# Curriculum Map

# Course: Vibration and Control

**Description**

This curriculum map provides a mapping of content from *Marks' Standard Handbook for Mechanical Engineers* to standard Vibration and Control course topics. The authors carefully selected relevant examples, videos, tables and figures which they felt would be valuable supplements to any standard Vibrations textbook. You can easily incorporate the content into your course by using our copy link functionality to paste a direct link into your school's LMS.

**Author**

Ali Sadegh, Editor, Marks' Standard Handbook for Mechanical Engineers, 11th Edition

## Course Topics

**VIBRATION**

- Free Vibration of Damped Systems
- Multi-Degree-of-Freedom Systems
- Vibration of Rods, Shafts and Strings
- Vibration of Continuous System, Membrane and Plates

**CONTROL**

- Transient Control System
- Block Diagrams
- Controller Mechanisms
- Control Elements
- Hydraulic-Valves Control Systems
- Closed-Loop Block Diagram
- Frequency Response
- Stability and Performance of an Automatic Control System
- Sampled-Data Control Systems
- LQG/LTR Controller Design

## Vibration

## Free Vibration of Damped Systems

## Multi-Degree-of-Freedom Systems

Relevant Material | Type | Description | Source |
---|---|---|---|

Multi-Degree-of-Freedom Systems | Text | Marks' Standard Handbook for Mechanical Engineers | |

Multi-degree-of-freedom system | Figure | Fig. 3.4.23 | Marks' Standard Handbook for Mechanical Engineers |

Vibration absorber | Figure | Fig. 3.4.25 | Marks' Standard Handbook for Mechanical Engineers |

## Vibration of Rods, Shafts and Strings

Relevant Material | Type | Description | Source |
---|---|---|---|

Vibration of Rods, Shafts and Strings | Text | Marks' Standard Handbook for Mechanical Engineers | |

Analogous Quantities for Rods, Shafts, and Strings | Table | Table 3.4.4 | Marks' Standard Handbook for Mechanical Engineers |

Normalized Natural Frequencies for Various Beams | Table | Table 3.4.6 | Marks' Standard Handbook for Mechanical Engineers |

## Vibration of Continuous System, Membrane and Plates

Relevant Material | Type | Description | Source |
---|---|---|---|

Vibration of Membranes | Text | Perry's Chemical Engineers' Handbook | |

Uniform circular membrane fixed at r = a. | Text | Marks' Standard Handbook for Mechanical Engineers | |

Circular membrane normalized natural frequencies | Table | Table 3.4.7 | Marks' Standard Handbook for Mechanical Engineers |

Circular plate normalized natural frequencies | Table | Table 3.4.8 | Marks' Standard Handbook for Mechanical Engineers |

Potential energy for various systems | Table | Table 3.4.9 | Marks' Standard Handbook for Mechanical Engineers |

## CONTROL

## Transient Control Systems

Relevant Material | Type | Description | Source |
---|---|---|---|

Transient Analysis of a Control System | Text | Marks' Standard Handbook for Mechanical Engineers | |

System response to a unit step-function command | Figure | Fig. 16.2.7 | Marks' Standard Handbook for Mechanical Engineers |

Transient response of a 2nd order viscous-damped control | Figure | Fig. 16.2.9 | Marks' Standard Handbook for Mechanical Engineers |

Derivative and integral compensation of a basic closed-loop system | Figure | Fig. 16.2.12 | Marks' Standard Handbook for Mechanical Engineers |

## Block Diagrams

Relevant Material | Type | Description | Source |
---|---|---|---|

Block Diagrams | Text |
Marks' Standard Handbook for Mechanical Engineers | |

Single-loop feedback control system | Figure | Fig. 16.2.15 | Marks' Standard Handbook for Mechanical Engineers |

Reduction of a closed-loop control system with multiple 2nd loops | Figure | Fig. 16.2.16 | Marks' Standard Handbook for Mechanical Engineers |

## Controller Mechanisms

Relevant Material | Type | Description | Source |
---|---|---|---|

Controller Mechanisms | Text |
Marks' Standard Handbook for Mechanical Engineers | |

Gain reduction of pneumatic amplifier by means of feedback bellows | Figure | Fig. 16.2.18 | Marks' Standard Handbook for Mechanical Engineers |

Proportional controller with negative feedback | Figure | Fig. 16.2.19 | Marks' Standard Handbook for Mechanical Engineers |

Proportional-derivative controller | Figure | Fig. 16.2.20 | Marks' Standard Handbook for Mechanical Engineers |

Proportional-integral controller | Figure | Fig. 16.2.21 | Marks' Standard Handbook for Mechanical Engineers |

Simplified circuit for a typical electronic controller | Figure | Fig. 16.2.22 | Marks' Standard Handbook for Mechanical Engineers |

Block diagram of PID controller | Figure | Fig. 16.2.23 | Marks' Standard Handbook for Mechanical Engineers |

Combined controller block diagram | Figure | Fig. 16.2.24 | Marks' Standard Handbook for Mechanical Engineers |

## Controller Elements

Relevant Material | Type | Description | Source |
---|---|---|---|

Final Control Elements | Text |
Marks' Standard Handbook for Mechanical Engineers | |

Control valve and pneumatic actuator | Figure | Fig. 16.2.25 | Marks' Standard Handbook for Mechanical Engineers |

Control valve linear flow characteristic | Figure | Fig. 16.2.26 | Marks' Standard Handbook for Mechanical Engineers |

## Hydraulic-Valves Control Systems

Relevant Material | Type | Description | Source |
---|---|---|---|

Hydraulic-Control Systems | Text |
Marks' Standard Handbook for Mechanical Engineers | |

Four-way valve-piston circuit | Figure | Fig. 16.2.27 | Marks' Standard Handbook for Mechanical Engineers |

Valve-piston position servomechanical feedback | Figure | Fig. 16.2.28 | Marks' Standard Handbook for Mechanical Engineers |

Two-stage electrohydraulic servo valve | Figure | Fig. 16.2.29 | Marks' Standard Handbook for Mechanical Engineers |

Flapper valve | Figure | Fig. 16.2.30 | Marks' Standard Handbook for Mechanical Engineers |

Equilibrium curve of P2 versus x for a flapper valve | Figure | Fig. 16.2.31 | Marks' Standard Handbook for Mechanical Engineers |

## Closed-Loop Block Diagram

Relevant Material | Type | Description | Source |
---|---|---|---|

Closed-Loop Block Diagram | Text |
Marks' Standard Handbook for Mechanical Engineers | |

Block diagram of a thermal system | Figure | Fig. 16.2.32 | Marks' Standard Handbook for Mechanical Engineers |

Process characteristics versus mode of control | Table | Table 16.2.3 | Marks' Standard Handbook for Mechanical Engineers |

## Frequency Response

## Stability and Performance of an Automatic Control System

Relevant Material | Type | Description | Source |
---|---|---|---|

Stability and Performance of an Automatic Control | Text | Marks' Standard Handbook for Mechanical Engineers | |

Typical KG (jv) loci illustrating application of Nyquist's stability criterion | Figure | Fig. 16.2.40 | Marks' Standard Handbook for Mechanical Engineers |

Nyquist stability criterion in terms of log magnitude KG (jv) diagrams | Figure | Fig. 16.2.41 | Marks' Standard Handbook for Mechanical Engineers |