In-plane vibration response of time and frequency domain with rigid-elastic coupled tire model with continuous sidewall

2017 ◽  
Vol 232 (4) ◽  
pp. 429-445 ◽  
Author(s):  
Zhihao Liu ◽  
Qinhe Gao
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Frequency Band ◽  
Structural Parameters ◽  
Bending Stiffness ◽  
Flexible Beam ◽  
Tire Model ◽  
Continuous Beam ◽  
Radial Tire ◽  
Plane Vibration

The in-plane vibration characteristic of time and frequency domain for heavy-loaded radial tire with a larger flat ratio (close to 1) is researched by utilizing the rigid-elastic coupled tire model with continuous sidewall. The sidewall bending stiffness is considered and the flexible beam on the elastic continuous beam tire model is proposed and investigated analytically to simulate the in-plane vibration of the heavy-loaded radial tire within more wider frequency band. The rigid-elastic coupled tire model is derived with finite difference method and the analytical stiffness matrix; mass matrix is formed based on the geometrical and structural parameters of heavy-loaded radial tire. Structural parameters are identified utilizing genetic algorithm based on the error between the analytical and experimental modal frequency. In-plane frequency domain transfer function and time domain dynamics response of heavy-loaded radial tire is investigated and compared with the experimental result. Experimental and theoretical results show that in-plane rigid-elastic coupled tire model with sidewall bending stiffness can be used to precisely predict the transfer function and vibration feature within the frequency band of 300 Hz, compared with the tire model with the distributed independent sidewall element. The flexible beam on the elastic continuous beam tire model and rigid-elastic coupled tire model with continuous sidewall can be extended to the dynamic analysis of the tire with larger flat ratio or the tire under the impulsive loading conditions.

Parametric analysis of in-plane rigid-elastic coupled non-contact tire model for heavily loaded radial tire

2018 ◽  
Vol 233 (1) ◽  
pp. 91-107
Author(s):  
Zhihao Liu ◽  
Qinhe Gao
Keyword(s):  
Transfer Function ◽  
Parametric Analysis ◽  
Transfer Functions ◽  
Structural Parameters ◽  
Mass Matrix ◽  
Flexible Beam ◽  
Vibration Characteristic ◽  
Tire Model ◽  
Modal Parameter ◽  
Radial Tire

Parametric analysis of in-plane vibration characteristic for unloaded heavily loaded radial tire is put forward and researched utilizing in-plane rigid-elastic coupled model. Coupled vibration characteristic between the flexible tread and circumferential sidewall is investigated with theoretical modeling and experimental modal method. In-plane analytical vibration feature is modeled with flexible beam on modified elastic foundation tire model. The rigid-elastic coupled tire model is derived with finite difference method and stiffness matrix and mass matrix are presented analytically with the geometrical and structural parameters. Structural parameters identification is implemented with genetic algorithm based on in-plane experimental modal parameter. The in-plane transfer functions with different structural parameters are compared and the parametric effect of structural parameters on in-plane transfer function is discussed. Experimental and theoretical result shows that the in-plane rigid-elastic coupled tire model can achieve the higher precision on predicting the transfer function and vibration feature of heavily loaded tire within the frequency band of 300 Hz.

Development and parameter identification of the flexible beam on elastic continuous tire model for a heavy-loaded radial tire

2018 ◽  
Vol 24 (22) ◽  
pp. 5233-5248 ◽  
Author(s):  
Zhihao Liu ◽  
Qinhe Gao
Keyword(s):  
Parameter Identification ◽  
Structural Parameters ◽  
Flexible Beam ◽  
Vibration Modes ◽  
Tire Model ◽  
Continuous Beam ◽  
Inflation Pressure ◽  
Bending Vibration ◽  
Radial Tire ◽  
Pressure Sensitive

Experimental modal analysis, dynamic modeling, and parameter identification were employed to investigate the flexible beam tire model for a heavy-loaded radial tire. The in-plane bending vibration of the flexible tread is researched with the flexible beam tire model. The coupled vibration equation of the flexible tread and continuous sidewall is modeled with a flexible beam on elastic continuous beam tire model. The nonlinear sidewall dynamics sensitive to the inflation pressure is obtained. The coupled modal features of a heavy-loaded radial tire are presented experimentally for different inflation pressures. Structural parameters are identified by a backward genetic algorithm based on the error between the experimental and analytical modal resonant frequency for different inflation pressures. Experimental and theoretical results show that the flexible beam on elastic continuous beam tire model developed for the heavy-loaded radial tire with a larger flat ratio can achieve higher precision in predicting the in-plane vibration modes of the heavy-loaded radial tire. It can be extended to analyze the vibration modes of the heavy-loaded radial tire with different inflation pressures by taking the inflation pressure-sensitive radial stiffness of the sidewall into consideration.

scholarly journals The Planar Wide-Frequency Vibration Characteristics of Heavy-Load Radial Tires

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Hongjie Cheng ◽  
Lei Gao ◽  
Zhihao Liu ◽  
Qinhe Gao ◽  
Xiuyu Liu
Keyword(s):  
Transfer Functions ◽  
Structural Parameters ◽  
Vibration Characteristics ◽  
Flexible Beam ◽  
Tire Model ◽  
Large Aspect Ratio ◽  
Heavy Load ◽  
Cross Sectional ◽  
Radial Tire ◽  
Damping Coefficients

This paper investigates the planar wide-frequency vibration characteristics of heavy-load radial tires with a large aspect ratio. A proposed tire model with a piecewise flexible beam on an elastic foundation is investigated and validated using experimental modal analysis and theoretical modeling method. The reproducibility of frequency response functions below 400 Hz is discussed. The experimental modal analysis particularly assesses the coupling of features across the circumferential and cross-sectional directions of heavy-load radial tire carcass. Piecewise circumferential modal characteristics were investigated experimentally, leading to the suggestion of a piecewise flexible beam on an elastic tire foundation. Using a genetic algorithm (GA), the structural parameters EI, ρ A , and kr and damping coefficients η and cr for the proposed tire model are identified, and the piecewise transfer functions and the planar transfer functions for a heavy-load radial tire are compared with planar hammer test. Experimental and theoretical results show the following: (1) the sectional vibration characteristics for a heavy-load radial tire with a large aspect ratio result from the cross-sectional vibration of the tire carcass; (2) the piecewise transfer function is mainly influenced by the circumferential vibration of the flexible carcass, and this is consistent with a model where a flexible beam is placed on an elastic tire foundation; (3) the analytical transfer functions calculated for the proposed tire model, drawing on the identified structural parameters and damping coefficients, agree well with the experimental results.

Integrated and frequency-band magnitude, two alternative measures of the size of an earthquake

1970 ◽  
Vol 60 (3) ◽  
pp. 917-937 ◽  
Author(s):  
B. F. Howell ◽  
G. M. Lundquist ◽  
S. K. Yiu
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Frequency Band ◽  
Transfer Functions ◽  
Body Wave ◽  
Average Amplitude ◽  
Equivalent Quantity ◽  
Short Period ◽  
Alternative Measures ◽  
Body Wave Magnitude

Abstract Integrated magnitude substitutes the r.m.s. average amplitude over a pre-selected interval for the peak amplitude in the conventional body-wave magnitude formula. Frequency-band magnitude uses an equivalent quantity in the frequency domain. Integrated magnitude exhibits less scatter than conventional body-wave magnitude for short-period seismograms. Frequency-band magnitude exhibits less scatter than body-wave magnitude or integrated magnitude for both long- and short-period seismograms. The scatter of frequency-band magnitude is probably due to real azimuthal effects, crustal-transfer-function variations, errors in compensation for seismograph response, microseismic moise and uncertainties in the compensation for attenuation with distance. To observe azimuthal variations clearly, the crustal-transfer functions and seismograph response need to be known more precisely than was the case in this experiment, because these two sources of scatter can be large enough to explain all of the observed variations.

scholarly journals Development of the Flexible Ring on an Elastic Continuous Foundation Tire Model for Planar Vibration of the Heavy Load Radial Tire

2018 ◽  
Vol 8 (11) ◽  
pp. 2064
Author(s):  
Zhihao Liu ◽  
Qinhe Gao ◽  
Hailong Niu
Keyword(s):  
Structural Parameters ◽  
Kinematic Characteristic ◽  
Vibration Characteristic ◽  
Tire Model ◽  
Inflation Pressure ◽  
Heavy Load ◽  
Coupling Vibration ◽  
Radial Tire ◽  
Planar Vibration ◽  
Flexible Ring

This paper investigates the planar vibration characteristic of heavy load radial tires with a large flat ratio. A proposed tire model with a flexible ring on an elastic continuous foundation is investigated utilizing kinematic modeling and experimental modal analysis. Planar coupling deformation of the radial and tangential direction is considered to enrich the kinematic characteristic of the flexible belt and the continuous sidewall; a flexible ring on an elastic continuous foundation tire model is proposed to investigate the coupling vibration characteristic between the flexible belt and the continuous sidewall. In-extensibility assumption is utilized to simplify the proposed tire model and the planar vibration modal features of the heavy load radial tire are discussed. The variation of the inflation pressure on the radial and tangential stiffness of the sidewall spring model is enriched into the flexible ring on an elastic continuous foundation tire model to extend the modal prediction of the tires with a different inflation pressure. Taking the relative error between the experimental and analytical modal resonance frequency of the tested tire with a different inflation pressure as the object value, structural parameters of the proposed tire model are identified by a backward genetic algorithm. Experimental and theoretical results show that: the planar coupling vibration characteristic of the heavy load radial tire can be predicted precisely with the flexible ring on an elastic continuous foundation tire model; meanwhile, considering the linear variations of the radial and tangential sidewall stiffness due to the inflation pressure, the proposed tire model can be extended to analyze the vibration characteristic of the heavy load radial tire with a different inflation pressure.

scholarly journals Vibration transfer function of in-plane rigid–elastic-coupled tire model for heavy-loaded radial tire

2017 ◽  
Vol 9 (10) ◽  
pp. 168781401772691
Author(s):  
Zhihao Liu ◽  
Qinhe Gao ◽  
Xu Wang ◽  
Zhun Liu
Keyword(s):  
Transfer Function ◽  
Tire Model ◽  
Radial Tire

In-Plane Flexible Beam on Elastic Foundation With Combined Sidewall Stiffness Tire Model for Heavy-Loaded Off-Road Tire

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Zhihao Liu ◽  
Qinhe Gao ◽  
Hailong Niu
Keyword(s):  
Elastic Foundation ◽  
Structural Parameters ◽  
Flexible Beam ◽  
Tire Model ◽  
Structural Stiffness ◽  
Inflation Pressure ◽  
Euler Beam ◽  
Large Section ◽  
Section Ratio ◽  
Beam On Elastic Foundation

Combining the flexible carcass beam and the radial sidewall element, flexible beam on elastic foundation with combined sidewall stiffness tire model is proposed for heavy-loaded off-road tire with a large section ratio. The circumferential vibration of flexible carcass is modeled as Euler beam and the influence of inflation pressure on the circumferential vibration of flexible carcass is investigated with the modal experiment and theoretical modeling. The structural stiffness caused by the sidewall curvature and pretension stiffness caused by the inflation pressure is combined for the radial sidewall element. The influence of the sidewall structural parameters on the combined stiffness of sidewall and modal resonant frequency is researched and discussed. The nonlinear combined stiffness of sidewall is investigated with respect to the radial sidewall deformation. Experimental and theoretical results show that: (1) the combined stiffness of sidewall can character the pretension stiffness caused by inflation pressure and the structural stiffness led by the sidewall curvature and material properties and (2) the combined stiffness of sidewall is nonlinear with respect to the radial sidewall deformation, which is prominent with high inflation pressure. Taking the flexibility characteristic of tire carcass and the nonlinear stiffness of sidewall into consideration, flexible beam on elastic foundation with combined sidewall stiffness tire model is suitable for the heavy-loaded off-road tire with a large section ratio or tires under impulsive loading and large deformation.

Error analyses of a Multi-Input-Multi-Output cantilever beam test

2021 ◽  
pp. 107754632110337
Author(s):  
Arup Maji ◽  
Fernando Moreu ◽  
James Woodall ◽  
Maimuna Hossain
Keyword(s):  
Transfer Function ◽  
Frequency Domain ◽  
Cantilever Beam ◽  
Transfer Functions ◽  
Linear Superposition ◽  
Transfer Function Matrix ◽  
Error Analyses ◽  
Pseudo Inverse ◽  
Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

Sign in / Sign up

Export Citation Format

Share Document