By Wodek Gawronski
The publication offers and integrates the equipment of structural dynamics, identity and keep an eye on right into a universal framework. It goals to create a typical language among structural and regulate process engineers.
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Extra resources for Advanced Structural Dynamics and Active Control of Structures
The standard models include structures that are stable, linear, continuous-time, and with proportional damping. We derive the structural analytical models either from physical laws, such as Newton’s motion laws, Lagrange’s equations of motion, or D’Alembert’s principle , ; or from finite-element models; or from test data using system identification methods. The models are represented either in time domain (differential equations), or in frequency domain (transfer functions). We use linear differential equations to represent linear structural models in time domain, either in the form of second-order differential equations or in the form of first-order differential equations (as a state-space representation).
These coordinates are often used in the dynamics analysis of complex structures modeled by the finite elements to reduce the order of a system. It is also used in the system identification procedures, where modal representation is a natural outcome of the test. Modal models of structures are the models expressed in modal coordinates. Since these coordinates are independent, it leads to a series of useful properties that simplify the analysis (as will be shown later in this book). The modal coordinate representation can be obtained by the transformation of the nodal models.
1) with the initial state x(0) xo . In the above equations the N-dimensional vector x is called the state vector, xo is the initial condition of the state, the s-dimensional vector u is the system input, and the r-dimensional vector y is the system output. The A, B, and C matrices are real constant matrices of appropriate dimensions (A is NuN, B is Nus, and C is ruN). We call the triple ( A, B, C ) the system state-space representation. Every linear system, or system of linear-time invariant differential equations can be presented in the above form (with some exceptions discussed in Chapter 3).