedback. The performance of the MDOF vibration absorber is first analyzed both numerically and experimentally. Then the proposed MDOF vibration absorber is applied to control the vibration of multiple resonances of a cantilever beam. The experimental results show that multimodal damping can be generated by the proposed MDOF vibration absorber.

The torsional aerodynamic instability of single-axis solar trackers under strong wind seriously threatens the safety of solar trackers due to the occurrence of large torsional vibrations, and the corresponding mechanism is still unclear. In this study, the torque coefficient and torsional angle of a single-axis solar tracker are tested synchronously using an aeroelastic sectional model in a wind tunnel. The critical wind speed, torque coefficients, and interaction between the torsional angle and torque coefficients at different tilt angles are analyzed, and the following results can be obtained. Torsional aeroelastic instability occurs in a tilt angle range of -10° to 15°, and the critical wind speed decreases as the tilt angle increases. The standard deviation of dynamic torque coefficients is much larger than that of static torque coefficients, and torque coefficients showed a significant dominant frequency characteristic in the vibration state due to torsional vibration instead of wind load. The wind load in the windward area promotes vibration, while the wind load in the leeward area may promote vibration with the PV module tilt angle being slight and suppress vibration with the tilt angle being significant.

Dynamic force reconstruction theory has been developed for many years, generating numerous effective methods. However, the applications of engineering structures are relatively rare, owing to the difficult experiment, low accuracy and noise disturbance, among others. Aiming at the support platform structure commonly used in engineering, we propose the complete dynamic force reconstruction process based on the direct inversion method in frequency domain. The dynamic calibration methods of experiment and simulation are both analyzed in this case. In order to improve identification accuracy, the Tikhonov regularization is introduced. The results validate the reliability of our proposed method in real scenarios and the necessity of regularization method. Moreover, dynamic load identification method of structural variable stiffness is derived by the four-terminal parameter method. This work provides engineering application–a reference for the engineering of dynamic load identification technology.

The three-parameter Weibull distribution is one of the most widely used probabilistic models for the characterization of fatigue failure data. The linear regression estimation (LRE), the minimum discrepancy estimation (MDE), errors-in-variables estimation (EIV) as well as the least squares estimation (LSE) are generally applied in the estimation of Weibull parameters for their simplicity, in which probability estimators play an important role. In this paper, compared with five commonly used estimators, an optimal probability estimator with the four methods for different sample sizes is obtained by Monte Carlo simulations. The optimal probability estimator shows more robustness and higher accuracy. In conclusion, an optimal probability estimator of the midpoint rank is recommended for LRE, MDE and EIV especially with small samples in practical applications.

With the application of energy dissipation and damping techniques such as viscous dampers and viscoelastic dampers in seismic engineering, dynamic equilibrium equations of overall structures involve nonlinear damping force. Therefore, numerical integration methods with explicit velocity expressions are more favorable. Based on the average acceleration method, a novel linearly implicit algorithm with explicit expression of velocity is proposed in which once Newton iteration is embedded. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The nonlinear stability of the proposed algorithm is also examined using a single-degree-of-freedom shear-type structure. The dynamic response analysis of a three-storey shear structure model equipped with viscous dampers, a three-storey shear structure equipped with metal dampers, and an eight-storey planar frame structure, are carried to investigate the accuracy and stability of the proposed method with respect to the Chang method and the CR method. The results show that the proposed algorithm exhibits higher accuracy and finer stability for nonlinear dynamic problems.

In this paper, an extended exponential-polynomial-closure (EPC) procedure is presented to investigate the transient probability density function (PDF) of stochastic oscillator under the stimulation being modulated white noise based on the conventional EPC approach. By the presented EPC procedure, an evolutionary exponential–polynomial function is defined as the PDF solution and a set of evolutionary independent base functions are introduced to span a $R^N$ space. By integrating the residual error with those evolutionary functions spanning the $R^N$ space, a group of ordinary differential equations can then be formulated. Three nonlinear oscillators are analyzed numerically and the results comparisons of various techniques validate the presented EPC procedure in solution efficiency and accuracy, particularly in the PDF solution tails which play a crucial role in reliability analysis. The transient PDF solutions acquired by the presented EPC procedure match well with Monte Carlo simulation even in the PDF solution tails, whereas the solutions obtained by the equivalent linearization are deemed to be unacceptable for the strongly nonlinear oscillators subjected to modulated stimulation. Notably, the presented EPC procedure can highly increase the computational efficiency by about 1000 times in all the presented numerical examples in comparison to Monte Carlo simulation.

Vortex shedding at the tail of a high-speed train changes the aerodynamic characteristics of the train, which affects the safety and stability of train operation. This paper takes CR400AF as the research object, and uses dynamic monitoring points to realize the whole process monitoring of the flow field at the tail of the train running in open air and in tunnel for the first time. The wake of the train in different infrastructure scenarios is analyzed by the proper orthogonal decomposition method. The study found that the wake vortex structure is quite different when the train runs in different scenarios, and the turbulent kinetic energy intensity of the wake in tunnel is higher than that of the open air running. Modal decomposition method can identify flow structures that have a large impact on train aerodynamics. Through frequency analysis, it is found that the modal frequency obtained from the decomposition is higher when running in open air than when running in tunnel. With the increase of train speed, the modal strouhal number increases when the train is running in open air, and decreases when the train runs in tunnel. After the train enters the tunnel, the reverse movement of the air around the train body suppresses the development and separation of the boundary layer, which is the main reason for the low frequency of wake vortex shedding in tunnel. The stability of the train running in tunnel is worse than that when running in open air, which is closely related to the more complex flow structure around the car body and the drastic change of aerodynamic force when running in the tunnel.