Download Ebook Vibration Analysis

Download Ebook Vibration Analysis

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Vibration Analysis

Download Ebook Vibration Analysis

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Book by Vierck, Robert K.

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Product details

Hardcover: 511 pages

Publisher: Intex Educational Pub; 2 edition (June 1, 1978)

Language: English

ISBN-10: 0700225250

ISBN-13: 978-0700225255

Package Dimensions:

9.3 x 6.2 x 1 inches

Shipping Weight: 1.9 pounds

Average Customer Review:

5.0 out of 5 stars

1 customer review

Amazon Best Sellers Rank:

#1,348,625 in Books (See Top 100 in Books)

Just a year of college physics would be adequate preparation for this text. An acquaintance with second order linear differential equations would help but the necessary math is presented in the book. The focus is of course on harmonic motion in its various manifestations. So the main function you deal with is the sine or exponential function. If you know the derivatives here you're pretty well set. When you get to the multi-degree systems in chapters 7 and 8 you'll need some matrix theory which is outlined in an appendix. Familiarity with linear algebra is a definite help here. Stuff like eigenvectors belonging to different eigenvalues are orthogonal you'll use frequently. I'll highlight chapter 9 which is on numerical methods used in these multi-degree systems to find the principal vibration modes (eigenvectors) and natural frequencies (their eigenvalues). I'll focus on sections 9.4 through 9.7 which describe the Stodola iteration method. This is particularly nice as it is easily programmable. You're given a square matrix which of course only operates on its basis vectors but its eigenvectors also furnish a basis. This means that any vector that it can operate on can be written as a linear combination of these vectors. We have enough for an iteration now. We choose some arbitrary nonzero vector in our n-dimensional Cartesian system assuming an nxn matrix. Pre-multiply this vector by the matrix. Remembering that it is also a superposition of eigenvectors, the eigenvector whose eigenvalue is largest(in absolute value) will begin to dominate after this operation since it is multiplied by its eigenvalue. If you normalize the resulting vector after this and continue the process you'll find the normalized vector begins to differ little from the previous and this will be the highest principal mode and its eigenvalue is the highest natural frequency (found by matrix pre-multiplication again). The others are found by imposing orthogonality relations on the remaining vectors and modifying the matrix appropriately here. Same process is continued. The matrix modification is a little more involved and can be found in section 9.7. This same method no doubt carries over to quantum mechanics though its justification will be more involved using Schauder or Brouwer fixed point theorems no doubt. Broad coverage yet not taxing. Worth it.

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