Download Twelve Lectures on Structural Dynamics by André Preumont PDF

By André Preumont

This textual content addresses the modeling of vibrating platforms with the viewpoint of discovering the version of minimal complexity which money owed for the physics of the phenomena at play. the 1st half the e-book (Ch.1-6) offers with the dynamics of discrete and non-stop mechanical platforms; the classical procedure emphasizes using Lagrange's equations. the second one half the e-book (Ch.7-12) offers with extra complex subject matters, infrequently encountered within the current literature: seismic excitation, random vibration (including fatigue), rotor dynamics, vibration isolation and dynamic vibration absorbers; the ultimate bankruptcy is an creation to energetic regulate of vibrations.

The first a part of this article can be used as a one semester direction for third 12 months scholars in Mechanical, Aerospace or Civil Engineering. the second one a part of the textual content is meant for graduate sessions. a collection of difficulties is supplied on the finish of each bankruptcy.

The writer has a 35 years adventure in a variety of elements of Structural dynamics, either in (nuclear and aerospace) and in academia; he was once one of many pioneers within the box of lively buildings. he's the writer of a number of books on random vibration, energetic buildings and structural control.

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B) Free to rotate in A and B. (c) Clamped in A and free in B. 8 Problems 39 Fig. f. lumped mass system with various damping configurations. Fig. 13 Shaft with two disks. Fig. 14 Three mass system. 3 Write the equations governing the vibration of the three-mass system of Fig. 14. Find the mode shapes in the particular case M = m. 4 Write the equations governing the vibration of the suspension system of Fig. 15. Find the natural frequencies, the modes and the modal damping ratios. 5 Show that if φi and φ j are mode shapes with the same natural frequency ωi , aφi + bφ j is also a mode shape with the same natural frequency, for any a and b.

8 Pole/Zero pattern of a structure with collocated (dual) actuator and sensor. (a) Undamped. (b) Lightly damped (only the upper half of the complex plane is shown, the diagram is symmetrical with respect to the real axis). axis. The pole / zero pattern is that of Fig. 8a. The situation depicted in Fig. 7 is that where there is no rigid body mode. In presence of rigid body modes, the FRF starts from −∞ at ω = 0 and there is an additional zero such that 0 < z 1 < ω1 . For a lightly damped structure, the poles and zeros are just moved a little in the left-half plane, but they are still interlacing, Fig.

2). f. ; they are usually ordered by increasing frequencies (ω1 ≤ ω2 ≤ . . ≤ ωn ). 6) The properties of K and M guarantee that the mode shapes φi are real. Note that Eq. 6) defines only the shape, but not the amplitude of the mode which can be scaled arbitrarily. The mode shapes are not just mathematical quantities: they can be observed even on lightly damped structures by exciting them at a natural frequency. As an example, consider the two mass system of the previous section in the particular case where m 1 = m 2 = m.

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