CBCGS [2019 - current]

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## University of Mumbai Semester 7 (BE Fourth Year) Structural Dynamics Revised Syllabus

University of Mumbai Semester 7 (BE Fourth Year) Structural Dynamics and their Unit wise marks distribution

### Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Introduction | - |

200 | Single Degree of Freedom (Sdof) Systems | - |

300 | Generalized Single-degree of Freedom System | - |

400 | Lumped Mass Multi Degree of Freedom (Mdof) System | - |

500 | Structure with Distributed Mass System | - |

600 | Random Vibrations | - |

700 | Stochastic Response of Linear Sdof Systems | - |

Total | - |

## Syllabus

100 Introduction

- Introduction to structural dynamics, definition of basic problem in dynamics, static v/s dynamic loads, different types of dynamic load.

200 Single Degree of Freedom (Sdof) Systems

- Undamped vibration of SDOF system, natural frequency and period of vibration, damping in structures, viscous damping and coulomb damping, effect of damping on frequency of vibration and amplitude of vibration, Logarithmic decrement.
- Forced vibration, response to harmonic forces, periodic loading, dynamic load factors, response of structure subjected to general dynamic load, Duhamel's integral, numerical evaluation of dynamics response of SDOF systems subjected to different types of dynamic loads.
- Introduction to frequency domain analysis, response of structure in frequency domain subjected to general periodic and non-periodic / impulsive forces of short duration, use of complex frequency response function.
- Use of Fourier Series for periodic forces, introduction to vibration isolation. Distributed mass system idealized as SDOF system, use of Rayleigh's method, response of SDOF system subjected to ground motion.

300 Generalized Single-degree of Freedom System

- Generalized properties, assemblages of rigid bodies,
- systems with distributed mass and elasticity,
- expressions for generalized system properties

400 Lumped Mass Multi Degree of Freedom (Mdof) System

- Coupled and uncoupled systems, direct determination of frequencies of vibration and mode shapes, orthogonality principle, vibration of MDOF systems with initial conditions, approximate methods of determination of natural frequencies of vibration and mode shapesvector iteration methods, energy methods and use of Lagrange's method in writing equations of motions.
- Decoupling of equations of motion, modal equation of motion, concept of modal mass and modal stiffness, forced vibration of MDOF system, modal analysis, and application to multi storey rigid frames subjected to lateral dynamic loads.

500 Structure with Distributed Mass System

- Use of partial differential equation, free vibration analysis of single span beams with various boundary conditions, determination of frequencies of vibration and mode shapes, forced vibration of single span beams subjected to the action of specified dynamic loads.

600 Random Vibrations

- Probability theory: Single random variable, important averages of single random variable, two random variables, important averages of two variables, principal axis of joint probability density function, Rayleigh’s probability density function.
- Random processes, stationary and ergodic processes, autocorrelation function, power spectral density function, relationship between power spectral and autocorrelation functions, power spectral density and autocorrelation functions for derivatives of processes, superposition of stationary processes, stationary Gaussian processes, stationary white noise, probability distribution for maxima and extreme values.

700 Stochastic Response of Linear Sdof Systems

- Transfer functions, relationship between input and output autocorrelation functions, relationship between input and output power spectral density functions, response characteristics for narrowband systems

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