International Journal of Structural Stability and Dynamics

Buried pipeline, as one of the crucial facilities of airport ground engineering, has been extensively utilized for the transportation of petroleum, natural gas, industrial wastewater, and more. However, there are significant gaps in the research on the dynamic response of buried pipelines in airports under the action of dynamic traffic loads, which severely hampers the design and engineering quality of oil transmission pipelines. This study builds a three-dimensional finite element model to simulate the action of vehicles on the pipe–soil structure with actual loads. Moreover, the current research establishes a dynamic analysis model of pipe–soil interaction to analyze the material damping and load parameters. Using the structural dynamic response equation and Rayleigh damping calculation theory, this study investigates the change law of pipe dynamic stress and influencing factors and presents the recommended values of the parameters related to the pipe–soil interaction. Results are as follows. A damping ratio of 0.05 can enhance the time lag of the dynamic response of the structure and weaken the response peak. For the Rayleigh damping parameters, the viscous damping coefficient $\alpha$ has almost no effect on the dynamic response of the pipe–soil structure, so it can be disregarded in the calculation. With the increase of the axial weight of the traffic load above the pavement structure, the peak value of each dynamic response quantity of the pipe–soil structure and load magnitude. The suggested value of the dynamic load coefficient of the pipe–soil structure is 1.5. Lastly, the earth pressure and dynamic load coefficients are suggested to take values for different load and axle type cases.

With wind farms expanding into seismically active areas, wind turbines face the combined hazard of wind and earthquakes. Strong winds often accompany strong earthquakes, posing a significant threat to wind turbine safety. When subjected to multihazard loads, ignoring the correlation between loads could underestimate the risk to the structure. However, there is limited research on wind turbines under the combined effect of wind and earthquakes. In this paper, based on historical data considering the correlation between wind and earthquakes, a failure probability analysis method for wind turbine towers under the joint action of wind and earthquakes is presented. To accurately simulate the mechanical behavior of lattice-type wind turbine towers, the bolt slippage effect is taken into account. A finite element model of a lattice wind turbine tower is established, and the failure probability of the tower under the joint action of wind and earthquakes is calculated. The study also analyzes the influence of the bolt slippage effect and load correlation on the reliability of lattice-type wind turbine towers. The results indicate that ignoring load correlation can underestimate the failure probability of the structure, thus decreasing its safety. Similarly, ignoring the bolt slippage effect can also underestimate the failure probability of the structure and seriously threaten the safety of wind turbines.

The stationary random response characteristics of irregular quadrilateral plates under the base acceleration excitation are investigated in this paper. The computational model chosen in this paper is functionally graded graphene platelet reinforced composites (FG-GPLRC). Simultaneously, the material parameters are calculated employing the modified Halpin–Tsai model. A unified dynamic model based on the first-order shear deformation theory (FSDT) is proposed for FG-GPLRC irregular plates, where the displacement variables are considered as the first kind Chebyshev polynomials combined with coordinate transformation. The Chebyshev–Ritz method is utilized to derive the kinetic equations of irregular quadrilateral plates, and then the pseudo-excitation method (PEM) is employed to solve the stationary stochastic response of the system under the base acceleration excitation. The free vibration and stationary stochastic response of the plates under various boundaries are validated by a sufficient number of numerical studies, and the computational results display a favorable match with the published literature and finite element method (FEM), which verifies the correctness and reliability of the present method. Finally, a detailed parametric analysis of the stationary stochastic response characteristics of FG-GPLRC irregular quadrilateral plates is presented. The effects of various mass fractions, number of layers, geometric dimensions of GPL, and boundary constraints on the stationary stochastic vibration behaviors of FG-GPLRC irregular quadrilateral plates are considered.

The investigation on vehicle–bridge interaction systems (VBIS) plays an important role in evaluating the performance of bridges and/or vehicles. However, due to the limitations of traditional simulation methods and testing methods, the impact of vehicle jumping (VJ) on the VBIS has never been precisely disclosed. In order to accurately and comprehensively reveal the impact of VJ on the dynamic performance of VBIS, one real-time hybrid simulation method (RHSM) for VBIS considering the impact of VJ (VBIS-VJ) is proposed in this paper. In the proposed method, the vehicle system is chosen as the experimental substructure loaded by servo-hydraulic actuator loading system in real-time, whilst the bridge system is chosen as the numerical substructure numerically simulated in one computer. During the vehicle jumping, the vehicle and bridge vibrate freely respectively, otherwise, the experimental substructure and numerical substructure are synchronized at the coupling points in terms of force equilibrium and deformation compatibility in RHSM for VBIS-VJ. Firstly, the principle and numerical models of RHSM for VBIS-VJ are proposed. Furthermore, numerical simulations of RHSM for VBIS-VJ are conducted for verifying the feasibility of the proposed method. Finally, the influence of jumping position, jumping height, and driving speed on the VBIS is disclosed by hybrid simulations. It is shown that compared with the ever-known investigation methods, the proposed method could economically and accurately disclose the dynamic performance of VBIS-VJ. It is shown from the simulation results that compared with the referenced results, the quantitative errors of the proposed method with quarter vehicle model and half vehicle model are less than 2.5152% and 3.5599% respectively, which prove the effectiveness and accuracy of proposed RHSM for VBIS-VJ. The peak displacement of the bridge at a quarter-span and mid-span exceeds the three-quarters span by about 1.9–2.9mm. The influence of jumping position of a quarter span and midspan of bridge is much huger than that in the three-quarters span. The dynamic response of bridge increases with the increase the jumping height, but the deformation of the bridge is reduced when the jumping height is more than 0.05m. Meanwhile, the requirements for experimental loading equipment are acquired through the hybrid simulations, which could be used as a reference for selecting the loading system of the RHSM for VBIS-VJ.

The excellent properties of graphene reinforced composites (GRC) enable them to be promising material candidates for developing high-performance and multifunctional devices and structures. When subjected to thermal environment, temperature can significantly affect the structural behaviors of these components. It is necessary to consider the effects of temperature while conducting structural analysis. This work first attempts to investigate the nonlinear vibration of functionally graded (FG) graphene nanoplatelet (GNP) reinforced composite (FG-GNPRC) dielectric beams with comprehensively considering the effects of FG distribution of the reinforcements, temperature, electrical field and damping. The established governing equations for the FG-GNPRC dielectric beam are discretized and solved by differential quadrature (DQ) and direct iterative methods. The numerical results demonstrate that the application of pre-strain can attenuate the effect of electric fields and temperature on the frequency ratio, resulting in a more stable structure. Among the FG distribution patterns as involved, the FG-GNPRC beam with profile $X$ exhibits lower frequency ratio and higher stability. This work is envisaged to provide guidelines for the design of FG-GNPRC structures with optimized performances in thermal environment.

The current investigation examines the vibrational properties of porous truncated conical structures made from a composite material consisting of polyvinylidene fluoride (PVDF) reinforced with Terfenol-D particles. The effective properties of the magneto-electro-elastic composite were determined using the Eshelby–Mori–Tanaka model. The governing equation of the system is obtained by applying the principles of minimal potential energy and Hamilton’s principle to the first-order shear deformation theory. The equations are solved utilizing the generalized differential quadrature technique. This study aims to examine the interconnections among the volume percentage, vertex angle, shell length, boundary conditions, and porosity of Terfenol-D. Moreover, to validate the results, a comprehensive analysis was performed by comparing them with the existing body of literature, resulting in a favorable and accurate agreement. The results demonstrate a consistent decrease in the linear natural frequency as the vertex angle gradually increases. The findings derived from this study have the potential to serve as a reference point for future analyses.

The nonlinear buckling and postbuckling of functionally graded carbon nanotube reinforcement composite (FG-CNTRC) plates resting on the nonlinear effect of elastic foundation under combined load including external pressure and axial compression loads with uniformly distributed temperature rises are fully investigated in this paper. The FG-CNTRC plates are reinforced by FG-CNTRC stiffeners and the plate-foundation interaction is modeled using a nonlinear model. The higher-order shear deformation plate theory with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Additionally, by using the anisotropic higher-order shear deformation beam theory, a new smeared stiffener technique is successfully developed for FG-CNTRC stiffeners. Galerkin’s method is used to achieve the equilibrium equation system in the nonlinear algebraic forms, and the critical load and postbuckling load–deflection curve expression are explicitly determined. The numerical investigations discuss the influences of FG-CNTRC stiffeners, hardening/softening nonlinear elastic foundation, uniformly distributed temperature rises, geometrical and material features on nonlinear stability of stiffened FG-CNTRC plates.

The paper deals with the problem of obtaining a given dynamic behavior of simply supported bridge beams from the impact of rolling stock. Resonant vibrations of beams become a reality at high speeds if the train is formed of identical cars, which is typical for passenger trains. The phenomenon of suppression of beam vibrations by a train, known from publications, is possible only with an exact ratio of the length of the car and the beam. This significantly reduces the possibilities of choosing the necessary spans of beams. Consideration of issues of interaction in the “bridge–track—train” system for security purposes requires the involvement of a rather complex mathematical apparatus and appropriate software. The paper proposes a new method for determining the specified dynamic behavior of bridge beams, suitable for any spans and available to engineers at the stage of pre-design assignment of dynamic parameters of beams. The requirements that are necessary and sufficient conditions for preventing the resonance of bridge beams on the HSR are determined. At the same time, it does not require the involvement of software based on a complex mathematical technique.

Replacing fossil fuels with renewable energy is one of the important means to improve energy scarcity and environmental protection, and is of great significance for achieving sustainable development of human society. Vertical axis wind turbine (VAWT) is one of the key equipment for applying green energy — wind energy. During the operation of VAWT, its blades not only have to withstand periodic aerodynamic loads, but also suffer from centrifugal force effects and the Coriolis force effect caused by coupling with multi-dimensional deformation. The complex stress situation makes the blades susceptible to damage, resulting in structural resonance and instability of aeroelastic stability. This paper applies the Euler beam model and Hamilton principle to establish a nonlinear structural vibration motion equation for large-span vertical axis wind turbine blades with fully coupled four-dimensional deformation (i.e. lateral bending deformation, chord bending deformation, axial torsion deformation, and axial tensile deformation), and retains the nonlinear term of the motion equation to the third-order infinitesimal. Separating the motion equation into equilibrium equation and dynamic equation, it can be seen that the displacement of equilibrium state caused by the centrifugal force of the rigid body exists in the form of a coefficient in the dynamic equation, which will have an impact on the dynamic characteristics. This modeling work can provide a research foundation for exploring the dynamic characteristics and aeroelastic stability of VAWT blades in the future.

It is crucial to comprehend the nonlinear vibration behavior of sophisticated engineering constructions to aid in the examination, creation and production procedures. The primary objective of this study, therefore, is to focus on exploring the nonlinear forced vibrational characteristics of two-directional functionally graded (TDFG) cone-shaped shell for the first time. To accomplish this, the motion equations of the TDFG cone-shaped shell are derived based upon the framework of first-order shear deformation theory (FSDT) in conjunction with von Kármán assumption. TDFG cone-shaped shell models have mechanical properties that can change smoothly and continuously across the thickness and length of the shell, following a power law distribution pattern. To discretize the partial differential equations and transform them into ordinary differential equations, the Galerkin approach was used and ultimately, these equations were solved using the multiple time scales method. The accuracy and effectiveness of this analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear behavior of the shell, highlighting the significant influence of transverse and longitudinal gradient indices on the nonlinear frequency response, which is not considered before. The new insights gained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear vibrations in future analysis and design processes.

A new beam finite element for non-prismatic (tapered and curved) beams with thin rectangular cross-section (“strip” beams) is proposed in this paper. The element is geometrically exact and constitutes the extension, to the large 3D displacement and rotation setting, of those proposed by the author for the 2D [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23 (2022) 2350037] and linearized lateral-torsional buckling [R. Gonçalves, Int. J. Struct. Stab. Dyn. 23(12) (2023) 2350139] cases. The element incorporates torsion-related warping, as well as arbitrary mid-line warping, and allows nonlinear tapered geometries, arbitrary initially curved configurations (including pre-twist) and eccentric loads (loads offset from the centroid). All expressions required to implement the proposed element are given in a straightforward vector/matrix format. Several numerical tests are presented to show that the element has a very good predictive capability and a low computational cost, when compared with solutions obtained with refined shell finite element meshes, even for members with a high taper ratio and initial curvature.

The structural dynamic response reconstruction of large-scale civil engineering structures using traditional methods results in heavy computational burden with low efficiency. To improve efficiency, a novel time-domain response reconstruction method based on model condensation and modal decomposition is proposed in this paper. The finite element model of the target structure is transformed and condensed. The system matrices of the condensed model have lower dimensionality than those of the original finite element model. A checking procedure based on the modal assurance criterion is developed to ensure the accuracy of the condensed system. Measured dynamic responses are decomposed to time-domain modal responses at measured degrees of freedom (DOFs) using band-pass filters. The mode shape matrix of the condensed model is used to calculate the modal responses at the unmeasured DOFs. Following modal superposition and coordinate transformation, the dynamic responses at unmeasured DOFs are reconstructed without knowledge of the excitation. The accuracy and efficiency of the proposed methodology are verified in a numerical case study of a three-dimensional building frame model and an experimental case study of a two-story steel frame under laboratory conditions. In contrast with the numerical case study, the effects of modeling error and measurement noise are considered in the experiment verification. The results show the outstanding performance of the proposed methodology when compared with a traditional response reconstruction method.

Natural vibration characteristics of a cantilever beam that is parametrically excited by pitch motion are theoretically investigated in this work. A partial differential equation governing the parametrically excited bending vibration of the beam is established by employing the generalized Hamiltonian principle. Normal modal functions of the bending vibration are obtained based on the method of separation of variables. It reveals that the dynamic pitch motion cannot change the modal shapes of the bending vibration of a uniform beam. Principal vibrations of the beam are studied by taking into account two cases of $E{I}_1=E{I}_2$ and $E{I}_1\ne E{I}_2$, where $E{I}_1$ and $E{I}_2$ are the first and second principal bending stiffness, respectively. The bending stiffness is considered as the superposition of a constant stiffness with a small perturbation. With the aid of the Fourier series theory and the method of multiple scales, the principal vibrations of the parametrically excited system at non-resonant and resonant cases are analyzed by introducing a small natural parameter $𝜀$, while natural vibration characteristics of the beam are obtained and the orthogonal properties of modal functions are illustrated. Theoretical methods provided in this work are verified by using the finite element method, assumed modes method and direct numerical integrations to the governing equation based on a rectangular beam model. It reveals that theoretical results coincide with numerical results very well. Finally, the influences of design parameters including the beam height, beam width, beam length, slender ratio, aspect ratio, pitch amplitude, pitch frequency and pitch phase on natural frequencies of a harmonic pitching beam are discussed. It shows that the width, height, length, slender ratio, aspect ratio and pitch amplitude have dramatic influences on the natural frequencies of the pitching beam, while the pitch frequency and pitch phase have little effect on natural frequencies.