Orthogonality conditions of the transverse vibration mode function for a stepped one-dimensional plate on a Winkler foundation and subjected to an in-plane force

2002 ◽  
Vol 216 (3) ◽  
pp. 271-273
Author(s):  
Y S Zhang
Keyword(s):  
Forced Vibration ◽  
Transverse Vibration ◽  
Vibration Mode ◽  
Constant Thickness ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Mode Function ◽  
Orthogonality Conditions

The transverse vibration mode equation of a stepped one-dimensional plate on a Winkler foundation and subjected to an in-plane force is derived. The orthogonality conditions for transverse vibration of such a plate are obtained. The conclusions of this work can be used to solve the problem of forced vibration of various stepped one-dimensional plates, plates of constant thickness and beams.

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

scholarly journals Investigation on indentation rolling resistance of belt conveyor based on Hertz contact theory compared with one-dimensional Winkler foundation

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878393 ◽  
Author(s):  
Lu Yan
Keyword(s):  
Rolling Resistance ◽  
Contact Theory ◽  
Theoretical Formula ◽  
Winkler Foundation ◽  
Hertz Contact ◽  
Belt Conveyor ◽  
One Dimensional ◽  
Hertz Contact Theory ◽  
Viscoelastic Theory ◽  
Indentation Rolling Resistance

Based on Hertz contact theory and one-dimensional Winkler foundation combination with viscoelastic theory, the author derived theoretical formulas of indentation rolling resistance, respectively. Using the laboratorial apparatus of indentation rolling resistance, the author mainly concentrates on the error analysis about two kinds of theoretical formula which bear on indentation rolling resistance compared with experimental result. The reason why author employs Hertz contact theory to discuss indentation rolling resistance is that indentation rolling resistance is a sort of contact resistance. As a result, Hertz contact theory is generally applicable to study it. On the other hand, because conveyor belt has viscoelastic property, it is appropriate to use viscoelastic theory by the aid of three-parameter Maxwell viscoelastic model combination with one-dimensional Winkler foundation. Ultimately, this article infers that theoretical formula based on the Hertz contact is brief and clear compared with one-dimensional Winkler foundation in principle. However, it is noticeable that when the belt is at high speed, the reliability of formula based on Hertz theory has decreased obviously. This conclusion can give a beneficial reference for the energy saving of belt conveyor.

scholarly journals Mobility Matrix of a Thin Circular Plate Carrying Concentrated Masses Based on Transverse Vibration Solution

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Desheng Li ◽  
Junhong Zhang
Keyword(s):  
Circular Plate ◽  
Transverse Vibration ◽  
Vibration Mode ◽  
Sound Power ◽  
Vibration Source ◽  
Thin Circular Plate ◽  
Mobility Matrix ◽  
Solution Point ◽  
Concentrated Masses ◽  
Mobility Solution

When calculating the vibration or sound power of a vibration source, it is necessary to know the point mobility of the supporting structure. A new method is presented for the calculation of point mobility matrix of a thin circular plate with concentrated masses in this paper. Transverse vibration mode functions are worked out by utilizing the structural circumferential periodicity of the inertia excitation produced by the concentrated masses. The numerical vibratory results, taking the clamped case as an instance, are compared to the published ones to validate the method for ensuring the correctness of mobility solution. Point mobility matrix, including the driving and transfer point mobility, of the titled structure is computed based on the transverse vibration solution. After that, effect of the concentrated masses on the mechanical point mobility characteristics is analyzed.

Vibration of Lifting Rope when Cage Is Locking

2012 ◽  
Vol 472-475 ◽  
pp. 1559-1562
Author(s):  
Juan Wu
Keyword(s):  
Fundamental Frequency ◽  
Vibration Mode ◽  
Step Function ◽  
Wire Rope ◽  
Vibration Characteristics ◽  
Vibration Displacement ◽  
Mode Function ◽  
Vibration Model

Analysis of vibration characteristics when the cage is locking. Deduce vibration model by elastic lifting rope, interaction of sheave and rope. Based on step function, a wire rope vibration mode function, vibration displacement and tension solution are given. Results show that the cage locking device reduces impact and avoids the slippery rope and the security hidden danger. The vibration model of locking cage process is applied to the cage jammed situation. If the frequency during sudden jam is greater than or equal to the fundamental frequency, hoisting wire rope fracture does not occur.

scholarly journals Single Frame Fringe Pattern Analysis for Phase Recovery with Analytic Signal

ISRN Optics ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Khalid Assid ◽  
Vamara Dembele ◽  
Faiçal Alaoui ◽  
Abdel Karim Nassim
Keyword(s):  
Fringe Pattern ◽  
Good Accuracy ◽  
Phase Distribution ◽  
Analytic Signal ◽  
One Dimensional ◽  
Hilbert Huang Transform ◽  
Mode Function ◽  
Single Frame ◽  
Mode Decomposition ◽  
Fringe Pattern Analysis

We consider a new application of the normalized Hilbert-Huang transform to extract directly the phase from a single fringe pattern. We present a technique to provide, with good accuracy, the phase distribution from a single interferogram without unwrapping step and this by a new exploitation of the analytic signal corresponding to each intrinsic mode function, resulting from one-dimensional empirical mode decomposition of the fringe pattern. A theoretical analysis was carried out for this technique, followed by computer simulations and a real experimental fringe pattern for verification.

Thermal Analysis of Laminar Fluid Film Under Side Cyclic Motion

1974 ◽  
Vol 96 (1) ◽  
pp. 100-106 ◽  
Author(s):  
R. I. Pedroso
Keyword(s):  
Power Dissipation ◽  
Analytical Study ◽  
Frictional Resistance ◽  
Fluid Film ◽  
Constant Thickness ◽  
Axial Motion ◽  
End Effects ◽  
One Dimensional ◽  
Moving Wall ◽  
Varying Thickness

An analytical study is presented for a constant-thickness incompressible laminar one-dimensional fluid film undergoing cyclic side motion. The fluid film is bounded by a stationary and a cyclically-moving wall. The heat flux is calculated at both the stationary and moving boundaries. Formulas are presented for the frictional resistance and power dissipation at the moving wall. Application is made to the varying-thickness fluid film between an eccentric round shaft with reciprocating axial motion and its stationary cylindrical housing. In the analysis, quantities assumed constant are the pressure along the edges of the fluid film, its properties, and the temperature along each of the two walls bounding the fluid. The lateral dimensions of the fluid film are assumed large compared to its thickness such that end effects can be neglected.

Vibration Analysis of the Load on Helicopter Swashplate Rod

2012 ◽  
Vol 226-228 ◽  
pp. 119-123
Author(s):  
Fang Wang ◽  
Ming Chen
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Vibration Mode ◽  
Rotor Speed ◽  
Helicopter Control ◽  
Flight Experiment ◽  
Control Precision ◽  
Mode Function

The swashplate rod is a key component of helicopter control system. The vibration environment of helicopter is quite complex. The natural frequency of the swashplate rod is generally low. So resonance occurs easily. Resonance could reduce control precision or even damage the whole control system. Established dynamic and mathematical model of swashplate rod. Analyzed the vibration characteristics. Obtained the natural frequency and vibration mode function of the rod. In the compression, tension and free state, the natural frequency of the rod is basically the same. Made flight experiment with a developing helicopter as object. Measured the load of the swashplate rod in flight conditions. Make Fourier analysis to the load. Obtained the frequencies of the load on the rod. The frequencies coincide with 1 and 2 times of the rotor speed.

The Natural Characteristics of Fluid Conveying Pipe under Different Supporting Conditions

2013 ◽  
Vol 372 ◽  
pp. 612-619 ◽  
Author(s):  
Ri Dong Bao
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Fluid Pressure ◽  
Vertical Vibration ◽  
Elastic Coefficient ◽  
Pipe Section ◽  
Mode Function ◽  
Constrained Coefficients ◽  
Natural Characteristics

The natural characteristics of fluid conveying pipe with its ends under different supporting conditions were investigated. The expression of vertical vibration mode-function of pipe beam was derived from the boundary conditions of similarly supported beam. The effect of different supporting elastic coefficient, fluid pressure, flowrate, and axial force of pipe section on its natural characteristics was calculated and analyzed based on the eigenequation of motion. The numerical computation results showed that its natural frequency was proportional to elastic supporting coefficient and axially pressed force of pipe section, but was proportional conversely to fluid flowrate, fluid pressure and axially sectional drawn force of pipe. The natural frequency of different modes can be coupled with each other, the primarily mode and secondly mode would change either. In order to improve the natural frequency of fluid conveying pipe, the elastically constrained coefficients should be extended and the axially pressed force of pipe section should be avoided.

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