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Engineering Vibration Analysis: Worked Problems 2 by Professor Valery A. Svetlitsky (auth.)

By Professor Valery A. Svetlitsky (auth.)

The two-volume paintings "Engineering Vibration research" is dedicated to difficulties on vibration idea research, that's presently one of many basic classes in mechanical engineering departments at technical universities.

The first quantity is dedicated to platforms with a finite variety of levels of freedom and non-stop platforms are analyzed within the moment. within the first a part of every one quantity difficulties are posed and within the moment half the exact suggestions to those difficulties are handled. traditional and complex difficulties requiring deeper wisdom of the vibration thought are analyzed. particularly, difficulties are formulated linked to the choice of frequencies and vibration modes, the examine of loose and compelled vibrations, in addition to with parametric and nonlinear vibration research. the issues linked to selection of serious parameters, dynamic balance and with random vibrations also are thought of. The algorithms for his or her strategies are offered with chance features calculation, and a reliability estimation (probability of non-failure operation) of the corresponding mechanical procedure.

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51. 63 Determine the first three frequencies of free longitudinal vibrations of the rod with mass Mat the end (Fig. 50) if M = m 0 l, where m 0 is the mass of the rod unit length. 64 Determine the first three frequencies of free vibrations of a rod with a concentrated mass at the end (Fig. 50) for the case when the upper section is free (M =mol, where mo is the mass of the rod unit length). 65 The upper section of the rod (Fig. 51) is forcibly displaced in the vertical direction according to the law z = A sin wt.

Determine using the Galerkin method the fundamental frequency of free vibrations under a single-term approximation. I Fig. 59. 77 Refine the fundamental frequency obtained under the first approximation (see Problem 76) by considering the second approximation. 78 Determine the first frequency of free vibrations of the rod (Fig. 60) whose bending stiffness is EJx, the mass per unit length is m 0 , the length is l, and the distance between supports is b = l/2. I z z l Fig. 60. Y Fig. 61. 79 At the moment t = 0 the force Po is suddenly applied to the rod of constant stiffness (Fig.

68. 86 A perfectly incompressible fluid flows with the constant velocity w inside the hinge-supported pipeline (Fig. 68). Derive the differential equation of 30 1 Problems and Examples small transverse vibrations of the pipeline taking t he moving fluid into account. Determine (by the approximate method) the first two frequencies of vibrations. P = 2700 kgjm3 ( duralumin), and the elasticity modulus of the first kind is E = 70 GPa. 68 kgjm. Determine the frequencies of vibrations for three values of the velocity of fluid motion: w 1 = 0 , w 2 = 10, and w3 = 20 m j s.

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