scholarly journals Hydroelastic waves propagating along a frozen channel with non-uniform thickness of ice

2021 ◽  
Vol 2057 (1) ◽  
pp. 012021
Author(s):  
K N Zavyalova ◽  
K A Shishmarev ◽  
E A Batyaev ◽  
T I Khabakhpasheva
Keyword(s):  
Cross Section ◽  
Elastic Plate ◽  
Rectangular Cross Section ◽  
Normal Modes ◽  
Elastic Beam ◽  
Wave Profile ◽  
Constant Thickness ◽  
Ice Thickness ◽  
Thin Elastic Plate ◽  
Uniform Thickness

Abstract Hydroelastic waves propagating along a channel covered with ice of non-uniform thickness are considered. The channel has a rectangular cross section. The fluid in the channel is inviscid and incompressible. The ice is modeled as a thin elastic plate. The ice thickness changes linearly. The problem is reduced to the problem of the wave profile across the channel, which is solved using the normal modes of an elastic beam with non-uniform thickness. It is shown that with the decrease in the change in the ice thickness, the modes approach the normal modes of an elastic beam with a constant thickness. The behavior of the dispersion relations of the hydroelastic waves depending on the parameter describing the change in the ice thickness is studied.

scholarly journals Excitation of normal modes of a thin elastic plate by moving dislocations

Wave Motion ◽  
1999 ◽  
Vol 29 (1) ◽  
pp. 35-46
Author(s):  
Rodrigo Arias ◽  
Fernando Lund
Keyword(s):  
Elastic Plate ◽  
Normal Modes ◽  
Thin Elastic Plate

Sensitivity of Non-Uniform Beams in Depositing Mass Process

2006 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Film Thickness ◽  
Relative Density ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Relative Sensitivity ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Slender Beams ◽  
Beam Dimension

This paper deals with the mass deposition influence on the natural frequencies of nonuniform cantilever resonator sensors of linear and parabolic thickness. Resonator sensitivity, defined as fraction of change in frequency per fraction of change in thickness deposition and relative density, was found. A constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular cross-section was assumed. Euler-Bernoulli theory was used, so only slender beams were considered. Mass deposition on the free end surface of the beams was neglected. The film thickness was considered very small compared to any beam dimension. The film had no contribution to the beam stiffness, only to the mass. Results show that for the same thickness deposition, the sensitivity in the first mode of beams of linear thickness is 2.5 to 3.5 higher when compared to uniform beams. For beams of parabolic thickness variation the relative sensitivity ranges between 1.5 and 2.1.

Reverse Lift-Off Process and Application for Cu-Zr-Ti Metallic Glass Thick Film Structures

2015 ◽  
Vol 9 (6) ◽  
pp. 646-654 ◽  
Author(s):  
Shigetaka Watanabe ◽  
◽  
Junpei Sakurai ◽  
Mizue Mizoshiri ◽  
Seiichi Hata
Keyword(s):  
Amorphous Alloy ◽  
Metallic Glass ◽  
Thick Film ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Film Structure ◽  
Sputter Deposition ◽  
Uniform Thickness ◽  
Target Structure ◽  
Lift Off

In technologies involving micro electromechanical systems, lift-off processes combined with sputter deposition are general patterning methods for the formation of amorphous alloy thick film structures. However, the thicknesses of structures fabricated in this manner are not uniform because sputtered particles are blocked by the sidewalls of the lift-off layer. In this paper, a reverse lift-off process is proposed as a new patterning method for fabricating amorphous alloy thick film structures of uniform thickness. In the reverse lift-off process, a template of the desired structure is formed on top of the chosen substrate. The thick film structure is then formed by sputter deposition on the top surface of the template. In contrast to a conventional lift-off process, here the thickness of the structure is uniform because there is nothing to hinder the sputtered particles. To demonstrate this process, we successfully fabricated a Cu-Zr-Ti metallic glass thick film structure with a uniform film thickness and a rectangular cross section across different target structure widths and thicknesses. This demonstrates that the reverse lift-off process is more suitable than conventional lift-off processes for the fabrication of metallic glass thick film structures.

On Sensitivity of Capacitive Microresonators Near Three Half Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Constant Thickness ◽  
Microcantilever Sensors ◽  
Electrostatically Actuated ◽  
Resonance Frequencies ◽  
Parametric Oscillations ◽  
Deposition Thickness ◽  
Beam Dimension

This paper deals with sensitivity of electrostatically actuated micro resonator sensors near three half natural frequency. Mass deposition changes resonance frequencies of structures. Resonator sensitivity, defined as a fraction of change in frequency per unit deposited mass, can be found for microcantilever sensors electrostatically actuated to include fringe and Casimir effects. These actuation forces produce nonlinear parametric oscillations. Constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular cross-section was assumed. The Euler-Bernoulli theory was used under the assumption that the beams are slender. Mass deposition on the free end surface of the cantilever was neglected. The deposition thickness was considered uniform and very small compared to any beam dimension. The deposited mass had no contribution to the stiffness, only to the mass. Analytical expression of the sensitivity of electrostatically actuated uniform microcantilever resonators sensor near natural frequency can be determined.

Fracture Toughness of Welds Using As-Welded-Geometry/SENT Specimens

2016 ◽  
Author(s):  
Mohammed Uddin ◽  
Gery Wilkowski
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Fracture Analysis ◽  
Constant Thickness ◽  
Circumferential Welds ◽  
Ongoing Work ◽  
Specimen Test ◽  
Initial Work ◽  
Edge Notch ◽  
Pipe Geometry

The single-edge notch tension (SENT) test is frequently used for the assessment of the integrity of welds with flaws in them; this is done since the SENT specimen has the same flaw orientation as a surface flaw in the weld, and has similar constraint that affects the brittle-to-ductile transition and upper-shelf value. Traditionally SENT specimens are machined with a rectangular cross-section from the weld, and the thickness might be reduced because of that machining operation. The toughness value of the constant thickness machined specimen is then used in a pipe fracture analysis. Of course real welds have crowns in the roots of the weldment, which are ignored in both the fracture specimen test and the pipe geometry fracture analysis. To assess the importance of the weld crown and root, SENT tests were conducted as an exploratory aspect to determine the effect on toughness. Additionally, assessment of results where the SENT specimen breaks in the weld or base metal outside the weld due to the reinforcing that is usually machined off and ignored were conducted. The use of a full-weldment cross-section in SENT testing can be done for axial seam welds or circumferential welds. The initial work was on axial seam welds, although there is ongoing work for circumferential welds as well.

Contribution to beam theory based on 3-D energy principle

2017 ◽  
Vol 23 (5) ◽  
pp. 775-786 ◽  
Author(s):  
Erick Pruchnicki
Keyword(s):  
Potential Energy ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elastic Beam ◽  
Beam Theory ◽  
Displacement Fields ◽  
Energy Principle ◽  
Lateral Boundary Conditions ◽  
The First Variation

This paper presents a general elastic beam theory, which is consistent with the principle of stationary three-dimensional potential energy. For the sake of simplicity we consider the case of a rectangular cross section. The series expansion of the displacement field up to fourth-order in h (dimension of the cross section) is defined by 45 unknowns. The first variation of the potential energy must be zero but we only impose that each term guarantees an [Formula: see text]error. By adding supplementary lateral boundary conditions and on two extremities end cross section of the beam, we finally arrive at a well posed system of unidimensional differential equations. A linear algebraic dependence with respect to 16 displacement fields allows us to reduce the unknown to 19 displacement fields. To our knowledge this work is the first contribution to this end when the beam problem is completely three-dimensional.

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.

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