International Journal of Structural Stability and Dynamics

Dynamic vehicle–bridge interaction (VBI) plays a crucial role in the train-induced vibrations of a railway bridge for its coupling effects may reduce the bridge response and down-shift the resonant speed. The commonly used nominal theoretical resonant speed ($=f_{b}D)$ of a typical railway bridge, however, is only related to the bridge frequency ($f_b)$ and car length ($D)$, but it neglects the VBI effects of the moving trains. Such a shifted resonance phenomenon would become significant for a bridge under two trains passing by each other. This study develops a method using an equivalent modal mass to be added onto the bridge to account for the frequency shift due to the presence of multiple train cars for estimation of the shifted resonant speed. The numerical study demonstrates that the proposed method can predict the shifted resonant speed and explain the shifted-resonance phenomenon of railway bridges under train passages.

To reduce the natural frequency of air isolators and realize low or ultra-low frequency air/magnetic composite vibration isolation with large payloads, a magnetically repulsive negative stiffness permanent magnetic array (MRNSPMA) is proposed. Specifically, we utilize cuboidal permanent magnets to form a spatial array that is mechanically repulsive in the horizontal direction and structurally parallel in the vertical direction. The superiority of MRNSPMA in achieving high amplitude negative stiffness is verified. Furthermore, the effects of structural parameters on vibration transmissibility under the base and force excitations are investigated with the introduction of MRNSPMA. The displacement transmissibility, the force transmissibility and the frequency corresponding to the peak transmissibility are significantly reduced, validating the promise of MRNSPMA for improving the isolation performance of cutting-edge scientific experimental systems and facilities.

Structures carrying moving loads present rich vibration phenomena and colorful spectrum characteristics. This study analytically investigates the moving-inertial-load-pumped frequency comb free vibration behavior of a single-span rectangular linear elastic Kirchhoff thin plate in the low-speed region. Multiple-time-scales expansion is made and the asymptotic solution describing the non-resonance modal oscillation is derived. Case studies on a single-span rectangular isotropic plate with the clamped opposite boundaries dominated by the first two transverse flexural modes are presented. Numerical computation based on finite element method structure modeling and response numerical integration verifies the modal frequency comb characteristics as predicted by the proposed theoretical model. The results also present the weak modal interaction for the studied single-span structure in the observed light-mass low moving speed region. The outcomes of this study will benefit the related structural dynamic system design and intervention.

The semi-periodic vortex-shedding phenomenon caused by flow separation at the windward corners of a rectangular cylinder would result in significant vortex-induced vibrations (VIVs). Based on the aeroelastic experiment of a rectangular cylinder with side ratio of 1.5:1, 2-dimensional (2D) and 2.5-dimensional (2.5D) numerical simulations of the VIV of a rectangular cylinder were comprehensively validated. The mechanism of VIV of the rectangular cylinder was in detail discussed in terms of vortex-induced forces, aeroelastic response, work analysis, aerodynamic damping ratio and flow visualization. The outcomes showed that the numerical results of aeroelastic displacement in the cross-wind direction and the vortex-shedding procedure around the rectangular cylinder were in general consistence with the experimental results by 2.5D numerical simulation. In both simulations, the phase difference between the lift and displacement response increased with the reduced wind speed and the vortex-induced resonance (VIR) disappeared at the phase difference of approximately 180^∘. The work done by lift force shows a close relationship with vibration amplitudes at different reduced wind speeds. In 2.5D simulations, the lift force of the rectangular cylinder under different wind speeds would be affected by the presence of small-scale vortices in the turbulence flow field. Similarly, the phase difference between lift force and displacement response was not a constant with the same upstream wind speed. Aerodynamic damping identified from the VIV was mainly dependent on the reduced wind speed and negative damping ratios were revealed at the lock-in regime, which also greatly influenced the probability density function (PDF) of wind-induced displacement.

In this paper, a closed-form frequency equation of the pipe-in-pipe (PIP) structure with arbitrary boundaries is obtained. The frequency equation is derived from Green’s function of the transverse forced vibration of the PIP structure and takes into account the effects of internal two-phase flow and axial pressure. The reliability of the method in this paper is proved by comparison with the published literature. In the numerical discussion part, the PIP structures with clamped-clamped, clamped-free, and elastic boundary conditions are used as examples to discuss. The effects of equivalent stiffness coefficient, internal flow velocity, and gas volume fraction on the stability of PIP structure are studied. The results show that the stability of the PIP structure is better than that of the single-pipe structure, and the greater the equivalent stiffness coefficient of the elastic layer, the higher the critical flow velocity of the structure. In addition, a modal conversion phenomenon existing in the PIP structure is discovered. There are different forms of modal conversion for different boundary conditions, and the modal conversion makes the order of instability of the PIP structure different from that of a single-pipe. The conclusion of this paper has positive significance for the dynamic research of PIP structure.

Purpose. Impacts appear in a wide range of mechanical systems. To study the dynamical behavior introduced by impact in practical way, a single-degree-of-freedom impact oscillator rig is designed. Originality. A simple piece-wise linear system with symmetrical flexible constraints is designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piece-wise models. The new design choice is based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness as well avoidance of the delay introduced by the structure. Meanwhile, the new design provides the possibility of the applications of the complex control algorithms. Design/methodology/approach. The design process is described in detail. The initial experimental results of the rig as well as numerical simulation results are given. In this rig, the mass driven force is generated by electromagnet, which can be adjusted and control easily. Also, most of the physical parameters can be varied in a certain range to enhance flexibility of the system allowing to observe subtle phenomena. Findings. Compared with the simulation results, the designed rig is proved to be validated. Then, the initial experimental results demonstrate potentials of this rig to study fundamental impact phenomena, which have been observed in various engineering systems. They also indicate that this rig can be a good platform for investigating nonlinear control methods.

The mode shape-aided method provides a simple and effective way for cable force determination, which, however, requires accurate parameter identification of the cable structure. This paper proposes a phase-based video motion magnification to process the image sequences of a cable. Digital image correlations were engaged to measure the dynamic displacement–time history, through tracking the surface characteristic features of the cable. Thereafter, a frequency–domain decomposition technique was applied to extract the natural frequency and mode shape of the cable from the displacement–time history measurements. The identified cable mode shapes, along with a tensioned pinned-pinned cable model, were used to estimate the cable force. The accuracy of the proposed methodology was subsequently verified through laboratory testing on an inclined cable model and field testing on a typical hanger cable of a real-world arch bridge. Overall, the study results indicated that the proposed methodology could expediently and cost-effectively estimate the tension forces of a cable with reasonably acceptable identification accuracy.

It was found that polyurea coating could improve the integrity and the corresponding durability of the structural components. However, the strengthening effect of polyurea coatings for structures built with emerging ultra-high-performance concrete (UHPC) is still unknown due to the lack of studies. Therefore, this paper investigated the effect of the polyurea coating on the lateral impact resistance of UHPC columns through a combined numerical and experimental study. A total of five specimens were fabricated, including two UHPC columns and three UHPC columns with polyurea coating. To better characterize the structural response under dynamic loading, impact cases with different drop weight impact heights and axial force ratios were employed. The results showed that the UHPC column with polyurea coating exhibited superior lateral impact resistance compared to the UHPC column. The presence of the axial force increased the lateral impact stiffness and further reduced the deflection of the specimen. In contrast, the polyurea coating improved the specimen’s ductility and mitigated the peak impact force, thereby maintaining the specimen’s integrity without sudden shear failure. A three-dimensional finite element (FE) model of polyurea-coated UHPC columns under impact loading was then established and confirmed the experimental results. With the validated FE model, an intensive parametric study was conducted to investigate the effects of polyurea thickness, axial force ratio and impact energy on the lateral impact resistance of the UHPC column. The presence of the polyurea coating could significantly improve the lateral impact resistance of the specimen, thereby preventing the shear failure of the UHPC column, and thus, the effective thickness of the polyurea layer for the UHPC column was determined to be 2–6mm. The outcome of this research demonstrates the great merits of polyurea coating in improving the ductility and integrity of the UHPC column under lateral impact loading.

Galloping of twin bundled overhead conductors accreted by ice is a frequent phenomenon during freezing weather, which may damage the operation of transmission lines. To analyze the galloping behavior of iced conductors, their aerodynamic characteristics must be studied. In this study, models with two different outlines were designed and tested to determine a more suitable ice-accreted conductor testing model. Subsequently, the influences of the conductor type, ice thickness, wind turbulence intensity, and wake effect of the windward conductor on the aerodynamic coefficients of the conductors with crescent-shape ice are investigated. The results show that the strand outline of overhead conductors must be considered to improve the accuracy of aerodynamic tests. With increasing ice thickness, the aerodynamic stability becomes rapidly deteriorated. Under the wind turbulence intensity of 4%, the aerodynamic stability gets the most enhancement. Moreover, different conductor types have little impact on the aerodynamic coefficients. The wake caused by the windward conductor is the leading cause for the twin bundled iced conductors to have weaker aerodynamic stability than a single conductor. The aerodynamic coefficients determined in this study are essential for predicting the galloping amplitudes of ice-accreted twin bundled overhead conductors under different weather conditions.

In this paper, dynamic instability of functionally graded carbon nanotubes (CNTs)-reinforced composite joined conical-cylindrical shell in supersonic flow is analyzed numerically. The higher-order shear deformation theory is applied to describe the stress–strain state of thin-walled structure. The assumed-mode method is used to derive the finite degrees-of-freedom dynamical system, which describes the structure motions. The structure motions are expanded by using the eigenmodes, which are obtained by the Rayleigh–Ritz method. The trial functions, which satisfy the continuity conditions at the cylindrical-cone junction, are used to obtain the eigenmodes.

The properties of free vibrations of thin-walled structure are analyzed numerically. The dynamic instability of the joined conical-cylindrical shell in supersonic flow is analyzed using the characteristic exponents. As follows from the numerical study, the dynamic instability is arisen due to the Hopf bifurcation. The dependences of the supersonic flow critical pressure on the Mach number and the type of CNTs distribution are analyzed numerically.

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.

This study proposes an approach to set up a continuum full bridge model with spatially inclined cables based on the Hamilton principle. The dynamic governing functions, considering the geometric non-linearities of cables and deck, represent simultaneously the vertical motion of deck and vertical–horizontal motion of cable. With the comparison of the modal properties obtained from the model to those from the accurate model, results show that the proposed model is capable of accurately simulating the modal properties. The primary resonance responses and corresponding frequency-response curves are obtained through the multiple-scale-method. A finite element (FE) model is established, and the corresponding non-linear dynamic analysis in time domain is conducted. Comparing the results from two models, it can be checked that the proposed model is reliable. According to the results of the proposed model, it is found that the second-order shape functions (SOSFs) play a significant role in the system response. Once the non-linear vibration of the bridge becomes significant only considering the excited mode with using the classical Galerkin decomposition cannot correctly predict the structure response. The SOSFs can be classified into stationary and vibrating components. The vibrating component can deviate the time-series of response from the harmonic wave, and the stationary component directly determines the mean value of the time-series.

A constrained variation modeling method for free vibration analysis of rotating double tapered functionally graded beams with different shear deformation beam theories is proposed in this paper. The material properties of the beam are supposed to continuously vary in the width direction with power-law exponent for different indexes. The mathematical formulation is developed based on the geometrically exact beam theory for each beam segment, the admissible functions denoting motion quantities are then expressed by a series of Chebyshev orthogonal polynomials. The governing equations are eventually derived using the constrained variational method to involve the continuity conditions of adjacent segments. Different shear deformation beam theories have been incorporated in the formulations, and the nonlinear effect of bending–stretching coupling vibration together with the Coriolis effect is taken into account. Comparison of dimensionless natural frequencies is performed with the existing literature to ensure the accuracy and reliability of the proposed method. Comparative discussions are performed on the vibration behaviors of the double tapered rotating functionally graded beam with first-order shear deformation beam theory and other higher-order shear deformation beam theories. The effect of material property graduation, power-law index, rotation speed, hub radius, slenderness ratio, and taper ratios is scrutinized via parametric studies, respectively.

This paper presents an analysis of the effect of a “slight” curvature of the axis of a thin-walled beam on its eigenfrequencies and forms. By “slight” we understand such a beam curvature at which no theory of curved beams (arches, horizontally curved girders), but classical beam theory is applied. The subject of the analysis is the open nonprismatic thin-walled beams with any geometrical parameters, and prismatic beams. The thin-walled beam model used in the analysis was derived on the basis of the momentless theory of plates, using the Vlasov assumptions. The free vibrations of the beams were analysed. Calculations were performed for four groups of beams. Each of the groups comprised two beams with the same configuration of flanges and identical geometrical cross section characteristics, but differing in web geometry. One of the beams had a symmetrical web (a beam with a rectilinear axis in the web plane), whereas the web of the other beam was asymmetrical (a beam with its axis curved in the web plane). The algorithm based on Chebyshev polynomials was used to solve the variable coefficient equations describing the model’s vibration. According to this algorithm, solutions are sought in the form of Chebyshev series and the closed analytical recurrence formulas generated by the algorithm are used to calculate the coefficients of the equations. It has been shown that even a “slight” curvature of the beam’s axis has a significant effect on its eigenfrequencies and forms, as confirmed by a comparison of the results with the ones obtained using Finite Element Method (FEM).

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.