Abstract

In this study, we propose a structural health monitoring and diagnostic method for layered (multi-story) structures using a convolutional neural network (CNN). The proposed method is a primary diagnostic one, and its purpose is to allow quick identification of the location of an abnormality after detecting it. An abnormality is defined as a decrease in the stiffness characteristics (spring constant) of the outer wall of a multi-story structure when it deteriorates or is damaged. The proposed method has the following features. A modal circle is generated by multiplying the frequency response functions (FRFs) simulated by a mathematical model and the FRFs from the actual structure, in frequency space, and then a CNN learns the features of the abnormality from the modal circle and diagnoses it in the actual multi-story structure. We first verified the validity of the proposed method by considering a three-story structure as a numerical example. When the method was applied to three types of abnormal conditions, it was shown that the abnormal diagnosis could be performed correctly. Next, we constructed an experimental model of a three-story structure, and realized three types of abnormal conditions similar to those in the numerical model. We verified the applicability of the proposed method and showed that correct diagnosis of an abnormality was possible. Both the validity and applicability of the proposed method were thus confirmed.

<div>This study develops an image measurement system that accurately measures rotating tires’ deformed shape. Noncontact image measurement presents challenges such as difficulty in achieving a high sampling frequency and high pixel count, and achieving high resolution in feature point tracking as a subset in image processing because of the curvature, expansion, and contraction of the tire sidewall. The shape of the sidewall affects the mechanical properties of the tire, and the deformation shape during actual operation provides important information for tire design. In this study, a system integrating phase-locked loop imaging, dot centroid tracking (DCT), and stereo methods is used to achieve high-resolution measurements of tire deformation shapes. In particular, the DCT method typically improves the accuracy of tracking by setting the markers in black and the background in white and ignoring imaging noise from the background with white halation depending on the amount of light. 3D measurements under static conditions were conducted to validate the proposed system. Consequently, the system was confirmed to be capable of capturing the differences in the sidewall deformation depending on the test conditions, and the validity of the system was confirmed.</div>

ABSTRACT

The influence of tires on vehicle dynamics, as the only automotive component in contact with the road surface, is significant. Mechanical models such as the Fiala model includes tire mechanical properties as parameters and are useful for tire design studies. These models assume a rectangular or trapezoidal tire contact shape, which does not always match the tire contact shape observed when slip angle is applied, leaving room for improvement in accuracy. This study proposes a new semiphysical tire model with an elliptical contact shape, termed the “elliptical contact model.” First, the expressions for the contact shape and contact pressure distributions in the elliptical contact model are formulated. Herein, we consider both the length- and width-direction distributions of the contact pressure in these expressions. Second, the formulation of the lateral shear stress distribution in the contact patch is presented based on the Fiala model, including the belt bending deformation by a lateral force and switching between the lateral shear and dynamic frictional forces. Lateral stresses proportional to the width coordinate are also introduced, enabling the calculation of lateral stresses acting in a direction counteracting each other at the widthwise edge of the tire contact surface. The model is validated by measuring a slick tire at a velocity of 100 km/h with slip angles of 0° and 3° using an Inside Drum Machine with an aluminum road segment with quartz piezoelectric sensors. Consequently, by setting appropriate model parameters, the contact pressure and lateral shear stress distribution results calculated using the model are consistent with experimental results. The accuracy of the proposed model could be further improved by revising the method of setting the static and dynamic friction coefficients.

As rubber materials are used for damping, clarifying the relationship between the loss factor and microstructure would help develop high-performance damping materials. Although nondestructive observations using X-ray computed tomography (CT) under repetitive deformation have been reported, no observations have been re-ported at the submicron order that capture low-strain deformation, such as vibration exposure. The internal deformation behavior of materials with different loss factors has not yet been evaluated. This study proposes a dynamic X-ray CT method for specimens under tensile amplitudes, directly evaluating the internal deformation behavior of materials under dynamic conditions. The proposed 4D-CT has an excitation of 1 Hz and a spatial resolution of 0.5 mu m. The local strain was obtained from X-ray CT at each phase, and the deformation behavior was evaluated. The results revealed that the peak of the local strain amplitude distribution curve decreased and the distribution widened as fine particles were mixed.

The vibration damping appears as a macroscopic material property due to the energy dissipation caused by the plastic deformation of the microstructure in the material, but the detailed mechanism is still unknown. This study prepared a damping material based on natural rubber (NR) and investigated its deformation behavior with/without fiber-shaped particles using synchrotron X-ray computed tomography (CT). High-resolution submicron X-ray CT was performed to evaluate the local strain in the microstructure from feature points scattered inside the NR. When the strain distribution changed under stepwise tensile loading, the NR-alone material deformed uniformly at the microscale, whereas the fiber composite rubber deformed nonuniformly. Furthermore, the number and volume of voids increased significantly with the compounding of fiber particles, and their values continued to increase depending on the strain amplitude and the loss factor. Controlling of non-uniform local strain and void formation will enable the design of damping characteristics.

In this study, we proposed a structural health monitoring and diagnostic method for layered structures using the transmissibility function. This method belongs to the primary diagnosis one, and its purpose is to identify the location of abnormality quickly after abnormality detection. It focuses on the following fact. When the ceiling or foundation of the first floor is excited in the horizontal direction, the transmissibility function of the top floor is constructed with only the characteristics of the top floor, and in the case of descending to the lower floor, only the characteristics of the floor of interest are unknown parameters. In the diagnosis of an actual structure, there may be a difference between the actual vibration characteristics and those obtained from the mathematical model. We also proposed a method for predicting the resonance and peak frequencies in an abnormal condition based on the difference between the actual measurement and the mathematical model under a normal condition. First, we considered a three-layered structure as a numerical example and verified the validity of the proposed method. When the method was applied to the three types of abnormal conditions, it was shown that the abnormal diagnosis could be performed correctly. Next, we constructed an experimental model of a three-layered structure, and verified the applicability of the proposed method. We realized three types of abnormal states similar to the numerical examples and showed that correct abnormal diagnosis was possible. As described above, the validity and applicability of the proposed method were clarified.

Few studies have investigated the vibration characteristics of motorcycle tires. Tires have high damping characteristics; therefore, resonance peaks do not appear clearly, and it is difficult to identify the existence of modes in a high-frequency region having many modes. A similar phenomenon occurs in automobile tires; therefore, the circumferential mode reduction method is used to reduce the number of degrees of freedom of the frequency response function. This method is specialized for periodic shell structures under the assumption that the circumferential mode shape can be represented by trigonometric functions. However, the applicability of this method to the experimental modal analysis of motorcycle tires with a double curvature remains unclear. Therefore, in this study, we verify whether this method can be applied to periodic shell structures with a double curvature. Next, we try to understand the modal characteristics of motorcycle tires. Finally, we compare the identified modal characteristics with those of automobile tires.

Experimental modal analysis is one of the key technologies in structural dynamics analysis. However, in cases involving extremely high or low modal damping, it is difficult to accurately identify all the modal parameters. In particular, for systems with extremely low damping, there may not be sufficient data to allow curve fitting in the vicinity of the resonant peaks. To overcome this difficulty, we propose a linear fit method of modal parameters on a new mapping plane. This method uses a basic equation linearized from the nonlinear equation of the frequency response function (FRF) by erasing the residue, which is a modal parameter. Then, the basic equation becomes linear on a mapping plane related to the ratios of the real and imaginary parts of the FRF. The linearized basic equation can identify the modal parameters of a vibration system with extremely low damping. It was observed that the influence of the measurement noise degrades the identification accuracy of the linear fit method. Consequently, it was confirmed that the identification accuracy deteriorates when data with low coherence and far from the natural frequency are used. Thus, a weighted least squares method using the coherence and Gaussian kernel function was proposed for the linear fit method. Finally, the modal parameters obtained using the proposed method and the conventional least-squares complex frequency (LSCF) method, from the FRF including noise, were compared, which indicated that the proposed method can produce estimation results with an accuracy comparable to that pertaining to the LSCF method.

© 2020, The Society for Experimental Mechanics, Inc. Nonlinear damping with respect to vibration amplitude is particularly important in mechanical dynamics. The addition of short fibers to damping materials is considered to result in strong nonlinear damping due to interfacial peeling at the edges of the fibers. However, little has been reported on the occurrence of nonlinear damping in short-fiber reinforced rubber due to compounding difficulties. In this study, we investigated the relationship between the damping characteristics and deformation behavior of microdeformed short-fiber reinforced rubber by X-ray computed tomography (CT). We prepared a damping material with a natural rubber (NR) matrix and micrometer-sized polyethylene terephthalate (PET) fiber filler. The loss factor was identified by dynamic mechanical analysis, and three-dimensional strain maps were obtained using marker tracking in the CT data. The addition of 5 wt% PET fibers to NR resulted in an increase in the loss factor. Experimentally, we found that the nonlinear damping of the composite rubber is affected by the peeling of the filler/matrix interface and the strain inside the material.

This study predicts the dynamic characteristics for tires in the development stages of a vehicle with a focus on the generated forces. In particular, this investigation proposes an approximation analysis for the deflection and contact characteristics of a pneumatic tire. This consists of an integrated model for a three-dimensional membrane ring and brush models. This model is more complex than conventional models, which resulted in increased computational costs. Because the tire dynamic characteristics affects the contact pressure, the deformation of the tread rubber caused an interaction of forces. Therefore, the tread ring deformation was defined as a summation of the mode basis functions, which expressed vibrational behavior. This approximation linearizes the energy function, which helped calculate the potential energy of the tire structure using a theoretical equation without discretization. The comparative results between the experimental and analytical data are related to the tire contact characteristics. This shows that the proposed approximation is simple, comprehensive, and accurate.

<p>A design method of a strongly coupled vibration system is required for improving noise and vibration performance of machinery. One of the authors proposed that analysis of the self-compliance matrix at interface degrees of freedom between two systems, called as kernel compliance matrix, gives the insight to work out satisfactory countermeasures for resonance frequency control of a strongly coupled vibration system. The approach, however, is only feasible for a two by two kernel compliance matrix. To expand this approach to an N by N kernel compliance matrix, a coordinate transform is available to reduce the matrix dimensions. However, the selection of the basis vector is not so easy. This paper presents a practical approach for the analysis of an N by N kernel compliance matrix. In this paper, it is shown that structural modification for resonance control can be derived using the Wedderburn's rank-one perturbation of a kernel compliance matrix. Finally, this approach was verified by a numerical case study.</p>

&lt;p&gt;The experimental modal analysis is widely used to identify the modal parameters: natural frequency, damping characteristics and mode shape, in the structural dynamic analysis. The existing method, however, is not adequate when the damping characteristics is too low. When the resonance frequency is not close to the measured frequencies, it is difficult to identify low damping characteristics due to lack of FRF data around resonance frequency. Thus, the linear fit method which is applicable to systems with very low damping characteristics is proposed in our previous study. In the proposed method, a set of linear functions with respect to the real and imaginary parts of original Frequency Response Function (FRF) is derived by canceling the residue of FRF. Then, the modal parameters are identified by fitting the experimental data to the obtained linear functions using the least-square method. However, there is a technical issue left in the method: the identified parameters are sensitive to the data range applied due to inhomogeneous error distribution. Here, the weighted least-square method is introduced to improve the identification accuracy. That is, smaller weight is assigned to the data with low accuracy, while larger weight is assigned to the data with high accuracy. A series of experiment was conducted to investigate influence of the data range and the difference of the governing equations derived from FRF. The result validates the modified method coupling with the weighted least-square method.&lt;/p&gt;

A flexible ring-based model is simple, comprehensive, and accurate, and has been most frequently adopted in tire models with a low degree-of-freedom. Despite the importance of parameter identification techniques, the literature pertaining to the discussion of these techniques is insufficient. This paper presents a novel parameter identification method based on a three-dimensional flexible ring-based model for the tires of a passenger car using experimental modal analysis. This method is able to identify modal parameters by using experimental modal analysis and by using the model to calculate the model parameters for comparison with the modal parameters. The experimental modal analysis entailed the use of a method based on an iterative simultaneous equation and confirmed that it was possible to estimate the modal parameters with high accuracy. The recalculated results using the model parameters showed good correlation with the experimental results.

&lt;p&gt;At present, there are many types of isolation system, and many of them are designed for the short-period ground motion. The long-period ground motion has recently attracted the attention, though the isolation system for the short-period ground motion does not have an ability to suppress the vibration due to the long-period ground motion because the frequency of the long-period ground motion is near the natural frequency of the isolation system. In this study, a new isolation system is proposed for not only the short-period ground motion but also the long-period one. The basic concept is that the dynamic property, which is the natural frequency, is changed by adding a spring when the amplitude of isolation table exceeds a threshold value. The validity of the method is checked by the numerical simulation using a single-degree-of-freedom system against the sine sweep ground motion and the actual earthquake ground motion. As a result, it is shown that the resonance can be suppressed by the proposed method. Then the applicability is checked by using the experimental setup. In the experiment, the additional spring is connected with the isolation table by using the clamping mechanism. The adequate clearance between the isolation table and the additional spring is determined in advance. As a result, the system can suppress the resonance phenomenon, so that it was concluded that the proposed system has a sufficient ability to suppress the resonance due to the long-period ground motion.&lt;/p&gt;

A rotor supported by gas bearings vibrates within the clearance. If the static imbalance of the rotor is large, even if the rotation speed is low, large amplitude vibration is generated by the centrifugal force. This is a serious problem because the risk of bearing damage increases. In order to solve this problem, an externally pressurized gas journal bearing with asymmetrically arranged gas supply holes has been developed. This type of bearing has a large load capacity as compared with the conventional symmetric gas supply bearing because pressurized gases are supplied to the loaded and counter-loaded side bearing surfaces via asymmetrically arranged gas supply holes. The bearing has a new gas supply mechanism in which gas is supplied from the rotor through inherent orifices. The characteristics of the developed bearing are beneficial from the viewpoint of using the bearing in rotational-type vibration exciters. In other words, this rotor has a large static imbalance. Numerical calculations of the characteristics of this bearing were performed, and the resulting characteristics were compared with those of a conventional symmetric gas supply journal bearing. The bearing load capacity of the developed bearing is considerably larger than that of conventional symmetric type bearings. The load capacity increases owing to the asymmetry of the gas supply holes. In the controlled gas supply pressure condition, rotor radial vibration during rotation can theoretically be zero. A test rig and gas control system to realize vibration reduction was constructed. A rotational test under the gas pressure control condition was conducted using a large unbalanced rotor taking advantage of this property. The control program was constructed using MATLAB and SIMULINK. The devices were driven by a digital signal processor. The magnitude of the unbalance of the rotor is 13.5 x 10(-3) kg m. The bearing diameter and length were 60 and 120 mm, respectively. The rotational vibration amplitude decreased at a high rotational frequency under the proposed bearing configuration, although the amplitude increases monotonically with the frequency in the conventional bearing. When the gas supply pressure was controlled synchronously with the rotation frequency modulation of the large unbalanced rotor, the amplitude of the vibration amplitude was greatly reduced. The rotor of the test rig was safely supported by this bearing, and effective data for practical operation were obtained.

&lt;p&gt;Structural health monitoring (SHM) of building structures is a very important technology in the effort to realize a sustainable society. Various studies on SHM have been carried out, and it is effective because it avoids accidents and predicts behaviour of structures. In this study, we proposed a method of SHM for a layered structure, in which the abnormal layer of the structure was identified by strain measurement. The main point of the study is that rotational degrees of freedom are constrained at both ends of the wall, so that the wall of each layer vibrates individually. First, in the normal condition, a location where the strain is almost zero on the outer wall of each layer is specified, and the strain at that point is constantly measured. Then, when an abnormality occurs in a certain layer, a significant value of strain appears in the abnormal layer where the strain is originally zero. We verify the proposed method by numerical simulation. We consider a three-layered structure, modelled as a cantilever beam. Abnormality is assumed to be the decrement of stiffness at a certain element, and it was shown that the effect of abnormality appeared throughout the structure in the natural vibration mode while it appeared locally in the strain measurement. The random response was then calculated by numerical integration, and the layer where the abnormality occurred could be identified by using the proposed method. Finally, we checked the applicability of the proposed method by experiment. As a result, it was shown that the method was possible to identify the layer where an abnormality occurred as well as numerical simulation.&lt;/p&gt;

Tire vibration characteristics influence noise, vibration, and harshness. Hence, there have been many investigations of the dynamic responses of tires. In this paper, we present new formulations for the prediction of tire tread vibrations below 150 Hz using a three-dimensional flexible ring-based model. The ring represents the tread including the belt, and the springs represent the tire sidewall stiffness. The equations of motion for lateral, longitudinal, and radial vibration on the tread are derived based on the assumption of inextensional deformation. Many of the associated numerical parameters are identified from experimental tests. Unlike most studies of flexible ring models, which mainly discussed radial and circumferential vibration, this study presents steady response functions concerning not only radial and circumferential but also lateral vibration using the three-dimensional flexible ring-based model. The results of impact tests described confirm the theoretical findings. The results show reasonable agreement with the predictions. (C) 2017 Elsevier Ltd. All rights reserved.

In this study, a novel rectangular slot restriction-type externally pressurized gas journal bearing was developed for use in high-speed rotating machinery, such as medical devices and industrial machines. The proposed bearing has several rectangular slot restrictors arranged in the inner surface of the bearing. To measure the bearing characteristics, a model was developed for the numerical calculation of the pressure distribution in the bearing clearance and the static characteristics of the bearing. The proposed bearing, which consists of two parts, was designed and can be manufactured using appropriate techniques. In this study, a prototype bearing with eight slots in its surface was manufactured as a test piece for fundamental tests. The diameter and length of the test bearing are 30 and 40 mm, respectively. The roundness of the bearing was measured using a three-dimensional coordinate measuring machine, and the results were used in the analysis. The pressure distribution and static characteristics obtained experimentally were found to be in good agreement with the calculated values. In the rotational tests, the rotor speed exceeded 380 Hz (22,800 rpm), and whirl vibration did not occur. During testing, the maximum rotor vibration amplitude was 0.002 mm, corresponding to an eccentricity ratio of 0.3. (C) 2017 Elsevier Inc. All rights reserved.

In numerical simulation, dynamic model is necessary to predict the product performance such as strength of structure, noise, and vibration. The prediction accuracy depends on the accuracy of parameter identification. For installed or completed products, an experiment must be done to identify structural properties such as Youngs modulus or density. This experiment allows us to accurately predict the product performance regardless of product dispersion and aging deterioration. Hence there are many studies about identification methods of the structural parameters of beams. In these studies, the structural parameters were derived from natural frequencies of a beam with/without an additional mass. However, no study can obtain the parameters under unknown boundary conditions. In this study, we proposed a new simple method to identify line density of beams. This method assumes that mode shapes of a beam do not change regardless of additional masses. This study proposes an experimental method for arrangements of additional masses, which can keep mode shapes unchanged. In the numerical analysis, a finite element method is used to obtain the natural frequencies of a beam with/without additional masses. The natural frequencies and the weight of the additional masses are used to identify line density of the beams. We also verify the method through experiment.

In this paper, two foot strike patterns, which are the rear foot strike (RFS) and the fore foot strike (FFS), are compared from the viewpoint of the joint moment, joint reaction force and muscle activity using the actual measurement of running for two subjects. As the results, the landing reaction force has two peaks for RFS while one peak for FFS, and the significant features can be observed in the ankle joint rather than the knee and hip joint. The joint moment of the ankle joint for RFS acts toward the dorsal flexion direction at the beginning of landing, and then toward the plantar flexion direction, while the one for FFS acts toward the plantar flexion direction during landing. The bone-on-bone force for RFS shows two peaks as similar with the landing impact force. For RFS, the Tibialis anterior much works while for FFS, the Gastrocnemius and the Soleus works much. Moreover, the differences of subject A and B are shown as the contribution of joints on the running.

It is said that the parameters that characterize structural damping, i.e., the loss factor, are identical to the material of the specimen, but in actuality, the damping property is sometimes affected by specimen size or the frequency. In this paper, we investigated the effect of specimen size and frequency on the structural damping property. First, we showed a simple identification method for modal parameters when the damping property is modeled as the structural damping. Next, we identify the modal parameters of the freely supported thin steel beam using the method. We obtain the relationship between the natural frequency and modal damping ratio for specimen with the same thickness but different length, and for specimen with the same length but different thickness. Then we identify the parameters that characterize the damping property. The results showed that the modal damping ratio was high in the lower frequency ranges, though light and constant in the higher frequency ranges, that is, the damping property depends on the frequency, so that the damping property could not be expressed only by the loss factor. And the relationship between the natural frequency and the modal damping ratio was identical for specimen with same thickness, though it is not for specimen with the different thickness, that is, the damping property depends on the thickness. We conclude that the effect of specimen size and frequency should be considered when predicting damping property in actual design processes.

One of the elements of tire stiffness is sidewall stiffness. This stiffness, which influences tire vibration characteristics, is also an important design parameter for carrying the vehicle body. Tire is one of pressure vessels and inflation pressure is dominant in sidewall stiffness. Thus, tire sidewall stiffness is decided from the tension of inflation pressure and the structural dynamic, including the properties of the rubber material.To reveal the dynamic characteristics of tire sidewall stiffness, this study describes differences in stiffness due to inflation pressure. It can be expected that variation of inflation pressure is monitored from the axle vibration response during vehicle traveling in the future. That is because the relationship of the vibration characteristics and the inflation pressure of tire are derived by sidewall stiffness. First, we derive a formula for sidewall stiffness based on the structural dynamics of Akasaka's theory. This formula includes two terms dependent on the inflation pressure and the rubber material. Second, sidewall stiffness is identified from experiments on the conditions that result from differences in inflation pressure. The sidewall stiffness parameter identified is calculated from a theoretical equation of natural frequency by tire ring model and experimental data. Finally, sidewall stiffness was evaluated by separating the terms dependent on the inflation pressure and the rubber material.

Dynamic model is necessary to predict the product performance in numerical simulation; strength of structure, noise and vibration. An experiment must be performed to identify the model parameter such as structural properties of installed or completed products because of preventing deterioration of prediction accuracy accompanying product dispersion and aging deterioration. Although several identification methods for elastic beams with frequency equation have been proposed in the previous studies. In these methods, the structural properties were derived from natural frequencies of the beam with/ without additional weights. The structural properties are not uniquely determined due to various factors such as boundary conditions and additional weights. Especially, no study deals with experimental conditions to enable the high prediction accuracy. This paper proposes novel methods to identify the structural properties of elastic beams of homogeneous, uniform cross-section in the lengthwise direction with free-free condition. In addition, the effects of controllable experimental parameters on the accuracy are examined. Two identification methods of the structural properties are derived; one is based on the frequency equation of the beam and the other is mass response method. It is necessary to measure natural frequencies of the beam with/ without additional weights on the beam to use both methods. The former can treat the change of mode shapes due to the additional weights, whereas the latter assumes that the mode shapes are unchanged. Finite element models are developed for validation of both methods. Various experimental conditions are adopted and the accuracy of the identified parameters by the both methods is compared. The mode shapes of the free-free beam are changed with additional weights. Thus, the method using the frequency equation is more applicable to the beam with the additional weights. Finally, the method based on the frequency equation of the beam is validated through the experiments.

Road noise is one of the main sound sources exciting passenger car interior noise. This noise is excited by road roughness. Vibration and noise characteristics in road noise have strong interaction with tire vibration characteristics. Car manufactures are keenly interested in studies on the prediction of NVH (Noise, Vibration and Harshness) performance, including viewing tire as substructure. Tire vibration has complex behavior due to tire contact with the road and rolling. In this paper, we focus on the effect of contact between tire and road as against tire vibration. First, experimental modal analysis is performed to grasp the tire vibration on the non-contact and contact condition. As a result, it was clarified that natural frequency and mode shapes change on the contact condition. Second, we studied the factor of changing tire vibration characteristics between contact and non-contact using a tire model. A tire on the non-contact condition was expressed as a shell model. Based on the tire model, we performed vibration analysis using the reseptance method and definition of eigen function. From this study, it was found that prediction accuracy by receptance method depends on the number of approximate modes. The best method for determing the number of approximate modes is based on the experiment. Additionally, analysis method by definition of eigen function also is valid sufficiently.

Recent years, we receive the full benefit of vehicle by the rapid progress of motorization with the development of economy. By contrast, environmental problem occurs from vehicle noise. The noise in Engine and Intake-Exhaust system which is typical source of noise until now has been improved because noise regulation advanced. This situation makes the tire contribution rate to vehicle interior noise increasing relatively. And the reduction of tire noise is the serious problem that we have to work on. It is important to reconstruct the input into the body from road to spindle and suspension for accurate prediction. One of the problems is how to express the tire vibration characteristics in operational condition, which are complex. It is difficult to construct a tire model that expresses the vibration characteristics on the contact and rolling condition because of the rolling effect, contact patch restriction, the property of rubber. In this study, we set a goal of performing vibration analysis on the contact and rolling condition and clear up the vibration characteristic analytically. First, Introducing tire vibration model based on the cylindrical shell theory and applying the receptance method for tire model. Additionally, we derived the mode shape function and the frequency equation on the contact and rolling condition. Secondly, we calculated natural frequency and mode shape on the contact and rolling condition. After that, we clarified the tire vibration characteristics analytically in the difference condition such as rolling speed. From this study, it was found that natural frequency on the contact and rolling condition depends on adapting mode numbers. Additionally, mode shape on the contact is determined by the components of forward wave and backward wave of the non-contact and rolling condition.

Road noise is one of the main vehicle interior noises. To minimize this, it is necessary to reveal the vibration characteristics of a rolling tire. Tire vibration has complex behavior due to tire contact with the road and rolling. In an earlier study, we clarified the effect of contact patch restriction for tire vibration characteristics in the non-rolling condition using the tire dynamical model. However, mode shapes were identified with circumferential wave number. Therefore, it is difficult to clarify the effect for tire vibration in the contact and rolling condition. In this paper, we will apply the receptance method, which is used as an analysis of the rotating disc and gear pair for the tire model toward the tire vibration analysis in the contact and rolling condition. Furthermore, the validity of the approach using this method will be verified from comparison with the result of an earlier study. 2013 SAE International.

The demand to reduce noise in the passenger cars is increasing. Tire vibration characteristics must be considered when studying road noise because of the strong interaction between tire vibration characteristics and interior car noise. Car manufacturers are keenly interested in studies on the prediction of NVH (Noise, Vibration and Harshness) performance, including viewing tires as substructure. Recently, studies have illustrated the effect that tire lateral bending mode have has on road noise, while most past studies of tire vibration focused on the circumference mode, which excited the vertical spindle force. Therefore, further study of tire lateral bending mode is necessary. Modeling of the tire lateral bending mode is described in this paper. First, lateral spindle force is measured under tire rolling conditions. Second, experimental modal analysis is performed to grasp tire lateral bending mode. Finally, a tire vibration model is built using the cylindrical shell theory. 2013 SAE International.

Structure borne noise is dominant in vehicle interior noise as frequencies below approximately 300Hz. Spindle force is a critical factor in structure borne noise for vehicle interior noise. To research the vibration characteristic of a rolling tire is essential for prediction of spindle force. This paper describes vibration analysis of a tire on the static and operational condition. Firstly, the surface vibration velocities are measured in the operational condition to comprehend the vibration behavior of a rolling tire using the scanning Laser Doppler Vibrometers. Secondly, the tire vibration model based on the cylindrical shell theory is build up. The basic equation, including the effects of the initial tension and the Coriolis force due to rotation, is derived by thin rotating cylindrical shell model and Hamilton principal. The results of the experiment and the theoretical analysis for a rolling tire are presented. Consequently, it is found that same shape of traveling-wave modes occur for a rolling tire, and the excited frequency of forward wave is different from that of backward wave. Finally, it is revealed that whether the rotation effect have affect on the vibration characteristics of a rolling tire.