Application of Gauss-Hermite Beam Model to the Design of Ultrasonic Probes

1989 ◽  
pp. 835-842
Author(s):  
S. J. Wormley ◽  
B. P. Newberry ◽  
M. S. Hughes ◽  
D. K. Hsu ◽  
D. O. Thompson
Keyword(s):  
Beam Model

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Equivalent Beam Model for Spatial Repetitive Lattice Structures with Hysteretic Nonlinear Joints

2021 ◽  
Vol 200 ◽  
pp. 106449
Author(s):  
Fushou Liu ◽  
Libin Wang ◽  
Dongping Jin ◽  
Xiangdong Liu ◽  
Pingli Lu
Keyword(s):  
Beam Model ◽  
Lattice Structures ◽  
Nonlinear Joints

A beam model of the hydrogen atom

1978 ◽  
Vol 55 (4) ◽  
pp. 260
Author(s):  
V. L. Chapman
Keyword(s):  
Hydrogen Atom ◽  
Beam Model

Determining the Rayleigh damping parameters of flexible pavements for finite element modeling

2021 ◽  
pp. 107754632110267
Author(s):  
Jiandong Huang ◽  
Xin Li ◽  
Jia Zhang ◽  
Yuantian Sun ◽  
Jiaolong Ren
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Natural Frequencies ◽  
Least Squares Method ◽  
Element Model ◽  
Beam Model ◽  
Element Modeling ◽  
Rayleigh Damping ◽  
Damping Matrix

The dynamic analysis has been successfully used to predict the pavement response based on the finite element modeling, during which the stiffness and mass matrices have been established well, whereas the method to determine the damping matrix based on Rayleigh damping is still under development. This article presents a novel method to determine the two parameters of the Rayleigh damping for dynamic modeling in pavement engineering. Based on the idealized shear beam model, a more reasonable method to calculate natural frequencies of different layers is proposed, by which the global damping matrix of the road pavement can be assembled. The least squares method is simplified and used to calculate the frequency-independent damping. The best-fit Rayleigh damping is obtained by only determining the natural frequencies of the two modal. Finite element model and in-situ field test subjected by the same falling weight deflectometer pulse loads are performed to validate the accuracy of this method. Good agreements are noted between simulation and field in-situ results demonstrating that this method can provide a more accurate approach for future finite element modeling and back-calculation.

The Calculation of the Supporting Stress of Track Plate in Ballastless High-Speed Rail Structure

2011 ◽  
Vol 97-98 ◽  
pp. 3-9
Author(s):  
Yang Wang ◽  
Quan Mei Gong ◽  
Mei Fang Li
Keyword(s):  
Stress Distribution ◽  
High Speed ◽  
Design Theory ◽  
Moving Load ◽  
Structure Design ◽  
Track Structure ◽  
Beam Model ◽  
High Speed Rail ◽  
Slab Track ◽  
Ballastless Track

The slab track is a new sort of track structure, which has been widely used in high-speed rail and special line for passenger. However, the ballastless track structure design theory is still not perfect and can not meet the requirements of current high-speed rail and passenger line ballastless track. In this paper, composite beam method is used to calculate the deflection of the track plate and in this way the vertical supporting stress distribution of the track plate can be gotten which set a basis for the follow-up study of the dynamic stress distribution in the subgrade. Slab track plate’s bearing stress under moving load is analyzed through Matlab program. By calculation and analysis, it is found that the deflection of track plate and the rail in the double-point-supported finite beam model refers to the rate of spring coefficient of the fastener and the mortar.The supporting stress of the rail plate is inversely proportional to the supporting stress of the rail. The two boundary conditions of that model ,namely, setting the end of the model in the seams of the track plate or not , have little effect on the results. We can use the supporting stress of the track plates on state 1to get the distribution of the supporting stress in the track plate when bogies pass. Also, when the dynamic load magnification factor is 1.2, the track plate supporting stress of CRST I & CRST II-plate non-ballasted structure is around 40kPa.

scholarly journals GENERALIZED SOLUTIONS FOR THE EULER–BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350017 ◽  
Author(s):  
GÜNTHER HÖRMANN ◽  
SANJA KONJIK ◽  
LJUBICA OPARNICA
Keyword(s):  
Differential Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variational Problems ◽  
Generalized Solutions ◽  
Beam Model ◽  
Order Partial Differential Equation ◽  
Viscoelastic Foundation ◽  
Regularization Techniques ◽  
Initial Boundary Value

We study the initial-boundary value problem for an Euler–Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is a fourth-order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener-type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.

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