Longitudinal Vibration Characteristics Research Articles

Numerical and experimental study of a suspension bridge with combined viscous-steel damping system under train and seismic loads

The longitudinal dynamic performance of long-span bridges with passive vibration control devices when subjected to vehicle and seismic loads has raised extensive attention of the civil engineering community. This study aims to provide numerical and experimental assessments of the dynamic performance of a railway suspension bridge with the Combined Viscous-Steel Damping System (CVSDS) under various excitations. The deck is simplified to a single-degree-of-freedom (SDOF) system according to the longitudinal vibration characteristics of the suspension bridge. The Dynamic Equation Method (DEM) and Fourier Expansion Method (FEM) are suggested for the equivalence of the spatiotemporal variable train loads to horizontal excitations. A simplified two-stage analytical model is proposed to simulate the restoring force characteristics and fuse-lock function of the CVSDS. Shake table tests are conducted to further illustrate the feasibility of the simplified model and evaluate the effectiveness of the CVSDS. The results indicate that the SDOF system is reasonable and satisfactory in simulating the deck displacement. The two-stage working mechanism of the CVSDS is verified by both the simulation and experiment, i.e. the viscous fluid damper works under train loads and the steel yielding damper operates under earthquakes. The vibration mitigation effectiveness of the CVSDS is remarkable.

Longitudinal vibration characteristics of a tapered pipe pile considering the vertical support of surrounding soil and construction disturbance

Longitudinal vibration characteristics of a tapered pipe pile considering the vertical support of surrounding soil and construction disturbance

Longitudinal vibration control strategy for long-span suspension bridges under operational and extreme excitations using eddy current dampers

A full-floating or a semi-floating system is conventionally employed in long-span suspension bridges (LSSBs) to reduce the excessive internal forces of main girders when subjected to various ambient loads/effects. However, such a system may induce appreciable back-and-forth longitudinal displacements of the main girder and result in the deterioration of auxiliary structural components (e.g., expansion joints). In light of this, this paper presents a vibration control strategy for mitigating the longitudinal girder vibrations of LSSBs under primary operational loads (i.e., wind and traffic) and extreme seismic effects using eddy current dampers (ECDs). A general computational framework of the seismic-wind-traffic-bridge system is first developed, whereby the longitudinal girder vibration characteristics of a prototype LSSB with and without ECD installations under various loading scenarios are investigated. Particularly, a novel multi-attribute decision-making (MADM) method is introduced to address a common challenge in developing optimal vibration control designs, i.e., the optimal vibration control design for one objective might adversely affect the others, which is especially critical from a life-cycle bridge management perspective. By using the MADM, typical bridge performance indices under various loading scenarios can be rationally involved in the associated optimization. The results show that different excitations can induce longitudinal girder vibrations with different dominant frequencies, which can be effectively mitigated by the ECD. However, for different bridge performance indices and different loading scenarios, the optimal ECD parameters may vary significantly. The proposed MADM method can help develop a balanced vibration control design that can ensure excellent bridge safety and serviceability simultaneously.

A Kirchhoff Plate Model for Longitudinal Vibration Analysis of Restrained Nanoplate Including Thermal Effects

This work attempts to apply the Kirchhoff plate theory to find out the vibrational analyses of a nanoplate incorporating thermal effects. The effects of thermal environments on the natural frequency of longitudinal vibration of restrained nanomaterials, especially for restrained nanoplates, have not been investigated, and most of the previous research has been carried out for unrestrained nanoplates. Therefore, it must be emphasized that the vibrations of restrained nanoplate, including thermal effects, are novel and applicable to the nanodevices, in which nanoplates act as the main structure of the nanocomposite. A novel motion and frequency equation are derived using the Kirchhoff plate model. The present study illustrates that a nanoplate’s longitudinal vibration characteristics strongly depend on the temperature change and stiffness coefficients. The numerical results clearly show that the longitudinal natural frequencies of the nanoplate are less than unity for both cases of low and high temperatures. This means that applying the Kirchhoff plate model for restrained nanoplate analysis would lead to an over-prediction of the frequency if the small thermal stress effect is neglected. Finally, the investigation of the restrained and thermal impact on longitudinal vibration of nanoplates may be used as a valuable reference for the application and the design of nanoelectronics and nano-drives devices, nano-oscillators, and nano-sensors, in which nanoplates act as essential elements.

Dynamic response analysis of scraper conveyor under the condition of chain broken

In view of the fact that the traditional study of the chain breaking condition of the scraper conveyor only considers the case of two-way simultaneous chain breaking, this paper mainly studies the single-side chain breaking condition and its influence on the longitudinal vibration and swing vibration characteristics of the scraper chain system. Using the tension calculation principle of the point-by-point tension method, each section of the scraper in the study area is taken as a unit. A coupled dynamic model of longitudinal and oscillating vibration of scrapers is established and connected with Voigt model. The dynamic response laws of the longitudinal and oscillating vibration of the scraper before and after the chain fracture under different transportation conditions are numerically simulated. The calculation results show that when there is material behind the broken chain, the longitudinal tension of the chain and the oscillating vibration of the scraper reach the maximum value, and the chain speed fluctuation reaches 543.1 % compared with the normal operating conditions. Only when there is material in front of the broken chain, the longitudinal tension mutation of the chain and the oscillating vibration value of the scraper are weaker than those of the previous working conditions. When there are materials at the front and back of the broken chain, the sudden change of the longitudinal tension of the chain and the oscillating vibration value of the scraper are the minimum, but they also reach twice the normal working condition, and the chain speed fluctuation reached 194.4 %. The research results of this paper provide a theoretical basis for grasping the operation status of the scraper conveyor in the coal mine and predicting the life of the scraper conveyor.

Longitudinal Seismic Response of a Pipe Pile Embedded in Saturated Thermoelastic Ground Subjected to Rayleigh Waves

This work investigates the longitudinal vibration characteristics of the pipe pile in the liquid-saturated ground due to Rayleigh waves propagation with considering the influence of the nonisothermal condition on the wave motion. Firstly, the Rayleigh wavefield in the liquid-saturated thermoelastic ground is deduced theoretically with taking advantage of the Biot theory and the non-Fourier law of heat conduction. Secondly, the longitudinal frequency domain solution of the pipe pile under Rayleigh waves is derived analytically. Finally, the dependence of the pipe pile response on the physical parameter is illustrated by utilizing several numerical examples. The result reveals that increase in the thermal expansion coefficient of saturated soil significantly augments the longitudinal displacement and side friction of pile body. Increase in the permeability of saturated soil will reduce the pile head displacement. When the pile length is less than its effective length, the rise of the pile length will reduce the pile head displacement. Augment of both the outer radius and wall thickness of the pipe pile will help to reduce the pile head displacement. However, the lateral inertia effect of the pipe pile has slight influence on its longitudinal behavior under Rayleigh waves.

Topological energy harvesting of surface acoustic waves in a phononic crystal slab with periodic stubbed surface

In this paper, we demonstrate energy harvesting of surface acoustic waves (SAWs) via topological interface states in a two-dimensional phononic crystal (PC) with the periodic arrangement of bar-like locally resonant units on its surface. The system can produce pure SAW bands in the subwavelength realm due to bar oscillation. Both transverse and longitudinal vibrations of the stubbed bar can selectively couple to the intrinsic SAWs in the PC slab. Subsequently, through constructing the typical Su–Schrieffer–Heeger model, we analyze the topological properties of zone-folding-induced SAW bands with transverse and longitudinal vibration characteristics, respectively. When two arrays with distinct topological bandgaps are spliced together, topological interface states will appear. Topological energy harvesting of SAWs with two different vibration characteristics is finally achieved in one structure. Our study expands the applicability of topological interface states for SAW in a compacted platform, such as polarization selection or sensing.

Analysis of longitudinal and torsional vibration of mining scraper conveyor under the over bending section working condition

Considering that the scraper will produce longitudinal and torsional pendulum vibration when passing through the bending section, and have a great influence on the motion characteristics of the scraper conveyor, this paper studies the longitudinal and torsional pendulum coupling vibration characteristics of the scraper conveyor under the working condition of over-bending section for the first time. Firstly, the simplified model of torsional pendulum vibration of scraper chain system is established based on Voigt model and point-by-point tension method. Then, the change law of scraper group vibration and chain tension under the condition of scraper bending is studied. Thirdly, through the influence area and attenuation characteristics of torsional pendulum vibration, the thumbnail model of torsional pendulum vibration is constructed. Finally, the longitudinal and torsional pendulum coupling vibration dynamic model of the scraper chain system is constructed based on the torsional pendulum vibration abbreviation model, and the overall longitudinal and torsional pendulum vibration characteristics of the scraper conveyor are studied when the scraper is over the bending section. The conclusion of this paper provides a theoretical basis for better understanding the operation characteristics of scraper conveyor in coal mine.

The comprehensive effect of friction self-excited and modal vibration on polygonal wear of high-speed train wheels

Wheel polygon wear has emerged as a critical issue in the development of high-speed trains in China, but the mechanism underlying its formation remains unknown. The formation mechanism and its effect factors of wheel polygonalization are investigated in depth in this paper using theoretical analysis and numerical simulation. A longitudinal self-excited vibration and vertical modal vibration coupling model of wheel-rail is established, considering the comprehensive effects of wheelset flexibility, vehicle spring mass, and foundation under rail. The critical condition of the system Hopf bifurcation is determined by theoretical analysis, and the longitudinal vibration characteristics of the wheel are studied using numerical simulation. Furthermore, the influence factors on wheel polygonalization are investigated. The research method makes a useful attempt to unify the relevant viewpoints of resonance theory and self-excited vibration theory, and the research results have theoretical guiding significance and engineering reference value for the prediction and suppression of wheel polygonal wear.

Longitudinal vibration characteristics analysis of nonlocal rod structure with arbitrary internal elastic supports

This manuscript obtained an exact solution for longitudinal vibrating characteristics of generally restrained nanorod structure with multiple internal elastic supports via an improved Fourier series method. Due to the nonlocal elasticity theory, the general boundary restraints have been formulated by introducing artificial springs. Then, classical boundary conditions can be easily realized by setting the restrained stiffness to zero or infinity accordingly. Energy formulation is derived for describing longitudinal vibration characteristics of generally restrained nanorod with multiple internal elastic supports. To improve the differential continuities at the elastically restrained boundary, nonlocal longitudinal vibrating displacement is expanded as the standard Fourier series combined with auxiliary polynomials, which makes the field function sufficiently smooth in the calculation region. By making use Rayleigh–Ritz procedure, the unknown coefficients can be obtained by solving the standard eigenvalue matrix. Then, numerical results are presented and compared with those in the literature to illustrate the reliability and effectiveness of the current model. The influence of parameters of the multiple internal elastic supports, nonlocal structural parameters, and boundary restraints on vibration characteristics are discussed and analyzed. This study provides an effective method for predicting longitudinal vibration characteristics of a generally restrained nanorod with multiple internal elastic supports, in which the nanorod has complex boundary and coupling conditions.

Experiment Research on Emergency Stop Vibrations of Key Components in the Friction Vertical Lifting System

In order to analyze emergency stop vibration of the friction vertical lifting system under different loads, a loading experiment was carried out, and the longitudinal vibration characteristics of the carriage, frame, and steel rope were measured during the emergency braking process of an elevator. Accordingly, it is found that the load mass does not affect the peak deceleration value of the car frame and the wire rope during downwards emergency stop. Then, vertical vibration is explored using the time-varying vibration analysis theory. The obtained results show that when analyzing the vibration of objects on both sides of the traction wheel, the deceleration of the wire rope on both sides of the traction wheel are not equal, and the influence of the pressure change during the traction-wheel friction should be considered in calculations. This article may provide a reference to calculate the steel rope tension of the elevator and mine hoist.

The longitudinal vibration characteristics and parametric analysis of a ship thrust bearing integrated with internal disc springs

To reduce the transmission of shafting longitudinal vibration in surface ships, a design of thrust bearing integrated with internal disc springs is proposed and the longitudinal vibration characteristics of the shafting are studied. According to the structural characteristics of thrust bearing and the deformation characteristics of disc springs, the specific size and combination forms of disc springs in the thrust bearing are designed, and the effective disc springs schemes are achieved according to the static and dynamic design requirements. With the integration of the disc springs into the thrust bearing, the peak of longitudinal displacement response at the base of thrust bearing can be reduced by 10 dB by two schemes of disc springs. The proposed design can effectively suppress the transmission of shaft longitudinal vibration to the hull, which has engineering significance for the longitudinal vibration control of the shafting of the surface ship.

Comparative Analysis of Longitudinal and Transverse Vibration Characteristics of Ocean Mining Pipe

In this paper, the 5000 m mining pipe is taken as the research object, and the transverse and longitudinal vibration laws of the pipe under different working conditions are analyzed. Based on the finite element method (FEM), the pipe is discretized and calculated by the Wilson-θ Wilson - θ integral method; finally, the corresponding vibration laws of the mining pipe are obtained. The research shows that the mining pipe vibration responses are irregular motion, with the obvious oscillation phenomenon, and the overall vibration trend decreases first and then increases from the top to the bottom; the maximum vibration response occurs at the pipe top. Under the same working conditions, increasing the towing velocity will decrease the overall longitudinal vibration amplitude and increase the overall transverse vibration amplitude. While the ore bin weight will increase the longitudinal vibration amplitude and decrease the transverse vibration amplitude, increasing the mining pipe large diameter stepped section length and damping will decrease the longitudinal and transverse vibration simultaneously. When the towing velocity is between 0–2.8 m/s, the longitudinal vibration intensity is large, which is the main vibration mode. When the towing velocity is 2.8 m/s, the critical point is reached, and the longitudinal and transverse vibrations have the same intensity. When the towing velocity is greater than 2.8 m/s, the transverse vibration intensity is gradually greater than the longitudinal vibration intensity; at this time, the control of the transverse vibration should be appropriately increased.

Analytical study on longitudinal vibration characteristics of the coupled shaft and conical-cylindrical shell

The inevitably produced vibrations during navigation will reduce the reliability of ships. The propulsion shaft system and the hull are connected by bearings to form complex longitudinal coupled vibrations. The study of longitudinal coupled vibration mechanism and its transmission characteristics during the navigation is of great significance for the reduction of vibration and noise. In this study, the longitudinal vibration model of the conical-cylindrical shell and homogeneous shaft is established by the analytical method, while the accuracy of the analytical solution is verified by finite element method (FEM). Both the propeller excitation on the shaft and the external excitation on the shell are under consideration, and in view of the uneven flow field around the hull, the excitation applied to the shell is set to be asymmetrical. Based on this model, the effects of coupling effect, fluid loading, excitations, bearing stiffness on the longitudinal vibration of the system are analyzed, respectively. The results show that the coupling effect between the longitudinal vibration of the shaft and shell is evident and is greatest under the excitation on the shell in a lower frequency range. Moreover, besides of damping and mass effects, the fluid loading on the hull also influence the vibration response of the shaft, due to the coupling effect. The increase of the bearing stiffness strengthens the coupling effect of shaft-shell. These findings are helpful for analyzing the vibration mechanism of the stern and provide control direction for ship structural vibration in the design stage.

Longitudinal vibration analysis of sucker rod based on a simplified thermo-solid model

The longitudinal vibration of a sucker rod may change plunger stroke, thus affecting the pumping efficiency. In the study, a simplified thermo-solid coupling model of the longitudinal vibration of a sucker rod is established based on the consideration of the effect of the temperature along the well depth. Then, with the finite element method, the influence of longitudinal vibration of a continuous steel sucker rod on plunger stroke is studied. The calculation model involves two stages. In the first stage, the polished rod position remains stationary, whereas the sucker rod vibrates only under its gravity and liquid column gravity. The final stable state of the sucker rod is the initial state of the second stage. This stage aims to eliminate the effect of the initial tensile vibration. The longitudinal vibration characteristics of the sucker rod in the second stage are calculated based on the consideration of the excitations of both the polished rod displacement and the liquid column load in order to ensure the accuracy of calculation results. The influences of the frequency of stroke, stroke, and the length of sucker rod on plunger displacement are studied. The plunger displacement is slightly lagged behind the excitation on the polished rod due to the joint action of elasticity and load. The frequency of stroke, stroke, and the length of sucker rod affect the overtravel. When the sucker rod length is 2000 m, the overtravel reaches 0.12 m. Other parameters can also be optimized with this model.

New Analytical Solutions for Longitudinal Vibration of a Floating Pile in Layered Soils with Radial Heterogeneity

Based on the theory of wave propagation in three-dimensional (3D) continuum, a new analytical approach for the longitudinal vibration characteristics of a floating pile in layered soils with radial heterogeneity is developed by employing a viscous-type damping model. Firstly, an analytical solution for the longitudinal complex impedance at the pile head is deduced by employing the Laplace transform and complex stiffness technique with the compatibility conditions of the pile and radially inhomogeneous surrounding soil. Secondly, a semi-analytical solution in the time domain is further acquired by using the inverse Fourier transform method. Furthermore, the corresponding analytical solutions are validated through contrasts with previous solutions. Finally, parametric analyses are underway to investigate the effect of radial heterogeneity of surrounding soils on longitudinal vibration characteristics of floating piles. It is indicated that the proposed approach and corresponding solutions can provide a more wide-ranging application than the simple harmonic vibration for longitudinal vibration analysis of a floating pile in soils.

Use of longitudinal vibration and visual characteristics to predict mechanical properties of No. S Southern pine 2x8 and 2x10 Lumber

The objective of this study was to evaluate the accuracy of single MOE and MOR and combined mechanical properties with visual characteristics to improve the prediction of 2 x 8 and 2 x 10 No. @ southern pine lumber. This study evaluated the following variables: nondestructive tests, knots (knot diameter ratio [KDR] and knot area ratio), density, and mechanical properties (stiffness [MOE] and strength [MOR]). A total of 486 pieces were used, and linear regression models were constructed using stepwise selects to determine the best variables to estimate the MOE and MOR of southern pine lumber. The best single predictor for MOE and MOR was dynamic MOE (dMOE) followed by density. Among the two knot measurement methods used, the KDR best predicted stiffness and strength. For predicting the MOE, the variables dMOE, density, and KDR. The results showed that the addition of knot measurements to the models is able to improve the prediction of mechanical properties.

Analysis and Research on Longitudinal Vibration Characteristics of Deep Sea Mining Pipe Based on Finite Element Method

This paper aimed to study the longitudinal vibration characteristics of the 5000 m mining pipe in the ocean under different working wind conditions, offset angle, damping, and ore bin weight. Based on the finite element method, the mining pipe is simplified into beam element and discretized, and the physical and mathematical models of the mining pipe system are established. The Wilson-θ direct integral method is adopted for numerical calculation. The results show that the longitudinal vibration of the mining pipe is irregular, which presents the phenomenon of oscillation. The vibration amplitude decreases first and then increases from top to bottom, the minimum vibration amplitude appears at 1000 m, and the maximum vibration amplitude appears at the top of the mining pipe. Under the same working wind condition, the overall longitudinal vibration amplitude of the mining pipe can be increased by increasing the ore bin weight and the offset angle, but neither of them can change the frequency of the longitudinal vibration. The closer the excitation frequency generated by different working wind conditions is to the natural frequency, the larger the mining pipe longitudinal vibration amplitude is. The closer the vibration frequency generated by the same excitation frequency is to the natural frequency, the stronger the vibration intensity is, and when damping is added, the vibration intensity decreases faster.

Beam Approximation for Dynamic Analysis of Launch Vehicles Modelled as Stiffened Cylindrical Shells

A beam approximation method for dynamic analysis of launch vehicles modelled as stiffened cylindrical shells is proposed. Firstly, an initial beam model of the stiffened cylindrical shell is established based on the cross-sectional area equivalence principle that represents the shell skin and its longitudinal ribs as a beam with annular cross-section, and the circumferential ribs as lumped masses at the nodes of the beam elements. Then, a fine finite element model (FE model) of the stiffened cylindrical shell is constructed and a modal analysis is carried out. Finally, the initial beam model is improved through model updating against the natural frequencies and mode shapes of the fine FE model of the shell. To facilitate the comparison between the mode shapes of the fine FE model of the stiffened shell and the equivalent beam model, a weighted nodal displacement coupling relationship is introduced. To prevent the design parameters used in model updating from converging to incorrect values, a pre-model updating procedure is added before the proper model updating. The results of two examples demonstrate that the beam approximation method presented in this paper can build equivalent beam models of stiffened cylindrical shells which can reflect the global longitudinal, lateral and torsional vibration characteristics very well in terms of the natural frequencies.

Coupled vibration characteristics of a submarine propeller-shaft-hull system at low frequency

The coupled longitudinal and transverse vibration characteristics of a submarine propeller-shaft-hull system at low frequency are studied in this paper. Two substructures, which are the propeller-shaft subsystem and the submarine hull, are first modelled using the finite element method. The two substructures are then connected through bearings, which are simplified as longitudinal and lateral springs and dampers. The modes, the natural frequencies and the coupled vibration characteristics of the two substructures and their synthesized system are simulated. An experiment studying the dynamic characteristics of a large-scale submarine test-rig is proceeded and compared with the numerical results, showing great consistency. Finally, transfer path analysis of the low frequency excitation forces using power flow method is discussed.