By Y. C. Fung
The target of this ebook continues to be just like that said within the first version: to offer a accomplished standpoint of biomechanics from the stand aspect of bioengineering, body structure, and scientific technology, and to improve mechanics via a chain of difficulties and examples. My three-volume set of Bio mechanics has been accomplished. they're entitled: Biomechanics: Mechanical homes of residing Tissues; Biodynamics: circulate; and Biomechanics: movement, circulate, rigidity, and progress; and this can be the 1st quantity. The mechanics prerequisite for all 3 volumes continues to be on the point of my publication a primary path in Continuum Mechanics (3rd version, Prentice-Hall, Inc. , 1993). within the decade of the Eighties the sphere of Biomechanics increased tremen dously. New advances were made in all fronts. those who have an effect on the fundamental knowing of the mechanical houses of residing tissues are defined intimately during this revision. The references are stated thus far.
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Additional info for Biomechanics: Mechanical Properties of Living Tissues
The veetor representation is very eonvenient for "eomposing" several simple harmonie oseillations of the same frequeney. For example, if x = Al eos(wt + q>l) + A 2 eos(wt + q(2) = A eos(wt + q», (4) then x is the real part of the resultant of two veetors as shown in Fig. 12: 2. Now, if the foree and displaeement are harmonie funetions of time, then we ean apply eomplex representation. Let u = Ueiwt . Then by differentiation with respeet to t, we have ü = iwUeiwt = iwu. 12:2 Veetor sum oftwo simple harmonie motions ofthe same frequency.
In terms of components, the velocity field is expressed by the functions U(X,y, z), V(X,y,z), W(X,y,z), or, if index notations are used, by Vi(X;, X2X3)' For continuous flow, we consider the continuous and differentiable functions Vi(Xb X2' X3)' To study the relationship of velocities at neighboring points, let two particles P and pi be located instantaneously at Xi and Xi + dx;, respectively. The difference in velocities at these two points is Ov· dVi = ~ dXj' uXj (1) where the partial derivatives OVi/OXj are evaluated at the partic1e P.
B is a eomplex number whose absolute value is the amplitude, and whose polar angle q> = are tan(Im B/RI B) is the phase angle of the motion. The veetor representation is very eonvenient for "eomposing" several simple harmonie oseillations of the same frequeney. For example, if x = Al eos(wt + q>l) + A 2 eos(wt + q(2) = A eos(wt + q», (4) then x is the real part of the resultant of two veetors as shown in Fig. 12: 2. Now, if the foree and displaeement are harmonie funetions of time, then we ean apply eomplex representation.