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During the lateral vibration of footbridge, the pedestrian lateral load shows two distinct features: one is the vibration-dependency; another is the narrowband randomness caused by the variability between two subsequent walking steps. In this case, the lateral vibration of footbridge is actually a complicated, nonlinear stochastic system. In this paper, a novel nonlinear stochastic model for lateral vibration of footbridge is proposed, in which a velocity-dependent load model developed from Nakamura model is adopted to represent the pedestrian-bridge interaction and the narrowband stochastic characteristic is considered. The amplitude and phase involved Itô equations are established using the multiscale method. Based on the maximal Lyapunov exponent derived from these equations, the critical condition for triggering a large lateral vibration can be obtained by solving the stability problem. The validity of the proposed method is confirmed, based on performing the case studies of two bridges. Meanwhile, through parameter analysis, the influences of several crucial parameters on the stability of vibration are discussed.

Through the condition analysis of the drill rod during the mining horizontal drilling for gas drainage, the finite element model of the drill rod lateral vibration is established. The drill rod lateral vibration is related to the diameter and length of the drill rod. With the increase of the diameter of the drill rod, the natural frequency of the lateral vibration of the drill rod increases constantly. The increasing amplitude of the natural frequency at the larger diameter of the drill rod is larger than that at the smaller diameter. When the drill rod is longer, the natural frequency of the lateral vibration of the drill rod is lower. From the modal images of the drill rod, the lateral vibration of the drill rod is similar to the sine curve. During the horizontal drilling in coal seam, the drill rod contact and impact with the hole wall which will bring about the fatigue fault of the drill rod and the collapse of the hole wall.

The influences of train length on vehicle dynamics and train stability were investigated using different vehicle models of various lengths. First, a reliable vehicle model was constructed to determine the cause of unstable lateral vibration. This model reflects the tendencies observed in the high-speed test line investigations. Analysis results show that the secondary lateral stiffness of the air spring is the most significant cause of lateral vibration in car bodies. Vibrations were stable in the analysis of short train formations, which had either 7 or 10 cars, even though lateral stiffness was high. However, long train formations that contained either 16 or 20 cars vibrated unstably. Mode analysis results suggested that an increase in wheel conicity can reduce the unstable, low-frequency vibration of long trains.

During the acceptance test of KTX, unexpectedly great lateral vibration in 14th~16th train at 150km/h~200km/h was appeared on a straight line in the winter season. Generally, stiffness of secondary suspension in KTX vehicle is one of the most sensitive components on air temperature. So, we examined that the secondary suspension to be mounted heating system was able to reduce the lateral vibration in the tail car of KTX. Also, we verified that lateral vibration from test results on KTX train with wheel conicity 1/20 disappeared. In this paper, we analysis effective reduction methods and the cause of the lateral vibration using model of KTX train and compare with the test results. The analysis results agree well with test ones. From mode analysis result, lateral vibration is occurred at natural frequency range 0.5~0.6Hz with a negative damping value and its natural frequency disappear gradually according to increasing of wheel concinicy.

Drilling string lateral vibration is a severe damage,which is influenced by many complex factors. This paper makes a theoretical analysis of the drilling string lateral vibration frequency caused by drilling fluid flow velocity inside and outside the drilling string, which supplies some evidence for calculating rotation speed of rotary table and reduces the times of drill string resonance. The influence of drilling fluid flow velocity inside the drilling string on lateral vibration frequency is analyzed by Euler method. Besides, through the use of mechanical analysis method and the introduction of additional mass coefficient. A differential equation of drilling string lateral vibration with the consideration of drilling fluid flow velocity inside and outside the drilling string is built up, and a mathematical model of drilling string lateral vibration under the influence of drilling fluid flow velocity is obtained. Field applications indicate that this model is in agreement with the field condition.

The objectives of this study were to analyze the first three critical frequency, critical speeds and mode shapes of the drilling string due to lateral vibration. Drilling string vibrations pose a major challenge to the operational efficiency of the drilling process in the oil and gas industry. The mass imbalance in the drilling string caused by Measured While Drilling (MWD) tools and drill collar sag disrupts the accuracy of the drilling operation and can give rise to huge vibration thereby damaging the down hole components. Since the surface readings are not reliable measured of drilling string lateral vibration, it becomes necessary to study drilling string vibration under Finite Element method. In this project, ANSYS software was used to build the geometry of a drilling string model and appropriate boundary conditions were applied to the model such that the drilling string experiences lateral vibrations. The component of mass imbalance was introduced to the drilling string by adding an equivalent weight eccentrically on one side of the drilling string. Modal analysis was performed to determine the mode shapes and the first three critical frequencies of the drilling string. The effect of mass imbalance was studied by comparing the first three critical frequencies before and after the addition of the imbalance. The results showed an increase in natural frequency to 2.03Hz, 2.23Hz, and 4.63Hz were imposed on the deformation of drilling string. Since the normal operating speeds of a drilling string rotary table is around 100-200 RPM, it was clear that the drilling string without mass imbalance, the resonance of the drilling string occurs at 85 and 262 RPM which is clearly out of the operating speeds. But when a mass imbalance is introduced to the drilling string, the resonance occurs at 121, 133 and 277 RPM. The two operating speeds cause resonance which can critically damage the drilling string. The drilling string which consists of the stabilisers and bit are subject to almost no displacements at all. The best practices of this study are very useful for identify the safe operating ranges of rotary speed for the drilling string and identify the lateral displacement of a critical component for a range of frequencies, thereby avoiding damage to the drilling string.

The feedback-controlled lubrication regime, based on a model-free designed proportional–derivative controller, is experimentally investigated in a flexible rotor mounted on an actively-lubricated tilting-pad journal bearing. With such a lubrication regime, both the resulting pressure distribution over the pads and hence the bearing dynamic properties are dynamically modified. The control strategy is focused on reducing the lateral vibrations of the system around its operational equilibrium within a wide frequency range. To synthesize the proportional–derivative controller gains, an objective function is optimized in the stabilizing gain domain and then chosen from a subdomain imposed by servovalve restrictions. This work demonstrates enhancements of the dynamic response of flexible rotor-bearing systems supported by an active tilting-pad journal bearing by means of the feedback-controlled lubrication regime featured via proportional–derivative controllers.

Energy harvesters are devices that convert mechanical energy, usually vibration, into electrical energy that can be used to supply low power circuits (e.g. sensors). In this work, an energy harvester is designed for converting the mechanical energy of the lateral vibrations of shafts into electrical energy. For that, permanent magnets are mounted in the shaft and coils are mounted in a fixed structure. A configuration analysis is performed to find the appropriated polarization of the magnets and orientation of the coils in order to have electromagnetic induction without resisting torque on the shaft. Experimental tests are done for different electrical configurations of the coils: independent, in series and, in parallel. The results show that more electric power is induced when the coils are connected in series, and vibration reduction is more evident when the coils are connected independently.

Contents: Machinery particulars ; Lateral scheme ; Conclusions ; Notes ; Calculation data ; Calculation results: Summary ; Journal bearing characteristics: P-bracket bearing ; Shaft log bearing ; Natural vibrations: I-mode ; II-mode ; Forced vibrations: Displacement levels, horizontal plane ; Stress levels, horizontal plane ; Displacement levels, vertical plane ; Stress levels, vertical plane ; Shaftline natural frequencies for various engine running conditions. Total: 26 pages

This paper studies the efficiency of a number of smooth non-linear energy sinks (NESs) on the vibration attenuation of a rotor system under mass eccentricity force. The non-linear energy sinks have a linear damping, linear stiffness and a cubic stiffness. To reduce the number of equations of motion, the modal coordinates and complex transformations are used. For analytical solution, the Multiple Scales-Harmonic Balance Method (MSHBM) is used. The most important parameters to examine NES efficiency is the range of happening of the SMR in the detuning parameter range. For different parameters of the system, the SMR, the WMR, the low amplitude periodic motion, and the high amplitude periodic motion happen in the system. It is shown that, the linear stiffness of the NES is canceled out by the stiffness which is created by the centrifugal force and therefore, by changing the linear stiffness of the NESs, the collection of the NESs to the desired rotational speed of the rotor can be tuned. It should be noted that after this cancellation, the remained stiffness is essentially non-linear (non-linearizable) stiffness. In addition, when the external force reaches its medium magnitude, the area of the occurrence of the SMR in the domain of the system parameters would be larger and the collection of the NESs demonstrates an impressive effect.

In-situ modal analysis of building structures often does not consider amplitude dependence of modal properties. In multi-storey timber buildings, such a consideration may be particularly im- portant. A growing number of mid-rise timber buildings have been built in Europe over the past decade, up to 14 storeys and 45m in height. A design challenge for the engineers of some of these buildings has been the assessment of wind-induced lateral vibration. Prediction of both nat- ural frequency and damping are difficult due to non-linear connection stiffness, and the shortage of precedent buildings for damping measurement. The practical constraints of testing occupied buildings have meant that it has not been possible to excite the buildings artificially, so output-only modal analysis techniques have been applied. The random decrement technique is of particular interest, since it has been used to assess the variation of natural frequency and damping with am- plitude of acceleration, and over recent years, researchers presented a variety of ways to do this. This paper presents a comparison of contemporary methods to assess amplitude dependence of modal properties from output-only data, using synthesised data. Appropriate methods are then applied to data measured from a multi-storey timber building, to comment on the consequences of the variation of modal properties with amplitude for design. It is shown that the damping ratios of these buildings should be expressed as their variation over a range of amplitude, and that long- term monitoring has the potential to bring out a more complete picture of this behaviour.

The paper shows a mathematical rotordynamic model for lateral vibration analysis of induction motors with dynamic eccentricities regarding start-up. With this mathematical model, different kinds of dynamic eccentricities—mass eccentricity, magnetic eccentricity and bent rotor deflection—can be analyzed. Beside the mechanical influences—e.g. the rotor mass, rotor shaft stiffness, oil film coefficients of the sleeve bearings, structural stiffness of the sleeve bearing housings and end shields—also electromagnetic influence—e.g. the electromagnetic field and magnetic eccentricity—can be analyzed for the start-up. The paper is based on the well-known theory of accelerated resonance passing and is an enhancement of the theory for induction motors, considering also electromagnetism during start-up. Based on this rotordynamic model, the absolute displacements of the shaft centre, the shaft journals and the sleeve bearing housings can be analyzed as well as the relative displacements between the shaft journals and the sleeve bearing housings. Additionally, also the vibration velocities at the sleeve bearing housings can be derived. The aim of the paper is not to replace a detailed finite-element-model by a simplified analytical model, but to show the mathematical coherences between rotordyamics and electromagnetics for a start-up of an induction motor, considering different dynamic eccentricities.

Nakamura’s model is proposed to describe lateral vibrations of a footbridge induced by pedestrians. The model is found to be a slow-fast system if the number of pedestrians on a footbridge increases slowly. Then, based on the delayed bifurcation theory, Nakamura’s model can be used to describe the delayed increase in the lateral vibration of the footbridge. The critical number of pedestrians on the footbridge is calculated by using the delayed bifurcation theory to quantitatively demonstrate our analysis. By comparison with a previously obtained formula, the rationality of the authors’ formula for predicting the critical number of pedestrians is illustrated. Based on the authors’ formula, the experimental parameter k=300 used in the previously obtained formula does not seem to be always applicable to other bridges. Based on Nakamura’s model, the value of the parameter k seems to be affected mainly by the properties of the pedestrians on the bridge rather than those of the bridge.

Drilling string lateral vibration is a severe damage,which is influenced by many complex factors. This paper makes a theoretical analysis of the drilling string lateral vibration frequency caused by drilling fluid flow velocity inside and outside the drilling string, which supplies some evidence for calculating rotation speed of rotary table and reduces the times of drill string resonance. The influence of drilling fluid flow velocity inside the drilling string on lateral vibration frequency is analyzed by Euler method. Besides,through the use of mechanical analysis method and the introduction of additional mass coefficient. A differential equation of drilling string lateral vibration with the consideration of drilling fluid flow velocity inside and outside the drilling string is built up, and a mathematical model of drilling string lateral vibration under the influence of drilling fluid flow velocity is obtained. Field applications indicate that this model is in agreement with the field condition. Key words: mass coefficient;differential equation; drilling fluid flow velocity; lateral vibration frequency

According to the vehicle dynamics theory, the dynamics simulation models of single-vehicle NX70H flat marked loading capacity of 70t with K5 bogies and NX70 flat marked loading capacity of 70t with K6 bogies under certain loading and running conditions were established by SIMPACK, in order to discuss the change rules of the roll angles, the yaw angles, the lateral offsets and the maximum lateral vibration offsets. Based on the statistical analysis of data calculated by SIMPACK, the results of dynamics single-vehicle models of the two wagon types running on Chinese I and III grade railway lines respectively were compared. Simulation results show that the running speed, the line condition and the height distancing the rail surface all have a significant impact on the maximum lateral vibration offset.

In this paper, the factors and variables that affect the amplitude of the lateral vibration of the footbridge induced by pedestrians in Nakamura’s model are investigated in the aspect of nonlinear dynamics. Nakamura’s model is based on the motion of equations including coefficients of the rate of a pedestrian’s lateral force, the pedestrian density, the rate of synchronized pedestrians, the function G(fB) describing how pedestrians synchronize with the bridge natural frequency, and the pedestrians’ attitude to large vibration amplitude. The important coefficient G(fB) cannot be decided in this model because of the lack of data available on the lateral load behaviors of walking people. Nakamura assumed that G(fB)=1.0 in his model by considering that pedestrians are most likely to synchronize at the bridge frequency around 1.0 Hz. The analysis results presented in this paper demonstrate that the amplitude of the lateral vibration increases when the function G(fB) increases. This suggests G(fB)=1.0 m...

A single piezoelectric resonator shows better excitation efficiency at bending modes than other vibration modes and the inherent operating principle of piezoelectric actuators has limited its practical use to suppressing bending mode vibrations. To achieve effective non-bending modal vibration attenuation using only one piezoelectric actuator, this paper presents an active vibration control method according to the theory of electrode configuration. Finite element based modal analysis was performed to determine proper electrode configuration and its corresponding resonant mode for vibration suppression control. In this study the first lateral mode of the structure was adopted for experimental investigation. Two vibration control algorithms, positive-position-feedback control and proportional-derivational control, were applied to analyze the vibration control performance with inclusion of electrode configuration. Experiments demonstrate that the proposed active vibration control embedded with prudent electrode configuration can effectively suppress vibrations subject to lateral modal excitation.

Dynamic fibre-optic curvature sensing is demonstrated by interrogating chains of fibre segments, separated by broadband Bragg grating reflectors, using range-resolved interferometry (RRI). Four fibre strings, containing four fibre segments each of gauge length 20 cm, are attached to the opposing sides of a support structure and the resulting differential strain measurements allow inference of lateral displacements of a cantilever test object. Dynamic tip displacement resolutions in the micrometre range at an interferometric bandwidth of 21 kHz demonstrate the suitability of this approach for highly sensitive and cost-effective fibre-optic directional vibration measurements of smart structures. © (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only

In this paper, a new modified finite element method that can be used in the analysis of transverse and lateral vibrations of the thin beams under a point mass moving with a variable acceleration and constant jerk is presented. Jerk is the change in acceleration over time. In this method, the classical finite element of the beam is modified by the inclusion of the inertial effects of the moving mass. This modification is made using the relations between nodal forces and nodal deflections and shape functions of six DOF beam element. The mass, stiffness, and damping matrices of the modified finite element are determined by forces caused by the corresponding transverse and lateral accelerations and jerks, and transverse Coriolis and centripetal accelerations and jerks, respectively. This method was first applied on a simply supported beam plate to provide a comparison with the previous studies in literature, and it was proved that the results were within acceptable limits. Secondly, it was applied on a CNC type box-framed beam to analyse the dynamic response of the beam in terms of variable acceleration and jerk as well as constant velocity and mass ratios.

The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations., {"references":["J. Yuh and T. Young, \"Dynamic Modeling of an Axially Moving Beam in Rotation: Simulation and Experiment,\" Journal of Dynamic Systems, Measurement, and Control, vol. 113, pp. 34-40, 1991.","H. B. S.K.Tadikonda, \"Dynamic and control of a translating flexible beam with a prismatic joint,\" Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 114 vol. 114, p. 5, 1992.","B. O. Al-Bedoor and Y. A. Khulief, \"Finite element dynamic modeling of a translating and rotating flexible link,\" Computer Methods in Applied Mechanics and Engineering, vol. 131, pp. 173-189, 1996.","M. Kalyoncu, \"Mathematical modelling and dynamic response of a multi-straight-line path tracing flexible robot manipulator with rotating-prismatic joint,\" Applied Mathematical Modelling, vol. 32, pp. 1087-1098, 2008.","S. E. Khadem and A. A. Pirmohammadi, \"Analytical development of dynamic equations of motion for a three-dimensional flexible link manipulator with revolute and prismatic joints,\" IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 33, pp. 237-249, 2003.","J. Chung, et al., \"Stability analysis for the flapwise motion of a cantilever beam with rotary oscillation,\" Journal of Sound and Vibration, vol. 273, pp. 1047-1062, 2004.","P. K. C. Wang and J.-D. Wei, \"Vibrations in a moving flexible robot arm,\" Journal of Sound and Vibration, vol. 116, pp. 149-160, 1987.","H. Karimi and M. Yazdanpanah, \"A new modeling approach to single-link flexible manipulator using singular perturbation method,\" Electrical Engineering (Archiv fur Elektrotechnik), vol. 88, pp. 375-382, 2006.","M. H. Ghayesh and S. E. Khadem, \"Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity,\" International Journal of Mechanical Sciences, vol. 50, pp. 389-404, 2008.\n[10]\tY.-Q. Tang, et al., \"Nonlinear vibrations of axially moving Timoshenko beams under weak and strong external excitations,\" Journal of Sound and Vibration, vol. 320, pp. 1078-1099, 2009.\n[11]\tL.-Q. Chen and W.-J. Zhao, \"A conserved quantity and the stability of axially moving nonlinear beams,\" Journal of Sound and Vibration, vol. 286, pp. 663-668, 2005.\n[12]\tL.-Q. Chen and X.-D. Yang, \"Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models,\" International Journal of Solids and Structures, vol. 42, pp. 37-50, 2005.\n[13]\tV. Kartik and J. A. Wickert, \"Vibration and guiding of moving media with edge weave imperfections,\" Journal of Sound and Vibration, vol. 291, pp. 419-436, 2006.\n[14]\tF Rahimi Dehgolan, SE Khadem, S Bab, M Najafee, \"Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System\", World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 12 (4) (2016) 349–357.\n[15]\tA. H. Nayfeh, Problems in perturbation. New York: Wiley, 1993.\n[16]\tA. Nayfeh, Introduction to perturbation techniques. New York: Wiley, 1981.\n[17]\tJ. Kevorkian and J. D. Cole, Perturbation methods in applied mathematics. New York: Springer-Verlag, 1981."]}

In this paper, vibration attenuation of a beam with circular cross-section by resonantly shunted piezo-elastic supports is experimentally investigated for varying axial tensile and compressive beam loads. Varying axial beam loads manipulate the effective lateral bending stiffness and, thus, lead to a detuning of the beams resonance frequencies. Furthermore, varying axial loads affect the general electromechanical coupling coefficient of transducer and beam, an important modal quantity for shunt-damping. The beam’s first mode resonance frequency and coupling coefficient are analyzed for varying axial loads. The values of the resonance frequency and the coupling coefficient are obtained from a transducer impedance measurement. Finally, frequency transfer functions of the beam with one piezo-elastic support either shunted to a RL-shunt or to a RL-shunt with negative capacitance, the RLC-shunt, are compared for varying axial loads. It is shown that the beam vibration attenuation with the RLC-shunt is less influenced by varying axial beam loads.

Modern footbridges are often characterized by architectural demands for light, slender, and long structures that may lead to excessive vibration problems. In past decades, occurrences of pedestrian-induced vibration on footbridges have been reported, notably at the Toda Bridge in Japan, the Millennium Bridge in London, and the Solferino in Paris. In 1989, we observed a peculiar type of lateral vibration at the Toda Bridge during the passing of congested crowds. Hundreds of pedestrians walked in a synchronized manner among themselves, which created remarkable lateral vibration in the structure. Approximately 10 years later, public attention on pedestrian-induced lateral vibration increased significantly when the Solferino Bridge in Paris and the Millennium Bridge in London showed a similar phenomenon during the passing of congested crowds. These three most well-known cases have triggered extensive study, and pedestrian-induced vibration has emerged as an important topic in vibration study. A consid...

The lateral vibration of railway bridges induced by moving trains has traditionally been solved through numerical integration. Although it provides practical prediction, the numerical approach does not explicitly reveal the underlying driving mechanism of the train–bridge interaction. In this paper, a closed-form solution is derived for the lateral vibration of a simply supported bridge subjected to hunting forces from running wheel sets. Through complex Fourier expansion, this solution leads to the formulation of three influential factors with explicit physical meanings, namely, the effective unit moving load on the bridge, the arrangement of all moving wheel sets, and the frequency response function of the bridge. On the basis of these factors, a simplified formula to estimate the maximum vibration of the bridge is proposed. The closed-form solution and the simplified formula are validated through comparison with results from numerical integration. The resonance conditions of the bridge due to m...