By Gheorghe Buzdugan, Elena Mihăilescu, Mircea Radeṣ (auth.)

Nowadays, the engineering perform increases way more vibration difficulties than may be theoretically defined or modelled. simply because Df this, measurements are utilized in just about all fields of undefined, transportation and civil engineering in experiences of mechanical and structural vibration. they're a useful instrument for designing items and machines with excessive reliability and occasional noise point, autos and constructions with more desirable convenience and resistance to dynamic so much, in addition to for acquiring elevated defense of opera tion and optimal working parameters. so as to take care of the expanding call for for experimental size of vibration features, younger engineers and architects want an introductory ebook with emphasis on "what should be measured" and "by what capacity" prior to studying "how measurements are done". The services to accomplish vibration measurements needs to be won in time, with each new investi gation and studied challenge . .A distinct presentation of instrumentation and measuring ideas is past the purpose of this publication. Such info are available in product information sheets, software manuals and hand books provided via apparatus brands. in simple terms common princi ples and universal equipment are awarded herein, which will give you the reader with an outline of the instrumentation and methods encountered in vibration measurement.

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L. _ ...... 1... ___-'------"------' is t111• cocHicknt giYen in the table; is the plate bt·nding stiffm·ss; g - acceleration of 12(1 - 1/) ;Iravity: y - wright drnsity: h - plat<~ thiclm('SS; a - plate length; 'J Poisson's ratio: E - mndulus of clns tici ty. 7 [9]. 8 may be used. for calculating natural frequencies of cantilevered rectangttlar plates. :~) (After M. V. b l ~ Mod('~ ~ . 472 3 . 49 563 . 71 105 . 7 and a it> the length of the edge perpendicular to the clamped. edge. 9. 47 Elements of theory 2 Natura[ Frequencies of Rectangular Plates (After R· F.

29) where ~f-~t = 1JN and ~f is the frequency resolution. ; X(im·~f)e' 2 "mnJN, n=O, ... ,N-1. 30) m=O The independent variables are the pair of indices m and n. If x(n·~t) is real, then X(m·~f) will be Hermitian, so that only the positive half-period of X( m ·~f) need be calculated. The DFT gives the correct Fourier transform for sampled periodic data. If the time function x(t) is indeed periodic, such that the time window length T is an integer number of periods, and if the frequency spectrum is ·hand-limited so as not to exceed the Nyquist frequency - 1 - = N ~f (see Chapter 5), then the 2~t 2 DFT will produce the correct spectrum without errors (like leakage or aliasing).

Co periodic. As T 0 increases, the distance w 0 = 2 7t between neighTo bouring harmonics decreases. 12) becomes +oo (' ~ x(t) e-i"'1 dt. 15) -oo or +oo X(if) = ~ x(t) e-i 2"f1 dt. 15 a) -00 IX! 15 a) is known as the Fonrier transform of x(t) and is often denoted by ff[x(t)]. The plot of the modulus I X( if) 1 against frequency (Fig. 4) is called the linea1· Fourier spectrum or the magnitude spectrum of x(t), being a continuous spectrum. 3 - 858 19 Elements of theory For nonperiodic functions, Parseval's theorem becomes E = ~ + oo +oo +co ~ x 2 (t) dt = 21,.