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Journal Articles
Journal:
Journal of Tribology
Article Type: Research-Article
J. Tribol. May 2019, 141(5): 051701.
Paper No: TRIB-18-1357
Published Online: March 4, 2019
Abstract
The performances of aerostatic bearings have an important impact on machining accuracy in the ultraprecision machine tools. In this paper, numerical simulation is performed to calculate the static and dynamic performances of a double-pad annular inherently compensated aerostatic thrust bearing, while considering the effects of the upper bearing and lower bearing. The static results calculated by the computational fluid dynamics (CFD) method are compared with the finite difference method (FDM) for the specific model. By using polynomial fitting, the load-carrying capacity (LCC) of the bearing is calculated and the relationship between eccentricity ratio, design parameters, and static stiffness is analyzed. The active dynamic mesh method (ADMM) is applied to obtain the dynamic performance of the double-pad aerostatic thrust bearing based on the perturbation theory. Meanwhile, the effects of supply pressure, orifice diameter, squeeze number, and eccentricity ratio are comprehensively considered. Moreover, the step response of the double-pad thrust bearing is analyzed by using the passive dynamic mesh method (PDMM) based on dynamic equation. Related dynamic parameters including natural frequency are obtained through a system identification toolbox with M atlab , which can be used to avoid resonance. It is found that the dynamic calculation results computed by the ADMM and the PDMM are very close. The proposed method can be used to provide guidance for the design and optimization of the double-pad aerostatic thrust bearings.
Topics:
Thrust bearings
Proceedings Papers
Proc. ASME. IDETC-CIE2018, Volume 6: 14th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, V006T09A058, August 26–29, 2018
Paper No: DETC2018-85700
Abstract
Natural vibration characteristics are important factors affecting the processing quality for an ultra-precision machine tool. The rapid and accurate calculation method for solving natural vibration characteristics has a significance in machine tool dynamics design. By applying the transfer matrix method for multibody systems (MSTMM), the dynamics model of a single-point diamond fly cutting machine tool is established and the rapid computation of natural vibration characteristics at different rotational speed is completed. The results calculated by MSTMM is compared with those by finite element software ABAQUS, the error between the first ten frequencies calculated by MSTMM and ABAQUS is less than 5.68%. However, as the rotational speed increases, the first eight frequencies and mode shapes have no obvious change, while the 9th and 10th modal change significantly. The mode shapes of 9th and 10th orders are vacillation of the spindle. The results show that the rotation of aerostatic spindle has significant effect on the spindle system and little effect on the other parts.
Proceedings Papers
Proc. ASME. OMAE2018, Volume 8: Polar and Arctic Sciences and Technology; Petroleum Technology, V008T11A027, June 17–22, 2018
Paper No: OMAE2018-78342
Abstract
Water logging problem in late production reservoir with abundant edge-bottom water and water-gas layer stagger is one of the main factors that lead to production wells stop flow. For the water plugging problem during gas well production, the common operation is coiled tubing through casing. So, coiled tubing technology without moving production string is explored. X oilfield is located in Sichuan basin of China southwest and belongs to the origin of gas pipeline from Sichuan to China east. Its main gas producing area is carbonatite full of edge water and controlled by structural and lithology. The relationship between water and gas is complex and water-gas system is independent of different blocks and different layers. Because the main gas producing layer is close to the water layer, lots of gas producing wells stop spray for high water cut. At the meantime, the difficulty and risk of water plugging increases for its high depth of main gas producing layer and high temperature at the well bottom. To solve the problem above, cement slurry system with the characteristics of high temperature and sulfur resistant and channeling preventing is developed. At the same time, the cement slurry system has low friction and high liquidity and is easy to flow through the coiled tubing. Besides, cement slurry pollution is reduced and the success rate of gas well produced water plugging is improved by the combination of coiled tubing and cementing process and the construction technology optimization, software simulation and laboratory evaluation is carried out. The key step is that log analysis of water and gas distribution is done first. Then, tubing-expansion bridge plug is placed under the water layer and the cement slurry is sent to the desired location. At last, coiled tubing is put down after cement solidification and gas production is recovered. The measurement of coiled tubing and cement slurry system is positive for water plugging in gas wells with high depth and temperature. The oilfield test results show that daily gas production is improved largely and liquid production is reduced by 90% of 4 wells with high water cut through water plugging. Besides, operation cost is reduced and the pollution problem caused by produced water is also solved, which can provide certain significance for the same type wells need water plugging operation.
Proceedings Papers
Proc. ASME. GT2017, Volume 2A: Turbomachinery, V02AT40A019, June 26–30, 2017
Paper No: GT2017-63898
Abstract
The nonaxisymmetric endwall profiling has been proven to be an effective tool to reduce the secondary flow loss in turbomachinery. In the present work, an endwall optimization design procedure for reducing secondary flow losses has been developed which allowed complete 3-dimensional parameterization design of the turbine endwall. A so-called shape function and a decay function were used for the definition of the nonaxisymmetric endwall. The shape function was used to control the curvature in the circumferential direction and the decay function was used to control the curvature in the axial direction. The design of the endwall was generated by the product of these two functions. The sinusoidal function was used for the shape function and the B-spline was used for the decay function. This parametrization allowed influencing the contouring of the specific endwall region. The profile of the endwall has been optimized using automatic numerical optimization by means of an improved efficient global optimization algorithm based on kriging surrogate model. The niching micro genetic algorithm was used to get the correlation vector of Kriging model, which eliminated the dependence of correlation vector starting search points. This method reduced the difficulty of finding appropriate penalty parameters and increased the robustness of the optimization method. The 3D-Reynolds-averaged Navier-Stokes flow solver based on CFX, with a k-ω model for turbulence model, was used for all numerical calculations. An in-house optimization design system was developed to close the loop of the geometry definition, flow solving and the optimization algorithm which allowed the solution of non-linear problems. A large-scale linear cascade with a low-speed wind tunnel has been chosen for the experimental validation of the optimization results. The experimental measurements and numerical simulations both demonstrated that the total pressure loss and secondary flow intensity were reduced with the nonaxisymmetric endwall used in the cascade passage. The detailed flow pattern comparisons between the passage with based flat endwall and the optimization nonaxisymmetric endwall were given by the numerical simulations method and entropy generation rates analysis were used for the investigation of the secondary flow loss reduction mechanism in the nonaxisymmetric endwall profile cascade.
Proceedings Papers
Proc. ASME. GT2016, Volume 8: Microturbines, Turbochargers and Small Turbomachines; Steam Turbines, V008T26A024, June 13–17, 2016
Paper No: GT2016-57102
Abstract
700°C HUSC technology is considered as the next generation of more efficiently coal-fired power generation technology, the heat rate of which can be reduced by more than 8% on the basis of current ultra-supercritical units. That means there is a huge energy saving benefits. With the main steam / reheat steam temperature increasing from 600°C / 620 °C to 700°C/ 720°C, the temperature of extraction steam increases dramatically, especially the first extraction stage after reheater, the temperature of which will increase to 630 ∼ 650 °C. That means a substantial increase in the cost of the initial investment because of the nickel-based material being used in extraction pipe and heaters. With EC system, the extraction steam temperature is reduced sharply because the high temperature extraction steam is moved from the main turbine to a small parallel extraction turbine and the steam source of the small extraction turbine is from the cold reheater. So the highest extraction steam temperature will not exceed 500 °C, and the high temperature risk of heat recovery system will be eliminated completely. In this paper, exergy theory is introduced to analyze the cycle efficiency of the new thermodynamic system and the conventional one. In order to obtain a better 700 °C high ultra-supercritical thermodynamic system solution, GA method is used to optimize the regenerative system parameters to lower the overall heat consumption. The exergy theory is also used to analyze the reason why optimal solution can bring economic benefits. Finally, the feasibility of the entire system project will be analyzed.
Proceedings Papers
Proc. ASME. GT2015, Volume 8: Microturbines, Turbochargers and Small Turbomachines; Steam Turbines, V008T26A036, June 15–19, 2015
Paper No: GT2015-43955
Abstract
Cyclic loads applied to a structure can develop local cyclic plasticity deformation, lead to fatigue damage and fracture at the high-stress regions, which can be assessed through a local strain approach. Each cycle of start-operation-stop steam turbine, making the low cycle fatigue (LCF) load of long blade, results in damage to the long blade, and the fatigue fracture occurs when the damage accumulated to its critical value. To evaluate the fatigue life, the experimental data illustrating the cyclic behavior of a material under simple loading condition must be gathered, and also a suitable local stress-strain range calculation approach needs to be chosen to represent the accurate material behavior under loadings. With the consideration of the difference between the specimen and actual blade, the influential factors, such as mean stress, geometry effect, blade surface quality, and water erosion, on the fatigue life should be investigated when using the cyclic fatigue data of specimen to predict fatigue life of actual blade. In this study, a new local stress-strain range approach is introduced based on elastoplastic finite element analysis and Neuber rule. And also a modified strain-life fatigue model is used by considering leading causes of fatigue and also the cumulative damage rule is set up to predict the LCF life of the steam turbine long blade. It is found that the assessment method proposed in this study is capable of predicting the LCF life of steam turbine long blade.
Proceedings Papers
Proc. ASME. GT2014, Volume 1B: Marine; Microturbines, Turbochargers and Small Turbomachines; Steam Turbines, V01BT27A017, June 16–20, 2014
Paper No: GT2014-25584
Abstract
To investigate the performances of the last stage of a huge power and half-rotation speed nuclear steam turbine, a 3-stage wet steam turbine performance test rig is designed. Experiments are carried out to test the performances of the modeled turbine at design and off-design operating points. Frozen-rotor steady-state computations are performed on design point as well as off-design operating points. The calculated massflow rate, power and efficiency are validated with the experimental data and the flow details are discussed. Steam humidity, temperature and pressure are compared with the tested results. With the detailed 3D flow results derived with numerical simulations, it is found that for the investigated steam turbine, the performances of the first two stages only changes slightly when turbine operation point changes, meanwhile, the aerodynamic quantity distribution characteristics also keep nearly almost the same. However, for the last stage, both efficiency and flow details changes significantly when operating point changes. It is also found that for the last stage, flow region with maximum steam humidity is located at downstream of stator near hub and downstream of blade near tip, where water droplets mostly likely to be formed and accumulated.
Proceedings Papers
Proc. ASME. GT2013, Volume 5B: Oil and Gas Applications; Steam Turbines, V05BT25A012, June 3–7, 2013
Paper No: GT2013-94652
Abstract
Sliding grid and dual-time step method-based unsteady flow simulation on the final two stages of a steam turbine is performed without geometry scaling. The behavior and characteristic of unsteady pressure fluctuations on the blade surfaces of stator and rotor blades are investigated in details. FFT is performed on the blade surface pressure fluctuation to estimate the region covered by the unsteady flow perturbation from upstream and downstream. Results show that for long blade turbine stage investigated, pressure loading fluctuation is significant, with the maximum amplitude being equivalent up to level of 61% pressure loading. The loading fluctuation follows the trend of increasing from hub to shroud in stator while contrary trend is followed by the rotor. Among the unsteady perturbation sources causing the significant pressure fluctuations in long blade turbine stage, trailing edge shock is the dominating one, leading significant pressure distortion along circumferential direction, which induces strong interaction on downstream blade row.
Journal Articles
Article Type: Technical Briefs
J. Dyn. Sys., Meas., Control. January 2014, 136(1): 014506.
Paper No: DS-13-1033
Published Online: October 15, 2013
Abstract
This paper studies the problem of designing insensitive H∞ output-feedback controllers for linear discrete-time systems. The designed controllers are insensitive to additive/multiplicative controller coefficient variations. An LMI-based procedure, which is a sequential linear programming matrix method (SLPMM), is proposed to solve the considered problem which is a nonconvex problem itself. It is worth mentioning that the nonfragile control design method is adopted to obtain an effective solution for accelerating convergence of SLPMM algorithm due to the fact that a good starting point for the iteration is very important.
Journal Articles
Article Type: Research-Article
J. Dyn. Sys., Meas., Control. May 2013, 135(3): 031005.
Paper No: DS-12-1254
Published Online: February 21, 2013
Abstract
This paper concerns the mode dependent H∞ filter design for continuous Markov jump linear systems. The filter gain to be designed is assumed to have additive variations and the transition probabilities are allowed to be known, uncertain with known bounds and unknown. Attention is focused on the design of a mode dependent nonfragile full order filter, which guarantees the filtering error system to be stochastically stable and has a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the desired filter design are given in the framework of linear matrix inequality. If the filter gain variations become zero and the transition probabilities are completely known, the proposed method is reduced to the standard H∞ filtering results. A numerical examples is given to show the effectiveness of the proposed method.
Journal Articles
Journal:
Journal of Turbomachinery
Article Type: Research-Article
J. Turbomach. January 2013, 135(1): 011040.
Paper No: TURBO-11-1177
Published Online: October 31, 2012
Abstract
Gas turbine engines operating in a hostile environment, polluted with sand or dust particles, are susceptible to erosion damage, mostly at the front axial fans and compressors. Accurately predicting the erosion pattern and rate due to sand ingestion is one of the major challenges faced by the transportation and power industries. Maintenance costs are scrutinized and intensive research efforts are currently deployed in predictive life assessment tools to minimize the overhaul down time. The conventional prediction methods were usually based on steady-state simulations of gas-phase flows through a single blade passage per blade row to reduce the computational cost. However, the multistage turbomachinery flows are intrinsically subject to unsteadiness, especially due to stator-rotor interactions, which may affect sand particle trajectories even if a one-way coupling method is considered. Furthermore, an unsteady stator-rotor interaction requires a whole-annulus model at great computational cost to avoid simplifications of the geometries or flow physics. To study the effects of the stator-rotor interaction on sand particle trajectories and erosion, an axial fan with inlet guide vanes is investigated, based on the whole annulus computations of both steady and unsteady gas-phase flows, each of which is then followed by a Lagrangian particle tracking step. A numerical algorithm for tracking particles driven by the unsteady gas-phase flow is presented. The comparison of the numerical predictions with the experimental data confirms the validity and necessity of the unsteady computational fluid dynamics (CFD) model in providing adequate predictions of sand erosion in the axial fan.
Proceedings Papers
Proc. ASME. GT2011, Volume 7: Turbomachinery, Parts A, B, and C, 1289-1299, June 6–10, 2011
Paper No: GT2011-45992
Abstract
Gas turbine engines operating in a hostile environment, polluted with sand or dust particles, are susceptible to the erosion damage, mostly at front axial fans and compressors. To accurately predict the erosion pattern and rate due to sand ingestion is one of the big challenges faced by the transportation and power industries. Maintenance costs are scrutinized and intensive research efforts are currently deployed in predictive life assessment tools to minimize the overhaul down time. The conventional prediction methods were usually based on steady-state simulations of gas-phase flows through a single blade passage per blade row to reduce computational cost. However, the multi-stage turbomachinery flows are intrinsically subject to unsteadiness, especially due to statorrotor interactions which may affect sand particle trajectories even if a one-way coupling method is considered. Furthermore, an unsteady stator-rotor interaction asks for a whole-annulus model at great computational cost to avoid simplifications of geometries or flow physics. To study the effects of the stator-rotor interaction on sand particle trajectories and erosion, an axial fan with inlet guide vanes is investigated based on the whole annulus computations of both steady and unsteady gasphase flows, each of which is then followed by a Lagrangian particle tracking step. A numerical algorithm for tracking particles driven by unsteady gas-phase flow is presented. The comparison of the numerical predictions with the experimental data confirms the validity and necessity of the unsteady CFD model in providing adequate predictions of sand erosion in the axial fan.
Proceedings Papers
Rui Yang, Jiandao Yang, Zeying Peng, Liqun Shi, Aping He, Hong Yang, Daiwei Zhou, Jun Li, Zhigang Li, Xin Yan
Proc. ASME. POWER2011, ASME 2011 Power Conference, Volume 1, 607-614, July 12–14, 2011
Paper No: POWER2011-55344
Abstract
The aerodynamic performance and internal flow characteristics of the last stage and exhaust hood for steam turbines is numerically investigated using the Reynolds-Averaged Navier-Stokes (RANS) solutions based on the commercial CFD software ANSYS CFX. The full last stage including 66 stator blades and 64 rotor blades coupling with the exhaust hood is selected as the computational domain. The aerodynamic performance of last stage and static pressure recovery coefficient of exhaust hood at five different working conditions is conducted. The interaction between the last stage and exhaust hood is considered in this work. The effects of the non-uniform aerodynamic parameters along the rotor blade span on the static pressure recovery coefficient of the non-symmetric geometry of the exhaust hood are studied. The numerical results show that the efficiency of the last stage has the similar values ranges from 89.8% to 92.6% at different working conditions. In addition, the similar static pressure recovery coefficient of the exhaust hood was observed at five working conditions. The excellent aerodynamic performance of the exhaust hood was illustrated in this work.
Proceedings Papers
Proc. ASME. GT2010, Volume 7: Turbomachinery, Parts A, B, and C, 2139-2148, June 14–18, 2010
Paper No: GT2010-22280
Abstract
Low pressure exhaust hood of steam turbine is used to connect the last stage turbine and the condenser. To further improve the recovery capability of low pressure turbine exhaust hood, an aerodynamic optimization system has been developed with Matlab platform. The system includes four modules: parametric geometry modeling, structured meshes generator, commercial aerodynamic simulator and Kriging surrogate based optimizer. The diffuser geometry profile in the exhaust hood is parameterized using cubic Bezier curve, and the control points of these curves are considered as design variables. The exhaust hood performance is optimized by changing those design variables to maximizing the average static pressure coefficient. The block-structured meshes are generated with ICEM-CFD Hexa. Aerodynamic performance evaluations of the hood are carried out by the three dimensional Reynolds-averaged Navier-Stokes computational fluid dynamics solver-CFX. Mesh generation and aerodynamic analysis are done automatically, which are driven by script commands in batch mode. Kriging model is used as surrogate, which establishes a global mapping between design variables and objective variable. In order to balance the exploration and exploitation with Kriging surrogate, Expected Improvement (EI) sample criteria is adopted to update Kriging surrogate. The proposed optimization framework drastically reduces the number of calling time-consuming CFD. Two aerodynamic optimization test cases are performed with the system. The aerodynamic performance of the original and optimal exhaust hood will be compared, while the flow filed in the both exhaust hood will be illustrated.
Proceedings Papers
Proc. ASME. GT2010, Volume 7: Turbomachinery, Parts A, B, and C, 933-942, June 14–18, 2010
Paper No: GT2010-23390
Abstract
Although unstructured grids have gained wide acceptance in many engineering applications, they still suffer from difficulties in achieving high accuracy at the inflow, outflow and mixing-plane interface boundaries of multi-stage turbomachinery configurations. To overcome these difficulties and hence to increase the accuracy of unstructured grid methods, a novel dual mesh approach is proposed. In contrast to conventional CFD techniques, the dual mesh approach works on two sets of meshes at the boundaries: one is the original mesh and the other is an auxiliary surface mesh created at run time. By properly coupling of such double meshes, the dual mesh approach can effectively increase the accuracy and conservation of the solutions at the inflow, outflow and mixing-plane interface boundaries, and it can also enjoy most of the sophisticated numerical algorithms originally developed for the structured-grid boundary conditions. With both compressor and turbine test cases, the dual mesh approach is demonstrated to be superior to the conventional method while its CPU-time penalty is marginal. Additionally the dual mesh approach may be also useful for any structured CFD solvers subject to some restrictions on the structured grid distributions at the inflow, outflow and mixing-plane interface boundaries, e.g. mesh uniformity in the circumferential direction.
Proceedings Papers
Proc. ASME. GT2010, Volume 4: Heat Transfer, Parts A and B, 1133-1142, June 14–18, 2010
Paper No: GT2010-22877
Abstract
Numerical investigations of leakage flow fields of two kinds of brush seals with four sealing clearances were conducted in this paper. The Reynolds-Averaged Navier-Stokes (RANS) and non-Darcian porous medium model solutions were applied as the numerical approach to analyze the flow characteristics of brush seal. The reliability and accuracy of the RANS and non-Darcian porous medium model for leakage flow in brush seals were established by comparison with the experimental data. The referenced labyrinth seal was changed into a multi-stage brush seal which has two configurations. One configuration had a traditional geometrical structure. The other had a shim structure installed between the front plate and brush bristle pack. The leakage flow rates of the brush seal with two different configurations were calculated for four bristle pack tip clearances (0 mm , 0.1 mm , 0.3 mm , 0.5 mm ) which were compared with the results for the referenced labyrinth seal. The numerical results show that the leakage flow rate increases rapidly with the increasing of clearance between the bristle pack tip and the rotor surface for two kinds of brush seals. The sealing performance of the brush seal with shim structure is similar to that of the traditional design with the same sealing clearance and flow conditions. In addition, as compared with the traditional brush seal, the brush seal with shim structure can reduce the pressure difference between the bristle free and fence height at 0.3 mm and 0.5 mm sealing clearance. The leakage flow patterns in brush seals with two different configurations were also illustrated.
Proceedings Papers
Proc. ASME. IDETC-CIE2007, Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 183-191, September 4–7, 2007
Paper No: DETC2007-34356
Abstract
In this paper, non-smooth bifurcations and chaotic dynamics are investigated for a braking system. A three-degree -of-freedom model is considered to capture the complicated nonlinear characteristics, in particular, non-smooth bifurcations in the braking system. The stick-slip transition is analyzed for the braking system. From the results of numerical simulation, it is observed that there also exist the grazing-sliding bifurcation and stick-slip chaos in the braking system.
Proceedings Papers
Proc. ASME. GT2007, Volume 6: Turbo Expo 2007, Parts A and B, 1805-1815, May 14–17, 2007
Paper No: GT2007-28111
Abstract
The unsteady wake-boundary layer interaction on a high lift low pressure ( LP ) turbine airfoil T106C was investigated by applying the hybrid structured-unstructured RANS solver developed at the DLR. The simulation domain was split into two parts: a translational one with moving bars and a stationary one with turbine airfoils, and in between was a sliding mesh interface. An unstructured grid was generated around the moving bars with particular clustering along the wake path to have a sharp resolution of the shedding vortex street, whereas the stationary blade airfoil subject to the incoming wakes was meshed with a block-structured grid to ease the implementation of the laminar-turbulent transition model around the airfoil. The Wilcox two-equation k-ω turbulence model was applied in conjunction with a multi-mode transition model developed by the authors taking into account several modes of transition, namely natural/bypass, separated-flow and wake-induced transition modes. In this paper, the hybrid-grid modeling is first validated against measurements from the VKI, and then the unsteady flow mechanisms associated with the shedding vortices and the multi-mode transition on the blade airfoil are analyzed. Furthermore, the quasi-steady mixing-plane model on the hybrid grids is also assessed by a comparison with the time-mean of the unsteady state solutions. In particular, different chopping to the incoming vortex street at the blade leading edge is found to have different effects on the separation and transition over the blade suction surface. At the end a composite picture of the boundary-layer development over the suction surface is summarized.
Proceedings Papers
Proc. ASME. FEDSM2002, Volume 1: Fora, Parts A and B, 1437-1442, July 14–18, 2002
Paper No: FEDSM2002-31058
Abstract
A theoretical model of harmonic perturbations in a compressible turbulent mixing layer is proposed. The model is based on the triple decomposition method. It is assumed that the instantaneous velocities, temperature, and pressure consist of three distinctive components: mean (time-averaged), coherent (phase-averaged), and random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large-scale coherent disturbances is incorporated by the Newtonian eddy viscosity model. The governing equations for the coherent disturbances have the same form as in laminar flow with substitution of the Reynolds number and the Prandtl number by their turbulent counterparts. A slight divergence of the flow is also taken into account. Theoretical results and comparison with experimental data reveal the significance of interaction between the coherent and random constituents of the flow.
Proceedings Papers
Proc. ASME. ESDA2004, Volume 2, 69-74, July 19–22, 2004
Paper No: ESDA2004-58253
Abstract
The calculation of the nonlinear time-response of structures such as RC (reinforced concrete) frames to base excitation such as earthquake waves is vital to ensure the safety of structures. Of course the response changes significantly with the applied base excitation. The usual approaches to compare the different earthquake waves are based on non-localized spectra, such as response spectra and power spectra, which do not contain any time information. However these non-localized spectra often do not explain the large difference between structural responses, and are not able to reflect all of the characteristics of the earthquake waves. Local spectra, which can be easily obtained by the wavelet transform, calculate the energy distribution of the waves in the time-frequency domain. Using the wavelet transform it is easy to see the differences in the energy distribution via the local spectra of each wave, and therefore to understand the very different structural responses. Hence the time-frequency distribution of the wave energy should be taken into account during the selection of earthquake waves to apply to structural models to determine the nonlinear time response.