International Journal of Structural Stability and Dynamics

For rail-cum-road bridges with single-level arrangement, there are not only dynamic interference, but also aerodynamic interference between trains and vehicles, which means that the train-induced winds generated by high-speed trains are non-negligible for vehicles. In this work, the test method of moving vehicle model is used to test the aerodynamic characteristics of vehicles under train-induced winds. Then, the model of coupled vibration of train–vehicle–bridge system considering train-induced winds is established. Finally, taking a rail-cum-road bridge with single-level arrangement as an example, the coupled vibration of train–vehicle–bridge system considering train-induced winds is analyzed, and the influence of train-induced winds, lateral spacing between trains and vehicles on train–vehicle–bridge system is discussed. The results show that train-induced winds decrease with the increase of the lateral spacing between trains and vehicles. Without considering train-induced winds, the moving train has a greater impact on the vertical response of the vehicle, and a smaller impact on the lateral response of the vehicle. When considering train-induced winds, the lateral response of the vehicle increases significantly, but decreases with the increase of the lateral spacing. In addition, road conditions and the setting of anti-dazzle plates can change traffic safety under train-induced winds.

Thermoelastic damping (TED) has been discerned as a definite source of intrinsic energy loss in miniaturized mechanical elements. The size-dependent structural and thermal behavior of these small-sized structures has been proven through experimental observations. As a first attempt, this article exploits nonlocal strain gradient theory (NSGT) and nonlocal dual-phase-lag (NDPL) heat conduction model simultaneously to acquire a mathematical formulation and analytical solution for TED in nanobeams that can accommodate size effect into both structural and heat transfer fields. For this purpose, the coupled equations of motion and heat conduction are firstly extracted via NSGT and NDPL model. Next, by deriving the distribution of temperature from heat conduction equation and substituting it in the motion equation, the unconventional thermoelastic frequency equation is established. By deriving the real and imaginary parts of the frequency from this equation and employing the definition of quality factor, an explicit solution is given for approximating TED value. The veracity of the proposed model is checked by comparing it with the solutions reported in the literature for specific and simpler cases. A diverse set of numerical results is then presented to appraise the influence of some factors like structural and thermal nonlocal parameters, strain gradient length scale parameter, geometrical parameters, mode number and material on the amount of TED. According to the results, use of NDPL model yields a smaller value for TED than DPL model, but prediction of NSGT about the magnitude of TED, in addition to the relative amounts of its two scale parameters, strongly depend on other factors such as aspect ratio, vibration mode and material type.

The current practice of real-time hybrid simulation (RTHS) often requires specialized finite element programs for computational modeling of the analytical substructures. Considering the limited nonlinear modeling capacity or the increasing computation cost for complex modeling, surrogate models of the analytical substructure provide novel alternatives for RTHS to avoid finite element analysis with fast computation. This study explores the use of arbitrary polynomial chaos expansion (APC) and nonlinear autoregressive with exogenous input (NARX) model to emulate the dynamic behavior of analytical substructures in RTHS. The NARX model training can be conducted numerically in an off-line mode using existing general purpose finite element analysis software, and its implementation presents minimum computational demands on the RTHS equipment. RTHS of a single-degree-of-freedom structure with a self-centering viscous damper is conducted as proof of concept to experimentally demonstrate the effectiveness and superiority of the proposed APC-NARX-based approach. The APC is further compared with other metamodeling techniques including polynomial chaos expansion (PCE) and Kriging to surrogate NARX model coefficients to account for ground motion uncertainties in RTHS. It is demonstrated that APC-NARX modeling with optimal order enables better accuracy of RTHS results than those of Kriging- and PCE-NARX.

Functionally graded material (FGM) beams are widely used in engineering as moving components. Nevertheless, their generated vibrations usually become annoying. To realize multi-broadband vibration reduction of FGM beams, an enhanced multiple dynamic vibration absorber (EMDVA), which utilizes an amplification mechanism, is proposed in this study. The devices are periodically arranged on the FGM beams. The dispersion and vibration transmission characteristics of the structure are investigated using the energy method and nullspace technique. The accuracy of the model is verified using the finite element method. The effects of parameter on its vibration damping performance are also analyzed. Finally, the relationship between the amplification coefficient and the operating performance of the EMDVA is revealed in terms of both the impedance principle and the energy method. The results show that the amplification mechanism can amplify the stiffness, damping, and mass of the MDVA by a factor of square of the amplification coefficient. Therefore, the proposed EMDVA has a wider damping band and stronger attenuation performance compared to the conventional MDVA. This study provides a simple and easy-to-implement solution for multi-band vibration reduction in FGM beams, which is useful for the engineering application of FGM beams in vibration and noise reduction.

Larger megawatt wind turbines are of significant height. The wind turbine tower (WTT) can suffer excessive vibration under external dynamic excitation, so an additional vibration control device is needed. Taking a novel prestressed tuned mass damper (PS-TMD) as the research object, its nonlinear vibration control performance induced by a flexible cable deformation effect was investigated. The dynamic coefficient amplitudes at two fixed points were derived based on the principle of virtual work, and results showed that the vibration amplitude considering flexible cable deformation is smaller than that of the linear PS-TMD system. For harmonic response, the numerical simulation of a 3.2 MW WTT indicated that vibration migration performance of the nonlinear PS-TMD is better than that of the linear PS-TMD. The Wilson-$\theta$ method was applied to analyze the vibration control effect under three fatigue and two ultimate wind loads. Results showed that the nonlinear PS-TMD can decrease the vibration amplitude more than the linear PS-TMD, and the vibration mitigation performance under the fatigue wind loads is slightly better than ultimate wind loads.

The frequency-domain vibration model of the vehicle-track structure is established based on the symplectic-spectral element method (S-SEM). To this end, the vehicle is considered as 10-degree-of-freedom, and the rail is modeled by an infinite Timoshenko beam supported by discrete sprung fasteners. Further, the track slab and base plate are regarded as two-dimensional Timoshenko beams supported by uniformly distributed sprung elements. Using the pseudo excitation method (PEM), the track irregularity is viewed as the pseudo load. The vibration response and the internal force of the single-layer or multi-layer beam models are obtained by solving the corresponding S-SEM-based equations. The spectral forces are also applied in frequency bands to the finite element (FE) and statistical energy analysis (SEA) acoustic models. The steel-concrete composite bridge deck is simulated with composite plate materials. The effectiveness of the proposed method is verified by comparing the predicted results with those obtained from the field test. The achieved results reveal that multi-layer beam structures effectively consume energy, and elastic fasteners and steel springs are capable of effectively reducing bridge noise.

An implicit truly self-starting time integration method for nonlinear structural dynamical systems is developed in this paper. The proposed method possesses unconditional stability, second-order accuracy, and controllable dissipation, and it has no overshoots. The well-known BN-stability theory is employed in the design of algorithmic parameters, ensuring that the proposed method can stably solve nonlinear structural dynamical systems without restricting the time step size. The spectral analysis shows that compared to existing second-order accurate time integration methods, the proposed method enjoys a considerable advantage in low-frequency accuracy. For nonlinear problems where the currently popular Generalized-$\alpha$ method and ${\rho }_{\infty }$-Bathe method fail, the proposed method shows strong stability and accuracy. Further, for nonlinear problems in which all methods’ results are convergent, the proposed method has greater accuracy, efficiency, and energy-conservation capability.

This paper presents a new geometrically exact beam finite element able to perform, accurately and efficiently, linear stability analyses of curved and tapered elastic strip beams (beams with thin rectangular cross-section) susceptible to lateral-torsional bucking. This element constitutes a non-trivial extension, to the spatial (3D) case, of that previously reported by the author for the in-plane (2D) case in Gonçalves [R. Gonçalves, A geometrically exact beam finite element for non-prismatic strip beams: The 2D case, Int. J. Struct. Stab. Dyn. (2022) 2350037]. To allow capturing accurately torsion effects, a torsion-related warping function is derived and included as an additional cross-section degree-of-freedom (DOF). Since the element is developed using a geometrically exact framework, complex effects such as load height and out-of-plane flexural-torsional effects are straightforwardly included. For implementation purposes, all fundamental expressions are provided in simple vector/matrix forms. A set of numerical examples is presented and discussed, to show that the proposed element provides very accurate solutions with a small DOF number, even for heavily curved and tapered members.

In a railroad wagon, the vertical excitation on the wheels originated from the track irregularities; the air spring model is reliably used to restrict these abnormal vibrations at a required level and improve traveler comfort. When air springs deflate during running, too much vibration occurs and the ride is less comfortable, which are common complaints among high-speed rail operators. In the situation that the air spring deflates, the laminated rubber spring acts as a temporary emergency spring to reduce the dynamic load. An approximation method for measuring laminated rubber’s static stiffness is presented and examined the effect on the air suspension. In this study the equations of motion for the pitch, roll, and the bounce motion of the bogies and the car’s body were developed with deflated state of air spring to systematically study the effect of deflated air spring on the ride comfort of passengers. The study show that passengers’ ride comfort was predicted accurately by the proposed model. It also observed that in the presence of a laminated rubber spring, the air spring’s dynamic stiffness is moved to higher frequencies. The air spring’s dynamic stiffness is reduced at lower frequency when the diameter of the surge pipe is increased. According to the results of the research, the vehicle’s speed should be reduced while the air spring is deflated in order to keep the passengers’ comfort.

This paper proposes a novel emergency aerodynamic measure, i.e. suspended flexible sheets (SFSs) with high strength, to suppress the vortex-induced vibrations (VIV) of bridge decks. The cost of the SFSs is very low, and the SFSs can be readily installed for an operational bridge in a short time. The control effectiveness of the SFSs is tested for a bluff box girder using wind tunnel experiments (the model scaling ratio is 1:36 and the range of Reynolds number is $1.71\times 10^3$ to $1.12\times 10^5)$. The relevant parameters of the SFSs (installation location, height, counterweight form, and arrangement form) are systematically optimized. The experimental results show that the in-wind postures of the SFSs are critical for the control performance. The random waving of SFSs can disturb the airflow around the bridge deck at the lower surface, weaken the interaction between the vortex shedding from the upper and lower surfaces, and hence reduce the VIV response. The control performance of the aerodynamic measure can be significantly increased by using appropriate arrangements of the SFSs and counterweights. For the tested cases, the maximum reduction ratio of the VIV amplitude approximately reached 2/3.

This paper presents a unified method for analyzing the dynamic behavior of spinning beams under elastic constraints. Based on the Timoshenko beam theory, a dynamic model of a spinning beam with elastic constraints is established. The displacement and bending angle are represented by a modified Fourier series. Compared with the traditional Fourier series, the improved Fourier series eliminates the discontinuity of the derivative at the boundary by introducing auxiliary polynomials, making it more suitable for elastic constraints. The governing equations and boundary conditions are coupled together using the energy method to form a set of standard linear equations. By solving this equation, the modes of the spinning beam structure under elastic constraints can be concisely and quickly obtained. Finally, by comparing with other methods, it is proved that the method has good convergence and practicability. Then, the effects of spinning speed, boundary stiffness and slenderness ratio on the whirling characteristics are analyzed. The results show that the linear spring has a more pronounced effect on the whirl frequency than the torsion spring. Different boundary constraints produce different elastic intervals. Mode exchange was found with increasing spinning speed. In the case of elastic constraints, the mode exchange occurs at lower spinning speed. This method has a certain universal applicability to the dynamic analysis of spinning beams under elastic constraints, and the research results can provide theoretical reference for subsequent research.

Dynamic modeling of lipid nanotubes as a drug carrier in the skin layer is important. The displacement fields of lipid nanotubes in the shunt path of the skin layer are considered twisting. The twisting of the lipid nanotube in the skin layer causes the warping of the structure and, as a result, causes normal strain. The normal strain in the strain fields is not considered in the torsional noncircular structures. Therefore, in this study, not only the effect of shear strains but also the effect of normal strain on the torsional vibration of lipid nanotubes are considered based on the Timoshenko–Gere theory for the first time. Also, the temperature can be considered in the modeling due to the normal strain in the torsional of warped structures. Then, the governing equations of the forced torsional vibrations of lipid nanotubes, by considering the general warping function of cross-section, are derived based on the nonlocal strain gradient theory. The governing equation is solved by utilizing the convolution integration, and the dynamic responses of lipid nanotubes in the presence of external nonlinear harmonic moving torque are obtained. In the results, dynamic and frequency responses in the presence of temperature for rectangular and elliptical lipid nanotubes have been analyzed. One of the methods of drug release in nanocarriers is stimulation with ultrasound waves. Therefore, stimulating the lipid nanotubes using ultrasound waves at the obtained frequencies makes it possible to release the drug from the lipid nanotubes. Also, the maximum dynamical response of Timoshenko–Gere torsion is less than typical torsion. Increasing the aspect ratio of cross-section dimensions of lipid nanotubes decreased the maximum dynamical response. Increasing the velocity parameter first increases the dynamical twist and then reduces it. Also, the effects of axial forces and temperature on the maximum dynamical responses and the dynamical twist of the lipid nanotubes are studied. For validation, the obtained results are compared with the results of previous research.