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36762 results in Cambridge Textbooks

Page 642 of 1839

  • 4 - Structural Dynamics

  • Sung W. Lee, University of Maryland, College Park, Peter W. Chung, University of Maryland, College Park
  • Book:
    Finite Element Method for Solids and Structures
    Published online:
    08 July 2021
    Print publication:
    17 June 2021, pp 111-137

  • Summary

    In this chapter, we consider time-dependent problems of discrete systems with N DOF. We will show how the finite element formulation is used to construct the element mass matrices, which are assembled into the global mass matrix. We will consider free vibration, to determine natural frequencies and natural modes of a finite element model through eigenvalue analysis, and numerical methods for integrating the equation of motion in time which can be used to determine dynamic response under applied loads and given initial conditions. The Lagrange equation will be shown to demonstrate how it can be applied to construct equations of motion. Once again we will consider slender bodies undergoing uniaxial vibration, torsional vibration, and bending vibration. A formal derivation of the Lagrange equation will be considered in a later chapter.

Advanced Optimization for Process Systems Engineering
  • Ignacio E. Grossmann
  • Published online:
    11 June 2021
    Print publication:
    25 March 2021
  • Based on the author's forty years of teaching experience, this unique textbook covers both basic and advanced concepts of optimization theory and methods for process systems engineers. Topics covered include continuous, discrete and logic optimization (linear, nonlinear, mixed-integer and generalized disjunctive programming), optimization under uncertainty (stochastic programming and flexibility analysis), and decomposition techniques (Lagrangean and Benders decomposition). Assuming only a basic background in calculus and linear algebra, it enables easy understanding of mathematical reasoning, and numerous examples throughout illustrate key concepts and algorithms. End-of-chapter exercises involving theoretical derivations and small numerical problems, as well as in modeling systems like GAMS, enhance understanding and help put knowledge into practice. Accompanied by two appendices containing web links to modeling systems and models related to applications in PSE, this is an essential text for single-semester, graduate courses in process systems engineering in departments of chemical engineering.

Page 642 of 1839