scholarly journals Dynamic Snap-Through of a Shallow Arch Under a Moving Point Load

2004 ◽  
Vol 126 (4) ◽  
pp. 514-519 ◽  
Author(s):  
Jen-San Chen ◽  
Jian-San Lin
Keyword(s):  
Critical Load ◽  
Energy Barrier ◽  
Equations Of Motion ◽  
Critical Energy ◽  
Point Load ◽  
Static Case ◽  
Shallow Arch ◽  
Finite Speed ◽  
Dynamic Case ◽  
Moving Speed

In this paper we study the dynamic behavior of a shallow arch under a point load Q traveling at a constant speed. Emphasis is placed on finding whether snap-through buckling will occur. In the quasi-static case when the moving speed is almost zero, there exists a critical load Qcr in the sense that no static snap-through will occur as long as Q is smaller than Qcr. In the dynamic case when the point load travels with a nonzero speed, the critical load Qcrd is, in general, smaller than the static one. When Q is greater than Qcrd, there exists a finite speed zone within which the arch runs the risk of dynamic snap-through either while the point load is still on the arch or after the point load leaves the arch. The boundary of this dangerous speed zone can be determined by a more conservative criterion, which employs the concept of total energy and critical energy barrier, to guarantee the safe passage of the point load. This criterion requires the numerical integration of the equations of motion only up to the instant when the point load reaches the other end of the arch.

Static and Dynamic Response of a Beam on a Winkler Elastic Foundation

2005 ◽  
Author(s):  
Timour M. A. Nusirat ◽  
M. N. Hamdan
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Initial Value Problem ◽  
Nonlinear Partial Differential Equation ◽  
Static Case ◽  
Initial Value ◽  
Characteristic Curves ◽  
System Parameters ◽  
Winkler Elastic Foundation ◽  
Dynamic Case

This paper is concerned with analysis of dynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation. The beam is assumed to be subjected to a uniformly distributed lateral static load, have an initial quarter-sine shape deflection. At one end, the beam is assumed to be restrained by a pin, while at the other end, the beam is assumed to be restrained by a torsional and a translational linear spring. The beam is modeled by a nonlinear partial differential equation where the nonlinearity enters the governing equation through the beam axial force. In the static case, because of a unique feature of governing equation, the analysis was carried out using the theory of linear differential equations, but takes into account the effect of actual deflection on the induced axial thrust. In the dynamic case, stability analysis of the beam is carried out by calculating the nonlinear frequencies of free vibration of the beam about its static equilibrium configuration. The assumed mode method is used to discretize and find an equivalent nonlinear initial value problem. Then the harmonic balance is used to obtain an approximate solution to the nonlinear oscillator described by the equivalent initial value problem. The analyses of results were carried out for a selected range of values of the system parameters: foundation elastic stiffness, lateral load, and maximum beam edge deflection. In the static case the results are presented as characteristic curves showing the variation of the beam static deflection and associated bending moment distribution with each of the above system parameters. In the dynamic case, the presented characteristic curves show the variation of the nonlinear natural frequency corresponding to the first and the second modes over a range of each of the above system parameters.

Radial component of vortex electric field force

2021 ◽  
Vol 11 (1) ◽  
pp. 32-35
Author(s):  
Vasyl Tchaban ◽  
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Spherical Body ◽  
Radial Component ◽  
Force Interaction ◽  
Finite Speed ◽  
The Third ◽  
Electric Field Force ◽  
Electrically Charged ◽  
Positively Charged

he differential equations of motion of electrically charged bodies in an uneven vortex electric field at all possible range of velocities are obtained in the article. In the force interaction, in addition to the two components – the Coulomb and Lorentz forces – the third component of a hitherto unknown force is involved. This component turned out to play a crucial role in the dynamics of movement. The equations are written in the usual 3D Euclidean space and physical time.This takes into account the finite speed of electric field propagation and the law of electric charge conservation. On this basis, the trajectory of the electron in an uneven electric field generated by a positively charged spherical body is simulated. The equations of motion are written in vector and coordinate forms. A physical interpretation of the obtained mathematical results is given. Examples of simulations are given.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (04) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Transient Compressional Waves in an Infinite Elastic Plate or Elastic Layer Overlying a Rigid Half-Space

1962 ◽  
Vol 29 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Julius Miklowitz
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Integral Transform ◽  
Formal Solution ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Frequency Equation ◽  
Point Load ◽  
Phase Method ◽  
Stationary Phase Method

The problem treated is that of an infinite free plate excited symmetrically by two equal and normally opposed step point-loads on its faces. The problem is equivalent to that of the surface normal point-load excitation of an infinite elastic layer, half the thickness of the plate, overlying a rigid half-space with lubricated contact. The formal solution is obtained from the equations of motion in linear elasticity with the aid of a double integral transform technique and residue theory. The stationary phase method, and known characteristics of the governing Rayleigh-Lamb frequency equation, are used to analyze and evaluate numerically the far field displacements. It is shown that the head of the disturbance is composed predominantly of the low-frequency long waves from the lowest mode of wave transmission.

Optimal stochastic scheduling of a two-stage tandem queue with parallel servers

1999 ◽  
Vol 31 (4) ◽  
pp. 1095-1117 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Numerical Study ◽  
Stochastic Scheduling ◽  
Static Case ◽  
Tandem Queue ◽  
Two Stage ◽  
Holding Costs ◽  
Parallel Servers ◽  
Cross Training ◽  
Dynamic Case ◽  
Sufficient And Necessary Conditions

We consider the optimal stochastic scheduling of a two-stage tandem queue with two parallel servers. The servers can serve either queue at any point in time and the objective is to minimize the total holding costs incurred until all jobs leave the system. We characterize sufficient and necessary conditions under which it is optimal to allocate both servers to the upstream or downstream queue. We then conduct a numerical study to investigate whether the results shown for the static case also hold for the dynamic case. Finally, we provide a numerical study that explores the benefits of having two flexible parallel servers which can work at either queue versus servers dedicated to each queue. We discuss the results' implications for cross-training workers to perform multiple tasks.

Effects of Flexural Stiffness, Axial Velocity and Internal Support Locations on Translating Beam’s Natural Frequencies

2014 ◽  
Vol 532 ◽  
pp. 316-319 ◽  
Author(s):  
Ferid Köstekci
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Flexural Rigidity ◽  
Equations Of Motion ◽  
Flexural Stiffness ◽  
Transverse Vibrations ◽  
Internal Support ◽  
Simple Support ◽  
Moving Speed

The aim of this paper is to examine the natural frequencies of beams for different flexural stiffness, internal simple support locations and axial moving speed. In the present investigation, the linear transverse vibrations of an axially translating beam are considered based on Euler-Bernoulli model. The beam is passing through two frictionless guides and has an internal simple support between the guides. The governing differential equations of motion are derived using Hamiltons Principle for two regions of the beam. The method of multiple scales is employed to obtain approximate analytical solution. Some numerical calculations are conducted to present the effects of flexural rigidity, mean translating speed and different internal support locations on natural frequencies.

A Generalized Model for Dynamic Contact Angle

2017 ◽  
Author(s):  
Joseph J. Thalakkottor ◽  
Kamran Mohseni
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Force Balance ◽  
Surface Tension Gradient ◽  
Static Case ◽  
Dynamic Case ◽  
Microscopic Dynamic

Contact angle is an important parameter that characterizes the degree of wetting of a material. While for a static case, estimation and measurement of contact angle has been well established, same can not be said for the dynamic case. There is still a lack of understanding and consensus as to the fundamental factors governing the microscopic dynamic contact angle. With the aim of understanding the physics and identifying the parameters that govern the actual or microscopic dynamic contact angle, we derive a model based on first principles, by performing a force balance around the region containing the contact line. It is found that in addition to the surface tension, the microscopic dynamic contact angle is also a function of surface tension gradient and the jump in normal stress across the interface. In addition to having a significant contribution in determining the microscopic dynamic contact angle, surface tension gradient is also a key cause for contact angle hysteresis.

scholarly journals Experimental detection of debonding of piezoelectric sensors with the segmented electrode

2019 ◽  
Author(s):  
Hector Andres Tinoco
Keyword(s):  
Structural Control ◽  
Adhesive Layer ◽  
Static Case ◽  
Linear Behavior ◽  
First Case ◽  
Electrode Voltage ◽  
Dynamic Case ◽  
The Right ◽  
Segmented Electrode ◽  
Left Middle

The piezoelectric transducers (PZT) are bonded to smart structures by means of an intermediate adhesive layer, with the main objectives of applying methodologies of structural health monitoring, nondestructive evaluation, nondestructive inspection and structural control to the structures. However, the application of these methodologies depends on the health of the adhesive joint that couples mechanically the PZT with the structure. This research shows an experimental technique based on the segmentation of electrodes of a PZT patch in sheet form. One electrode is segmented in three equal parts (end left, middle and end right) to obtain three electrical signatures of a PZT. The electrical signatures (voltage) of the end electrodes are related to the middle electrode voltage. Three experiments were carried out in this study: two static cases and one dynamic case. For the static case, the left end (first case) and the right end (first case) were debonded. In the dynamic case, only one side was debonded. The results show that the voltage relations present linear behavior and the changing in the slope of the voltage ratio allows identifying which electrode is debonded. This technique showed to be effective in the three studied cases of debonding and it could be used to identify debonding in real time

scholarly journals Atomic-scale ion transistor with ultrahigh diffusivity

Science ◽  
2021 ◽  
Vol 372 (6541) ◽  
pp. 501-503
Author(s):  
Yahui Xue ◽  
Yang Xia ◽  
Sui Yang ◽  
Yousif Alsaid ◽  
King Yan Fong ◽  
...  
Keyword(s):  
Ion Transport ◽  
Energy Barrier ◽  
Critical Energy ◽  
Bulk Water ◽  
Atomic Scale ◽  
Optical Measurements ◽  
Threshold Behavior ◽  
Ion Diffusion ◽  
Reduced Graphene

Biological ion channels rapidly and selectively gate ion transport through atomic-scale filters to maintain vital life functions. We report an atomic-scale ion transistor exhibiting ultrafast and highly selective ion transport controlled by electrical gating in graphene channels around 3 angstroms in height, made from a single flake of reduced graphene oxide. The ion diffusion coefficient reaches two orders of magnitude higher than the coefficient in bulk water. Atomic-scale ion transport shows a threshold behavior due to the critical energy barrier for hydrated ion insertion. Our in situ optical measurements suggest that ultrafast ion transport likely originates from highly dense packing of ions and their concerted movement inside the graphene channels.

On the Parametrically Excited Response of the Quadratically Nonlinear Model of a Rotating Ring on an Elastic Hub

1993 ◽  
Author(s):  
Rick I. Zadoks ◽  
Charles M. Krousgrill
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Parametric Excitation ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Excitation Frequency ◽  
Normal Modes ◽  
Point Load ◽  
Tangential Displacement ◽  
Partial Differential

Abstract As a first approximation, a steel-belted radial tire can be modeled as a one dimensional rotating ring connected elastically to a moving hub. This ring can be modeled mathematically using a set of three nonlinear partial differential equations, where the three degrees of freedom are a radial displacement, a tangential displacement and a section rotation. In this study, only quadratic geometric nonlinearities are considered. The system is excited by a temporally harmonic point load f^(t) and a temporally harmonic hub motion z^(t) that have the same harmonic frequency. The point load f^(t) appears in the equations of motion as a single in-homogeneous term, while the hub motion z^(t) appears in inhomogeneous and parametric excitation terms. To simplifying the ensuing analysis, the rotation rate of the hub is assumed to be constant. The partial differential equations of motion are reduced to a set of four second-order ordinary differential equations by using two linear normal modes to approximate the spatial distribution of the displacements. A region of the parameter space, as defined by ranges of values of the excitation amplitude z and the excitation frequency ω (or detuning parameter σ), is identified, from a Strutt diagram, where the parametric excitation is expected to be dominant. In this region σ is varied to locate a secondary Hopf bifurcation that leads to a set of complex steady-state quasi-periodic solutions. These solutions contain two families of frequency components where the fundamental frequencies of these families are non-commensurate, and they are characterized by Poincaré sections with closed or nearly closed “orbits” as opposed to the distinct points displayed by periodic responses and the strange attractor sections displayed by chaotic solutions.

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