Response of a Rotating Beam Subject to an Accelerating Force

1991 ◽  
Author(s):  
A. Argento ◽  
R. A. Scott
Keyword(s):  
Constant Velocity ◽  
Integral Transforms ◽  
Beam Model ◽  
Rotating Beam ◽  
Velocity Function ◽  
Distributed Load ◽  
Fixed Direction ◽  
Convolution Integrals ◽  
Rotating Timoshenko Beam ◽  
Set Up

Abstract A method is given by which the response of a rotating Timoshenko beam subjected to an accelerating fixed direction force can be determined. The beam model includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up in general form using multi-integral transforms and the inversion is expressed in terms of convolution integrals. These are numerically integrated for a uniformly distributed load having an exponentially varying velocity function. Results are presented for the displacement under the load’s center as a function of position. Comparisons are made between the responses to a constant velocity load and a load which accelerates up to the same velocity.

Application of the Influence Line on the Bridge Testing

2012 ◽  
Vol 594-597 ◽  
pp. 1586-1589
Author(s):  
Run Feng Zhang ◽  
Xian Min Zhang ◽  
Chun Xiang Qi
Keyword(s):  
Beam Model ◽  
The Finite Element Method ◽  
Shearing Force ◽  
Unit Load ◽  
Bridge Testing ◽  
Damage Degree ◽  
Influence Line ◽  
The Difference ◽  
Set Up ◽  
The Moment

In order to discuss the sensibility of influence line on the damage, a two-span continuous beam model is set up using the finite element method in the paper. The two damage positions at the middle span and 1/4 span are considered. And different damage degrees are simulated by the different crack depths. The shearing force and moment at four key positions of the beam are calculated under the moving unit load separately. Results show that the moment influence line at the middle support of the beam is very sensitive to the beam damage, while the moment influence line at other positions and the shearing force influence line at each position are insensitive. In the moment influence line of the beam middle support position, the obvious different values appear at the middle span when damage in the middle span. As damage in the 1/4 span, the obvious different also appear at the damage position, and the difference is increased unconspicuous up to the middle span, and then decreased soon. The conclusion is beneficial to determine the position of damage by means of comparing the moment influence line with that of undamaged bridge. Moreover, the difference value of moment influence line can also be used to estimate the damage degree.

Fresnel-zone binning: Fresnel-zone shape with offset and velocity function

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. T9-T14 ◽  
Author(s):  
David J. Monk
Keyword(s):  
Velocity Gradient ◽  
Constant Velocity ◽  
Fresnel Zone ◽  
Geometric Approach ◽  
Velocity Function ◽  
Zero Offset ◽  
Limiting Case ◽  
Fresnel Zones

The concept of the Fresnel zone has been explored by many workers; most commonly, their work has involved examining the Fresnel zone in the limiting case of zero offset and constant velocity. I have examined the shape of the Fresnel zone for nonzero offset and in the situation of constant velocity gradient. Finite-offset Fresnel zones are not circular but are elliptical and may be many times larger than their zero-offset equivalents. My derivation takes a largely geometric approach, and I suggest a useful approximation for the dimension of the Fresnel zone parallel to the shot-receiver azimuth. The presence of a velocity gradient (velocity increasing with depth) in the subsurface leads to an expansion of the Fresnel zone to an area that is far larger than may be determined through a more usual straight-ray determination.

Real-Time Structure Shape Estimation Using Distributed Fiber Bragg Grating Sensors

2009 ◽  
Author(s):  
Hong-Il Kim ◽  
Lae-Hyong Kang ◽  
Jae-Hung Han
Keyword(s):  
Real Time ◽  
High Speed ◽  
Estimation Method ◽  
Time Estimation ◽  
Flexible Beam ◽  
Beam Model ◽  
Shape Estimation ◽  
Rotating Beam ◽  
Structural Shape ◽  
Beam Structures

One of the emerging issues in lightweight aerospace structures is the real-time estimation of the structural shape changes. In order to reconstruct the structure shape based on the measured strain data at multiple points, the displacement-strain transformation (DST) method has been used. In this study, simulation for a 1-D beam model was performed to verify the DST method. Bending displacements for various excitation conditions were successfully estimated using the simulated strain signals. Strain sensor positions were optimized by the minimization of the condition number of the DST matrix for the 1-D beam. We further expanded the shape estimation method to rotating beams. A rotating flexible beam experimental model was constructed and a numerical simulation model was also prepared. Multiplexed four FBG sensors were fabricated and attached to the rotating beam structures to measure strains at four different locations. The experimental device has an optical rotary coupler, and the sensor signals are transmitted through the optical rotary coupler. Bending displacements were estimated based on the FBG signals and compared with directly measured displacement data using photographs taken by a high-speed camera. This shows the validity of the proposed shape estimation technique based on DST matrix for rotating beam structures.

scholarly journals Stabilization and Observability of a Rotating Timoshenko Beam Model

2007 ◽  
Vol 2007 ◽  
pp. 1-19 ◽  
Author(s):  
Alexander Zuyev ◽  
Oliver Sawodny
Keyword(s):  
Timoshenko Beam ◽  
Galerkin Approximation ◽  
Sufficient Conditions ◽  
Beam Equation ◽  
Distributed Parameter ◽  
Dimensional System ◽  
Beam Model ◽  
Finite Dimensional ◽  
Galerkin Approximations ◽  
Rotating Timoshenko Beam

A control system describing the dynamics of a rotating Timoshenko beam is considered. We assume that the beam is driven by a control torque at one of its ends, and the other end carries a rigid body as a load. The model considered takes into account the longitudinal, vertical, and shear motions of the beam. For this distributed parameter system, we construct a family of Galerkin approximations based on solutions of the homogeneous Timoshenko beam equation. We derive sufficient conditions for stabilizability of such finite dimensional system. In addition, the equilibrium of the Galerkin approximation considered is proved to be stabilizable by an observer-based feedback law, and an explicit control design is proposed.

scholarly journals Limiting probability measures

2020 ◽  
Vol 12 ◽  
Author(s):  
Irfan Alam
Keyword(s):  
Asymptotic Behavior ◽  
Classical Result ◽  
Nonstandard Analysis ◽  
High Dimensional ◽  
Probability Measures ◽  
Dimensional Sphere ◽  
Spherical Means ◽  
Fixed Direction ◽  
Set Up ◽  
Gaussian Moment

The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We revisit this classical result from a nonstandard analysis perspective, providing a new proof by working with hyperfinite dimensional spheres. We also set up a nonstandard theory for the asymptotic behavior of integrals over varying domains in general. We obtain a new proof of the Riemann--Lebesgue lemma as a by-product of this theory. We finally show that for any function $f \co \mathbb{R}^k \to \mathbb{R}$ with finite Gaussian moment of an order larger than one, its expectation is given by a Loeb integral integral over a hyperfinite dimensional sphere. Some useful inequalities between high-dimensional spherical means of $f$ and its Gaussian mean are obtained in order to complete the above proof.

scholarly journals Convolution Integral: How a Graphical Type of Solution Can Help Minimize Misconceptions

2021 ◽  
Vol 3 (2) ◽  
pp. 103
Author(s):  
Hendra J. Tarigan
Keyword(s):  
Impulse Response ◽  
Physical System ◽  
Convolution Integral ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Convolution Integrals ◽  
Low Pass ◽  
Simulation And Experiment ◽  
Rc Circuit ◽  
Set Up

A physical system, Low Pass Filter (LPF) RC Circuit, which serves as an impulse response and a square wave input signal are utilized to derive the continuous time convolution (convolution integrals). How to set up the limits of integration correctly and how the excitation source convolves with the impulse response are explained using a graphical type of solution. This in turn, help minimize the students’ misconceptions about the convolution integral. Further, the effect of varying the circuit elements on the shape of the convolution output plot is presented allowing students to see the connection between a convolution integral and a physical system. PSpice simulation and experiment results are incorporated and are compared with those of the analytical solution associated with the convolution integral.

scholarly journals Study on Development Law of Mining-Induced Slope Fracture in Gully Mining Area

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tao Yang ◽  
Yiran Yang ◽  
Jie Zhang ◽  
Shoushi Gao ◽  
Tong Li
Keyword(s):  
Mining Area ◽  
Force Model ◽  
Beam Model ◽  
Beam Structure ◽  
Distributed Load ◽  
Load Beam ◽  
Fracture Development ◽  
Nonuniform Load ◽  
Induced Fractures ◽  
Step Distance

The development law of mining cracks in shallow coal seams under gully topography was used as the research base to analyze the development characteristics of mining cracks in the 5-2 coal mining face of Anshan Coal Mine, and the weak strength was established. The basic top force model under the action of the overburden is the “nonuniformly distributed load beam” structure model. Through similar simulation research and theoretical calculation analysis, the fracture development law of the working face passing through the valley is studied. Based on the mechanical analysis of the beam structure with nonuniform load, the discriminant conditions of the stability of the bearing structure of the bedrock are derived, the calculation formulas of the parameters such as the pressure, shear force, and the ultimate span of the basic roof at both ends are determined, the influence law of the thickness and slope change of the weak strength overburden on the mining crack spacing is revealed, and the influence of the slope of the weak strength overburden on the weighting step distance on the beam with nonuniform load is obtained. The phenomenon is that the burial depth has a great influence on the step distance of weighting. The practice shows that the distance between the mining-induced fractures determined by the nonuniformly distributed load beam model and the periodic weighting step, the height of fracture development, and the buried depth are approximately the same; the mining-induced fractures in the overburden develop and evolve periodically with the failure and instability of the bedrock. The research results will clarify the development mechanism of surface cracks in the gully mining area, which is of great significance to reduce terrain disasters.

3-D time‐variant dip moveout by the f-k method

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 1030-1041 ◽  
Author(s):  
Hans A. Meinardus ◽  
Karl L. Schleicher
Keyword(s):  
Impulse Response ◽  
Constant Velocity ◽  
Decomposition Method ◽  
Three Dimensional ◽  
Velocity Variation ◽  
Velocity Function ◽  
Discrete Values ◽  
Zero Offset ◽  
Event Times ◽  
Arbitrary Velocity

The standard seismic imaging sequence consists of normal moveout (NMO), dip moveout (DMO), stack, and zero‐offset migration. Conventional NMO and DMO processes remove much of the effect of offset from prestack data, but the constant velocity assumption in most DMO algorithms can compromise the ultimate results. Time‐variant DMO avoids the constant velocity assumption to create better stacks, especially for steeply dipping events. Time‐variant DMO can be implemented as a 3-D, f-k domain process using the dip decomposition method. Prestack data are moved out with a set of NMO velocities corresponding to discrete values of in‐line and crossline dips. The dip‐dependent NMO velocity is computed to remove the trace offset and azimuth dependence of event times for an arbitrary velocity function of depth. After stacking the moved out CMP gathers, a three‐dimensional (3-D) dip filter is applied to select the particular in‐line and crossline dip. The final zero‐offset image is obtained by summing all the dip‐filtered sections. This process generates a saddle‐shaped 3-D impulse response for a constant velocity gradient. The impulse response is more complicated for a general depth‐variable velocity function, where the response exhibits secondary branches, or triplications, at steeper dips. These complicated impulse responses, including amplitude and phase effects, are implicitly produced by the f-k process. The dip‐decomposition method of 3-D time‐variant DMO is an efficient and accurate process to correct for the effect of offset in the presence of an arbitrary velocity variation with depth. The impulse response of this process implicitly contains complex features like a 3-D saddle shape, triplications, amplitude, and phase. Field data from the Gulf of Mexico shows significant improvement on a steep salt flank event.

scholarly journals Parameters Online Detection and Model Predictive Control during the Grain Drying Process

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Lihui Zhang ◽  
Helei Cui ◽  
Hongli Li ◽  
Feng Han ◽  
Yaqiu Zhang ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Constant Velocity ◽  
Variable Temperature ◽  
Structural Characteristics ◽  
Cross Flow ◽  
System Control ◽  
Drying Process ◽  
Grain Drying ◽  
Set Up

In order to improve the grain drying quality and automation level, combined with the structural characteristics of the cross-flow circulation grain dryer designed and developed by us, the temperature, moisture, and other parameters measuring sensors were placed on the dryer, to achieve online automatic detection of process parameters during the grain drying process. A drying model predictive control system was set up. A grain dry predictive control model at constant velocity and variable temperature was established, in which the entire process was dried at constant velocity (i.e., precipitation rate per hour is a constant) and variable temperature. Combining PC with PLC, and based on LabVIEW, a system control platform was designed.

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