By Wodek Gawronski
The ebook offers and integrates the equipment of structural dynamics, indentification and keep watch over right into a universal framework. It goals to create a typical language among structural and keep watch over procedure engineers.
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Extra resources for Advanced Structural Dynamics & Active Control of Structures
3. Determine the first four natural modes and frequencies of the beam presented in Fig. 5. Using the finite-element model we find the modes, which are shown in Fig. 3. 7 rad/s. mode 4 displacement, y-dir. 3. Beam modes: For each mode the beam displacements are sinusoidal and have the same frequency, and the displacements are shown at their extreme values. 4. Determine the first four natural modes and frequencies of the antenna presented in Fig. 6. We used the finite-element model of the antenna to solve this problem.
Clearly the total response as in Fig. 7 is a sum of the individual responses. Note that each response is a sinusoid of frequency equal to the natural frequency, and of exponentially decayed amplitude, proportional to the modal damping ] i . Note also that the higher-frequency responses decay faster. 5. Transfer function of a simple system: (a) Magnitude shows three resonance peaks; and (b) phase shows three shifts of 180 degrees; Z1 , Z 2 , and Z3 denote the natural frequencies. 6. The transfer functions of single modes and of the structure: (a) Magnitudes; and (b) phases.
17) where D1 and D 2 are nonnegative scalars. Modal models of structures are the models expressed in modal coordinates. In order to do so we use a modal matrix to introduce a new variable, qm , called modal displacement. This is a variable that satisfies the following equation: q )qm . 7) by )T , obtaining )T M )qm )T D) qm )T K ) qm y Coq )qm Cov )qm . 16) we obtain the above equation in the following form: M m qm Dm qm K m qm )T Bo u , y Coq )qm Cov )qm . Next, we multiply (from the left) the latter equation by M m1 , which gives qm M m1Dm qm M m1K m qm M m1)T Bo u , y Coq )qm Cov )qm .