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.

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.

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.

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.

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 Suboptimum Maximum Likelihood Estimation of Structural Parameters from Multiple-Excitation Vibration Data

1992 ◽  
Vol 114 (2) ◽  
pp. 260-271 ◽  
Author(s):  
J. E. Lee ◽  
S. D. Fassois
Keyword(s):  
Maximum Likelihood ◽  
Structural Parameters ◽  
Laboratory Data ◽  
Estimation Algorithm ◽  
Parameter Extraction ◽  
Frequency Domain Method ◽  
Flexible Beam ◽  
Modal Parameter ◽  
Type Representation ◽  
Vibration Data

In this paper an effective stochastic and multiple-excitation single-response approach to structural dynamics identification is introduced. The proposed approach accounts for many previously unaccounted for aspects of the problem, as it is based on: A proper, special-form, scalar ARMAX-type representation of the structural and noise dynamics; a new Suboptimum Maximum Likelihood (SML) discrete estimation algorithm (Fassois and Lee, 1990); systematic and efficient modeling strategy and model validation procedures; as well as accurate modal parameter extraction that is compatible with the employed model structure and excitation signal forms. In addition to its comprehensiveness, the proposed approach overcomes the well-known limitations of deterministic time-domain methods in dealing with noise-corrupted data records, while also circumventing some of the major difficulties of existing stochastic schemes by featuring guaranteed algorithmic stability, elimination of wrong convergence problems, very modest computational complexity, and minimal operator intervention. The effectiveness of the approach is verified through numerical simulations with noise-corrupted vibration data, and structural systems characterized by well-separated and closely-spaced vibrational modes. Comparisons with the classical Frequency Domain Method (FDM) are also made, and the approach’s advantages over deterministic methods are demonstrated through comparisons with the Eigensystem Realization Algorithm (ERA). Experimental results, where the proposed approach is used for the modal analysis of a flexible beam from laboratory data, are also presented.

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.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Trombone Transfer Functions: Comparison Between Frequency-Swept Sine Wave and Human Performer Input

2012 ◽  
Vol 37 (4) ◽  
pp. 447-454
Author(s):  
James W. Beauchamp
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Cutoff Frequency ◽  
Sine Wave ◽  
Nonlinear Propagation ◽  
Linear Filter ◽  
Wave System ◽  
General Effect ◽  
Filter Characteristic ◽  
High Pass

Abstract Source/filter models have frequently been used to model sound production of the vocal apparatus and musical instruments. Beginning in 1968, in an effort to measure the transfer function (i.e., transmission response or filter characteristic) of a trombone while being played by expert musicians, sound pressure signals from the mouthpiece and the trombone bell output were recorded in an anechoic room and then subjected to harmonic spectrum analysis. Output/input ratios of the signals’ harmonic amplitudes plotted vs. harmonic frequency then became points on the trombone’s transfer function. The first such recordings were made on analog 1/4 inch stereo magnetic tape. In 2000 digital recordings of trombone mouthpiece and anechoic output signals were made that provide a more accurate measurement of the trombone filter characteristic. Results show that the filter is a high-pass type with a cutoff frequency around 1000 Hz. Whereas the characteristic below cutoff is quite stable, above cutoff it is extremely variable, depending on level. In addition, measurements made using a swept-sine-wave system in 1972 verified the high-pass behavior, but they also showed a series of resonances whose minima correspond to the harmonic frequencies which occur under performance conditions. For frequencies below cutoff the two types of measurements corresponded well, but above cutoff there was a considerable difference. The general effect is that output harmonics above cutoff are greater than would be expected from linear filter theory, and this effect becomes stronger as input pressure increases. In the 1990s and early 2000s this nonlinear effect was verified by theory and measurements which showed that nonlinear propagation takes place in the trombone, causing a wave steepening effect at high amplitudes, thus increasing the relative strengths of the upper harmonics.

Structural-parametric model of an electroelastic actuator for nanomechanics

2020 ◽  
pp. 3-11
Author(s):  
S.M. Afonin
Keyword(s):  
Transfer Function ◽  
Piezoelectric Actuator ◽  
Transfer Functions ◽  
Piezoelectric Effect ◽  
Parametric Model ◽  
Elastic Compliance ◽  
Parametric Models ◽  
Piezo Actuator ◽  
Structural Scheme ◽  
Model Transfer

Structural-parametric models, structural schemes are constructed and the transfer functions of electro-elastic actuators for nanomechanics are determined. The transfer functions of the piezoelectric actuator with the generalized piezoelectric effect are obtained. The changes in the elastic compliance and rigidity of the piezoactuator are determined taking into account the type of control. Keywords electro-elastic actuator, piezo actuator, structural-parametric model, transfer function, parametric structural scheme

Sign in / Sign up

Export Citation Format

Share Document