Amplitude Of Dynamic Response Research Articles

Reliability-based design optimization scheme of isolation capacity of nonlinear vibration isolators

Nonlinear vibration isolators (NVIs) are beneficial to isolate or suppress the adverse effects caused by harmful vibration. To a large extent, the isolation capacity of NVIs depends on the selection of design parameters (including structural, geometric, and excitation parameters) of vibration isolators. However, existent uncertainties of these parameters are unavoidable, which influence the reliability of the isolation capacity of NVIs. In this respect, an effective reliability-based design optimization (RBDO) scheme of isolation capacity of NVIs is presented by taking into account the parameter uncertainties of NVIs. In the proposed RBDO scheme, the force transmissibility of nonlinear isolators is regarded as the objective function, and the fundamental frequency, the dynamic displacement response amplitude, and reliability of vibration isolation performance are supplied as the constraints to search the optimal design parameters of NVIs. Considering the influence degree of design parameters uncertainties, the global reliability sensitivity analysis is employed for identifying the critical design parameters in NVIs. A surrogate model of the failure probability function is established by the adaptive learning Kriging approach to decrease the computational cost of the reliability evaluation nested in the RBDO scheme. An advanced meta-heuristic algorithm is executed to search for the design parameters for optimal isolation capacity of NVIs. The proposed scheme provides a potential direction for optimizing the isolation capacity of complicated vibration isolators.

Equivalent Dynamic Modeling for the Relative Rotation of Bolted Joint Interface Using Valanis Model of Hysteresis

Dynamic modeling of the joint interface is critical to the performance analysis of bolt-jointed structures. In this work, an equivalent modeling method was presented for modeling the relative rotation of the joint interface in bolt-jointed beam structures. As the transverse vibration of the studied structure is closely related to the rotation of the joint, which is different from previous studies that focused on the tangential slip of the joint interface, the Valanis model is used to model the relative rotation of the joint. In addition, the shear deformation and rotational inertia of the beam were considered in the modeling, using a finite element method that employed Timoshenko beam elements. The parameters of the Valanis model were determined by fitting a series of hysteresis loops obtained from the transient nonlinear analysis of a 3D FEM model. The results show that the proposed equivalent modeling method can accurately simulate the dynamic response and dissipation of the jointed beam structure with a significantly high computational efficiency. The maximum errors of the dynamic response amplitude and the energy dissipation are 5.5% and 8.3%.

Estimation of wind-induced response of large membrane structures with nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness

Wind-induced dynamic response for large membrane structures with consideration of the coupling influences of nonlinear motion-induced aerodynamic force and nonlinear geometric stiffness is analytically evaluated in this study. By utilizing the equivalent nonlinear system approach, the Fokker-Planck-Kolmogorov equation of the membrane structures is derived, and the analytical response solutions, including probability density function, root-mean-square value, kurtosis, peak response, and peak factor, are presented. The accuracy of the proposed analytical solutions is checked by the numerical results obtained with the fourth-order Runge-Kutta approach. The findings reveal that vortex-induced vibrations occur at high wind speed regions due to the effect of nonlinear negative aerodynamic damping. Additionally, the geometric stiffness nonlinearity caused by large deformation is found to be significant for reducing the dynamic response amplitude in membrane structures. This study proposed herein presents an effective analytical approach for predicting the aero-elastic response of such flexible structures subjected to wind loads.

Vibration Mitigation in the Railcar Floor Panel Using a Topologically Optimized Auxetic Layer

This paper aims at to improve the vibration behavior of the train floor panel by the use of a cellular auxetic layer. A field measurement is performed to obtain the vibrational frequency content of the body floor moving on the tangent track. Using acceleration sensors, the vibrational response is measured on the bogie (as the input excitation) and on the floor panel (as the observation response). Finite Element modeling for the floor panel is accomplished and measurement data are used for both the input excitation and the verification of the numerical results. The floor panel is a sandwich panel containing multiple layers. In this study, the conventional wooden layer of the panel is substituted with a cellular auxetic one with a re-entrant hexagonal pattern. Then, an optimization problem is defined while the topological parameters of the auxetic layer are the design variables and the dynamic performance of the panel is the objective function. The parameter of power–mass–ratio (PMR) is defined taking the effects of both weight and dynamic response amplitude into calculation. It is found that the PMR is reduced to almost 0.6 by replacing the wooden layer with an auxetic one, and after topological optimization, it is reduced to 0.35.

Vibration control of beams under moving loads using tuned mass inerter systems

Traditional tuned mass dampers (TMDs) have been proven efficient for the moving-load-induced vibration control of beams. However, a large tuned mass is required in TMDs to adjust the structural dynamic characteristics and achieve the demanded performance targets, which leads to additional dynamic effects and inconvenience of installation. The tuned mass inerter system (TMIS) is an ungrounded lightweight passive control device, which contains a suspended mass, a parallel-connected tuned spring and an inerter-based subsystem. In this study, the application and optimization of TMISs on vibration suppression of multi-span beam models under moving load series are investigated. Using the Bubnov-Galerkin integration method, the modal-superposition generalized system for specified modes of a beam with TMIS under successive moving load series is established. Then, a design strategy for TMISs is proposed to achieve the structural target performance demand by decreasing the moving load-induced resonant responses and attached tuned mass. In the optimization algorithm, the tuned mass ratio is taken as the optimal objective, and the limited dynamic response amplitude under different speed parameters is the constraint condition. A single-span simply supported beam with the TMIS under a moving load series is analyzed. The designed TMISs are tuned to the dominating mode with the maximum mass participate factor of the main structures. TMISs show good vibration mitigation compared to TMDs with equal tuned mass. Meanwhile, under the premise of identical structural performance demands, TMISs require less tuned mass than TMDs and achieve a lightweight control effect. The corresponding dynamic amplitude vs speed curves and time history response curves of beams with TMISs and TMDs are also depicted through comparative analyses. The vertical deflection and acceleration responses apparently decrease, and the resonance is mitigated due to the designed TMISs. The sensitivity analysis results indicate that TMISs attached to beams are insensitive to the perturbance of their parameters and the input moving load excitations; thus, TMIS proves to be a robust tuning system.

Experimental parametric study on hydroelastic behaviour of a 15000-TEU container ship based on segmented ship model

ABSTRACT Large-scale ships with high elasticity and low natural frequency, behave high dynamic response amplitude under impulsive wave loads (whipping) and short period waves (springing), which could result in serious ultimate loads and fatigue damage. The segmented model test is a more powerful approach for the ship hydroelastic analysis compared with ship seakeeping test. However, the effect of some test parameters on the hydroelastic responses is still not a clear statement. Therefore, the number of segments, propulsion mode and backbone form are chosen for the parametric study on ship hydroelastic behaviour. A three-dimensional (3-D) nonlinear time-domain hydroelastic method is developed, in which the nonlinearity of instantaneous wetted surface and slamming force are considered. Through the analysis of natural frequencies and vertical bending moments (VBM), the impact on hydroelastic behaviour is discussed. Results show that self-propelling models with variable cross-section backbones are more suitable and reliable in studying nonlinear hydroelastic behaviour.

Study on dynamic safety distance of multi-storey buildings on the top of loess slope

In view of the frequent occurrence of strong earthquakes and the actual characteristics of buildings built on the top of slopes in the loess region of Western China, the dynamic response and stability law of loess slope under the building load on the top of the slope are discussed by using the three-dimensional finite element numerical calculation method. Taking the slope safety factor, acceleration amplification coefficient, building permanent displacement and slope sliding range as evaluation indexes, the dynamic safety of buildings on the top of the slope under earthquake is analyzed, and the recommended value of dynamic safety distance between top building and slope shoulder is put forward. The results show that: firstly, affected by the amplification effect of slope elevation, the dynamic response of buildings on the top of slope is stronger than that of buildings under slope. At the same time, affected by the amplification effect of the free surface of the slope, the dynamic response amplitude of the building is negatively correlated with the distance from the slope shoulder. Secondly, the horizontal acceleration ratio between the top building and the under building is the largest at the height of 3–6 m, indicating that the multi-storey building with pile raft foundation is most prone to damage at this height. Thirdly, the dynamic safety distance of multi-storey buildings with pile raft foundation located on the top of loess slope with slope height H ≤ 30 m and slope gradient 25° ≤ α ≤ 70° can be 24 m.

Experimental Research on Vibration-Damping Effect of Combined Shear Hinge Prefabricated Steel Spring Floating Slab Track.

Objective: The cast-in-place steel spring floating slab track (SSFST) is difficult to maintain and repair, while the mechanical strength of the end of the traditional prefabricated SSFST is poor. In order to overcome the above shortcomings, a shear-hinge-combined prefabricated SSFST was developed, and an indoor test was carried out to analyze its vibration-damping effect. Methods: A combined shear hinge SSFST connection model with two length sizes was established. The dynamic response amplitude and frequency response characteristics of the foundation (ground) under different isolator installations and fatigue loads were studied, and the vibration-damping performance of two sizes of combined shear hinge SSFST was evaluated. Results: The vibration-damping effect of the steel spring vibration isolator mainly acts in the middle and low-frequency bands of 16–400 Hz, and the vibration near 10 Hz will be aggravated after the vibration isolator is installed. The vibration index and variation law of the two sizes of SSFST are similar, and the vibration response of 4.8 m SSFST is slightly less than 3.6 m SSFST. There is almost no change in each index when the load is 5 million times, and there is a certain range of change when the load is 10 million times, but the overall change is small. Conclusions: The combined shear hinge prefabricated SSFST can have an excellent isolation effect on vibration and can still maintain good vibration-damping ability within 10 million fatigue loads (about 5 years); 4.8 m SSFST should be laid in straight sections with higher train speeds, while 3.6 m SSFST should be applied in curved sections to ensure smooth lines.

Research on Dynamic Performance of CRTSⅢ Type Slab Ballastless Track under Long-Term Service.

To fill the blank in the research on the dynamic performance of track structure under long-term service, the dynamic response study of China Railway Track System Ⅲ type slab ballastless track (CRTSIII SBT) under the action of fatigue for 30 million times and the parting between track slab and self-compacting concrete (SCC) was carried out. By establishing the finite element model of the CRTSIII SBT structure and taking the stiffness change of isolation layer and fastener under fatigue state and the parting during service as the research objects, combined with the full-scale model test, the dynamic response amplitude and vibration law of track structure was analyzed based on the finite element model of axle falling test method. The results show the following: (1) Under the fatigue load, the acceleration of rail and base increases obviously, the longitudinal tensile stress of SCC surface decreases, the longitudinal tensile stress of base surface increases, and the vertical stress of each layer of track structure increases as well. (2) Under the action of the parting, the dynamic response of each structural layer increases, and the change of acceleration and stress of each layer under the action point of axle falling is the most obvious. (3) The fatigue load will weaken the vibration damping performance of the track, and the parting will continue to develop under the action of the falling axle, resulting in partial or total failure of the SCC layer. Both of them will aggravate the dynamic response of the track structure and affect driving safety, which should be paid attention to during maintenance.

Study of the Immediate Effects of Autostereoscopic 3D Visual Training on the Accommodative Functions of Myopes.

PurposeStereoscopic viewing has an impact on ocular dynamics, but its effects on accommodative functions are not fully understood, especially for autostereoscopic viewing. This study aimed to investigate the changes in dynamic accommodative response, accommodative amplitude, and accommodative facility of myopes after autostereoscopic visual training.MethodsWe enrolled 46 adults (men = 22 and women = 24; age = 21.5 ± 2.5 [range = 18–25] years, spherical equivalent: −4.52 ± 1.89 [−8.88 to −1.75] diopters [D]) who visited the Eye & ENT Hospital of Fudan University. The study population was randomly divided into three-dimensional (3D) and two-dimensional (2D) viewing groups to watch an 11-minute training video displayed in 3D or 2D mode. Dynamic accommodative response, accommodative facility, and accommodative amplitude were measured before, during, and immediately after the training. Accommodative lag and the variability of accommodation were also analyzed. Visual fatigue was evaluated subjectively using a questionnaire.ResultsAccommodative lag decreased from 0.54 ± 0.29 D to 0.42 ± 0.32 D (P = 0.004), whereas accommodative facility increased from 10.83 ± 4.55 cycles per minute (cpm) to 13.15 ± 5.25 cpm (P < 0.001) in the 3D group. In the 2D group, there was no significant change in the accommodative lag (P = 0.163) or facility (P = 0.975), but a decrease in accommodative amplitude was observed (from 13.88 ± 3.17 D to 12.71 ± 2.23 D, P = 0.013). In the 3D group, the accommodative response changed with the simulated target distance. Visual fatigue was relatively mild in both groups.ConclusionsThe immediate impact of autostereoscopic training included a decrease in the accommodative lag and an increase in the accommodative facility. However, the long-term effects of autostereoscopic training require further exploration.

Vibration and nonlinear dynamic response of temperature-dependent FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio

This paper reports a study on natural frequency, nonlinear dynamic response and frequency amplitude relation of temperature-dependent FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio. The nonlinear motion equations and the compatibility equation are retrieved from first order shear deformation theory including the effect of von Karman nonlinearity terms, elastic foundations and initial imperfection. The system of dynamic governing equations is obtained by utilizing the Airy stress function and Bubnov–Galerkin procedure. The nonlinear dynamic response is also obtained by applying the 4th-order Runge–Kutta method. The frequency–amplitude relations of the shell is determined by using the assumption of inertia caused by a rotation. Besides, the analytical method and the finite element method are proposed to calculate the vibrational frequencies. Five types of FG-CNTRC laminate shell, three types of the structures and different thermal environments with the shell’s material properties depending on the temperature are also considered in this study. The numerical results are presented, verified with available studies in the literature. Finally, the effects of elastic foundations, initial imperfection, and temperature-dependence, typing double curved shallow shell, angle of lamination against the shell x-axis on the natural frequency and nonlinear dynamic response of FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio are discussed.

Advanced kriging-based surrogate modelling and sensitivity analysis for rotordynamics with uncertainties

Rotating machinery are present in many engineering applications. Such rotor systems often subjected to high vibration loads that can be at the origin of noise or failure. For these reasons, it is of main importance to predict with accuracy the critical speeds and the dynamic response amplitude of such structures. However, they are often subjected to many potential uncertainties that may rise from environmental variations or manufacturing tolerances. These uncertain parameters, often described as random, are often numerous and must be taken into consideration during the design stage. For this, some design parameters are usually adjusted to propose a robust design of the rotor, considering the possible variation of the random parameters. Performing such studies require to be able to deal with a high number of uncertain parameters and with parameters of different nature, namely parametric and random.This work proposes to illustrate the efficiency of advanced kriging-based surrogate modelling in order to achieve such a goal. The proposed hybrid surrogate-model combines polynomial chaos expansion and kriging to deal with both parameter natures, to consider nine varying parameters of a full finite element model of the rotating system under study. For the first time, this hybrid surrogate model is applied to perform rotordynamics analysis and more specifically the prediction of critical speeds and the associated unbalance responses for a complex rotor system with uncertainties. Compared to previous works, the kriging performances are significantly increased by integrating some physical properties of the rotor directly in its construction. Finally, the hybrid surrogate model gives a direct access to the Sobol indices which makes it possible to carry out without additional computation costs an extensive sensitivity analysis.

Reliability assessment method for environmental vibrations of a tunnel embedded in layered foundation

This paper proposes a reliability assessment method for environmental vibrations of a tunnel embedded in layered foundation under moving train load. Based on wave functions transformation, a vehicle-track-tunnel-soil model for evaluating system dynamic response can be established. Then combined with the Monte Carlo simulation, the reliability assessment of environmental vibrations is realized. The effect of soil parameter uncertainty on the prediction result of environmental vibrations is analyzed via case studies. The results show that the predictions from the deterministic model tend to be conservative, which is less than the superior limit of 95% confidence interval of the uncertainty model predicted outcome. The soil parameter uncertainty has less influence on the distribution of system dynamic response, which mainly affects the system dynamic response amplitude.

On the non-uniqueness of friction forces and the systematic computation of dynamic response boundaries for turbine bladed disks with contacts

Turbine bladed disks with friction contacts may have a large scattering of dynamic response amplitudes in laboratory conditions even for two consecutive tests. The non-repeatability of experimental studies might directly be related to a physical phenomenon associated with an uncertainty in contact forces. This observation has also been computationally shown in many studies with non-unique contact forces and multiple responses obtained for the same set of inputs. This study presents a numerical aspect and a deeper insight for understanding the variability observed in the periodic vibration analysis of turbine bladed disks with friction damping. A novel method based on an optimization algorithm is proposed to systematically detect the nonlinear dynamic response boundaries. The main idea of the developed approach is to minimize the system loss factor which ultimately determines the damping ability of the structure. In the meanwhile, algebraic set of dynamic balance equations are simultaneously imposed as the nonlinear constraints to be satisfied. In this way, two cases with the minimum values of the positive and negative loss factor determine the upper and the lower boundaries, respectively. The method is validated and demonstrated on a realistic turbine bladed disk with friction interfaces on the shrouds and on the blade-disk interface. Several case studies are performed on different cases by using the state of the art 2D friction model with varying normal load. The results show that the limits of the variability range can be successfully captured by utilizing the offered optimization algorithm. The great contribution of the study is also discussed with some accompanying numerical drawbacks.

An optimal parameter identification approach in foil bearing supported high-speed turbocharger rotor system

High-speed turbocharger rotors are often supported on double film floating ring bearings. In recent times, foil bearings are increasingly used as an alternative to floating ring bearings for supporting such lightweight rotors. Present work aims at the dynamic modeling and stability studies of the automotive turbocharger rotor system supported on the airfoil bearings under varying operating conditions. The effects of different parameters including rotor spin speed, bearing clearance, bump foil thickness, and foil pitch on the dynamic response of the rotor system are illustrated. The nonlinear relationship between the bearing parameters and vibration response data is modeled using supervised neural network scheme. With the use of counter propagation neural network model, inverse identification methodology of the bearing parameters is performed. Further, an optimal design of foil bearing parameters using a surrogate model is proposed with a modified particle swarm optimization scheme. The resultant design parameters are employed, and the percentage reductions in vibration amplitudes of dynamic response are reported.

Dynamic responses analysis of P and S-FGM sandwich cylindrical shell panels using a new layerwise method

This research work presents a comparison of the dynamic response of the functionally graded sandwich cylindrical shell panels (FGSCS) using a new layerwise method. The layerwise method developed assumes a first-order shear deformation theory (FSDT) for top and bottom facesheets and a third-order shear deformation theory for the core. The strain-displacement relation for FGSCS panels is obtained using Sander's first approximation. Two different sandwich configurations are considered, one having a pure metallic core with top and bottom facesheets made of functionally graded material (FGM) and the other one having an FGM core with top and bottom facesheets made of pure ceramic and pure metal, respectively. Material properties of the FGM layers for the two configurations are varied along the thickness direction according to the power-law (P-FGM) and the sigmoid models (S-FGM) respectively. The newly developed layerwise finite element model in conjunction with Hamilton's principle is employed to obtain the governing differential equation. Subsequently, the Newmark-Beta time integration scheme is used to obtain the dynamic response of P and S functionally graded sandwich cylindrical shell (P and S-FGSCS) panels for two configurations. The results obtained are first compared with the exact analytical results available in the literature. Numerical results are presented to investigate the effect of volume fraction index, loading conditions, core-to-facesheet thickness ratio, curvature ratio and boundary conditions on the transient response of P and S-FGSCS panels. The analysis reveals by selecting optimum parameters and gradation model, the amplitude and frequency of dynamic response of P and S-FGSCS panels can be controlled substantially.

Determination of periodic response limits among multiple solutions for mechanical systems with wedge dampers

Wedge dampers are commonly used to utilize the frictional behavior in many engineering fields such as vehicle dynamics and turbo-machinery. However, the presence of non-unique contact forces in the damper interfaces creates an uncertainty that provides different dynamic response amplitudes even for the same input parameters. The maximum limits of the variability range always take the core attention in most of the damper design processes. In this paper, determination of an upper and a lower boundary among multiple steady-state solutions is presented by using a numerical approach. The method is specifically suitable for the mechanical systems with wedge dampers modeled by macro-slip frictional contact elements in the joint interfaces. In the approach proposed, a criterion that determines the periodic response boundaries according to the limit tangential force values is utilized. The method is demonstrated by illustrating several case studies on a lumped parameter system which represents a turbo-machinery application with a symmetric wedge damper pressed against two vibrating adjacent blades. A point-to-point 1D friction model with varying normal force is used in both contact sides. A parametric investigation on the variability range and response limits is performed for different damper configurations. Harmonic Balance Method with Newton's iteration scheme is used in the numerical solution of the governing equations. The results show that a large variability exists for damper geometries where a strong coupling is present between tangential and normal contact forces. The method proposed successfully captures the limits of the variability range in all cases.

A semi-analytical model of aerodynamic damping for horizontal axis wind turbines and its applications

A semi-analytical model of the aerodynamic damping for horizontal axis wind turbines was established. Considering the translational and rotational degrees of freedom of tower-top, aerodynamic damping forces on the rotor were calculated by the blade element momentum theory and simplified to a resultant force at the tower-top and a resultant couple. Thereafter, the semi-analytical solution of modal aerodynamic damping ratios was suggested. Subsequently, the modal aerodynamic damping ratios of the NREL 5 MW and WP 1.5 MW wind turbines were calculated by the semi-analytical solution and identified from their dynamic response to validate this solution. And, the sensitivity analysis was performed to evaluate the influence of control parameters on the modal aerodynamic damping ratios of wind turbines. Finally, the uncouple analysis method with this aerodynamic damping model was used to predict the dynamic response amplitude of wind turbines, wherein the aero-servo-elastic fully coupled analysis were set as the reference method to examine the reliability of this uncoupled method. The results indicated that the uncoupled analysis method employing this aerodynamic damping model can accurately predict the dynamic response of horizontal axis wind turbines excited by a combined wind-earthquake loading, which is significantly better than the existing uncoupled model.

DYNAMICS MODELING, SIMULATION, AND CONTROL OF ROBOTS WITH FLEXIBLE JOINTS AND FLEXIBLE LINKS

The effects of flexible joints on the dynamic response and control of robot are studied in this paper. Firstly, the spatial robot model consisting of $n$ flexible joints and $n$ flexible links is built, and the dynamic equations of the robot system are derived via the Lagrangian's equations. The tensile deformation, bending deformation, torsional deformation, and nonlinear coupling deformation of the flexible link are considered. Furthermore, the effects of the flexible joint are also considered in order to provide an important theoretical basis for the research of the vibration suppression and control of robots. The flexible joint is simplified as a linear torsion spring with damping, and the mass effect of the flexible joint is also considered in the model. Secondly, the dynamic simulations of the spatial manipulators are done to explore the effects of the joint stiffness and damping on the dynamic response of the robot system. The results show that as the stiffness coefficient increases, the amplitude of dynamic response of the flexible robot decreases, and the vibration frequency of the system becomes larger. As the damping coefficient increases, the dynamic response of the flexible robot decreases, and the dynamic response decays faster. The vibration of the flexible robot can be suppressed by adjusting the values of the stiffness and damping of the flexible joint. Finally, in order to study the effects of the flexibility of the joint on the control system, the rigid-joint manipulator and flexible-joint manipulator are made to move under the same circular motion. Then the joint torques of the two system are obtained respectively by solving the inverse dynamics equations, and the influence of the flexibility of the joint on the dynamics control is studied. The results show that the actuating torques required in the flexible-joint system are reduced compared to that required in the rigid-joint system.

Dynamic Response Computation of Single-Point Mooring of Product Tanker Based on AQWA

This paper took the product tanker at sea and its mooring positioning system as the research object and used the time-frequency domain method to calculate the movement of the product tanker. In the three-dimensional potential flow theory, a single-point mooring system was established as a numerical model in the ANSYS Workbench. The frequency-domain computing module was to analyze the hydrodynamic response of the tanker under the unit regular waves, the dynamic response amplitude operators (RAOs) of the tanker, and the motion conditions under different frequency distributions. The time-domain computing module was to analyze the response of a single-point mooring system under the actions of wind, wave, and current. Setting the mooring point, pretension, layout, mooring radius, and other parameters, of the mooring product tanker was calculated lasted 1 hour for the time-domain coupling analysis under the extreme offshore environment. The tension of each cable was compared with the minimum breaking strength of the mooring cable to determine its safety.