Tables of Integrals and Other Mathematical Data.

Dwight, H. B.; Romer, Robert H.

doi:10.2307/2333782

Cited by 367 publications

(92 citation statements)

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“…By using (5.2), (5.3), and the well-known results (e.g., [29], Sections 21.4 and 22.3 of Chapter V, [30], 440.11), one can show that the expansion is…”

Section: Exact Analytical Expression For the Steady-state Stressmentioning

confidence: 93%

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

Mamontov¹,

Berbyuk²

2017

JAMP

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As is well known, hand-arm vibration syndrome (HAVS), or vibration-induced white finger (VWF), which is a secondary form of Raynaud's syndrome, is an industrial injury triggered by regular use of vibrating hand-held tools. According to the related biopsy tests, the main vibration-caused lesion is an increase in the thickness of the artery walls of the small arteries and arterioles resulted from enlarged vascular smooth muscle cells (VSMCs) in the wall layer known as tunica media. The present work develops a mechanobiological picture for the cell enlargement. The work deals with acoustic variables in solid materials, i.e., the non-equilibrium components of mechanical variables in the materials in the case where these components are weakly non-equilibrium. The work derives an explicit expression for the infinite-time cell-volume relative enlargement. This enlargement is directly affected by the acoustic pressure in the soft living tissue (SLT). In order to reduce the enlargement, one can reduce either the ratio of the acoustic pressure in the SLT to the cell bulk modulus or the relaxation time induced by the cell osmosis, or both the characteristics. Also, a mechanoprotective role of the above relaxation time in the cell-volume maintenance is noted. The above mechanobiological picture focuses attention on the pressure in an SLT and, thus, modeling of propagation of acoustic waves caused by the acceleration of a vibrating hand-held tool. The present work analyzes the propagation along the thickness of an infinite planar layer of an SLT. The work considers acoustic modeling. As a general viscoelastic acoustic model, the work suggests linear non-stationary partial integro-differential equation (PIDE) for the weakly non-equilibrium component of the average normal stress (ANS) or, briefly, the acoustic ANS. The PIDE is, in the exponential approximation for the normalized stress-relaxation function (NSRF) reduced to the third-order linear non-stationary partial differential equation (PDE), which is of the Zener type. The unique advantage of the PIDE is that it presents a compact model for the acoustic ANS in an SLT, which explicitly includes the NSRF, thereby enabling a consistent description of the lossy-propagation effects inherent in SLTs. The one-spatial-coordinate version of this PDE in the planar SLT layer with the corresponding boundary conditions is considered. The relevance of these settings is motivated by a conclusion of other authors, which is based on the results of the frequency-domain simulation in three spatial coordinates. The boundary-value problem at arbitrary value of the stress-relaxation time (SRT) and arbitrary but sufficiently regular shape of the external acceleration is analytically solved by means of the Fourier method. The obtained solution is the steady-state acoustic ANS and allows calculation of the corresponding steady-state acoustic pressure as well. The derived analytical representations are computationally implemented. Propagation of the pressure waves in the SLT layer at zero ...

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“…By using (5.2), (5.3), and the well-known results (e.g., [29], Sections 21.4 and 22.3 of Chapter V, [30], 440.11), one can show that the expansion is…”

Section: Exact Analytical Expression For the Steady-state Stressmentioning

confidence: 93%

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

Mamontov¹,

Berbyuk²

2017

JAMP

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“…Noting from Figure 2.1 that 3.34, and 3.35 constitute the exact formal solution for the fields generated by the charge separation process and the accompanying current flow. The quantities Rf and Of may be found in terms of zf using Equations 2.7 and 3.22, while zf can be found as a function of t by inverting the time-distance quation (Equation 2.10) as discussed in Appendix A.…”

Section: S(321)mentioning

confidence: 99%

“…This integral is readily evaluated using standard forms, (for example Dwight 3 Items 90.1 and 92.1) and after some algebraic reduction it is found that…”

Section: -1mentioning

confidence: 99%

Electromagnetic Fields from the Generation and Absorption of Discontinuous Linear Current Fronts.

Lewis¹

1984

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“…(16)-(18), we establish the formal relation between the  m and  t (19)Since the elements dS, dS m , dS t form a right-angled triangle, it can be reasoned that With allowance for the trigonometric relations in[7…”

mentioning

confidence: 99%

Solution of the problem of the form and tension of a filament in its three-dimensional balloon during twisting

Koval¹

2011

Fibre Chem

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Systems of differential equations in cartesian and cylindrical coordinates are obtained to describe a fl exible fi lament rotating in a resisting medium. The concept of the unit aerodynamic drag coeffi cient of the fi lament is introduced in addition to the assumptions used in previous studies. The systems of differential equations that were obtained are solved in analytical form using the assumptions that were made. A value is found for the new concept of unit aerodynamic drag coeffi cient, and ways are described to study it and determine its value for different fi laments in practical applications. Complete mathematical expressions are obtained to calculate parameters that are of practical importance in the twisting of a fi lament -its tension, the maximum radius (diameter) of the torsion balloon, and the conditions under which multiple balloons are formed. It is established that the problem of the form and tension of a fi lament during its twisting cannot be solved in fi nal form without allowance for the resistance of the medium.The theoretical framework that determines the main operational and design parameters of the working spindle of doubling machines is the spatial position of a fi lament that freely rotates about the vertical axis of the spindle and is unwound from or wound onto a package. This position is usually referred to as the balloon of the fi lament, and the process itself is referred to as ballooning. The most signifi cant progress in the study of this topic was made by Prof. A. P. Minakov, who was the fi rst to obtain a system of differential equations that describe the form and tension of a fi lament positioned spatially in an balloon and rotating in a resisting medium while moving along its own axis [1,2]. This and subsequent treatments of the problem of the location of a fi lament in space with allowance for the resistance of the surrounding medium were solved only with the problem in its most basic formulation, i.e. a system of differential equations was obtained in cartesian coordinates. It was shown that in special cases, without allowance for the resistance of air, the system leads to particular solutions [3][4][5]. However, the problem of calculating the form and tension of a fi lament in two and three dimensions has not been completely solved in analytical form. Such a solution is obtained below with certain assumptions.

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Tables of Integrals and Other Mathematical Data.

Abstract: Abscissa of convergence 403 Active filter circuits 353, 359, 361 Admittance 344, 366, 485, 495 Aliasing 228, 229, 452 Aliasing (eliminating it) 235 Allpass digital filter 307 Allpass digital filter (1st-order) 449 Allpass digital filter (2nd-order) 450

Cited by 367 publications

References 0 publications

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

Propagation of Acoustic Waves Caused by the Accelerations of Vibrating Hand-Held Tools in Viscoelastic Soft Tissues of Human Hands and a Mechanobiological Picture for the Related Injuries

Electromagnetic Fields from the Generation and Absorption of Discontinuous Linear Current Fronts.

Solution of the problem of the form and tension of a filament in its three-dimensional balloon during twisting

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