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# Mechanical Vibrations

The course will cover fundamental concepts on the vibration of mechanical systems including, but not limited to, review of systems with one degree for freedom, Lagrange's equations of motion for multiple degree of freedom systems, introduction to matrix methods, transfer functions for harmonic response, impulse response, and step response, convolution integrals for response to arbitrary inputs, principle frequencies and modes, applications to critical speeds, measuring instruments, isolation, torsional systems, introduction to nonlinear problems.

## ME56300

3

### Learning Objective:

1. Develop equations of motion for single degree of freedom, multiple degree of freedom and continuous systems through Newton's Methods and Lagrange Equations
2. Analytically solve the equations of motions for a lumped parameter and continuous system
3. Analyze and understand the time and frequency dependent behavior of a mechanical system

### Description:

The course will cover fundamental concepts on the vibration of mechanical systems including, but not limited to, review of systems with one degree for freedom, Lagrange's equations of motion for multiple degree of freedom systems, introduction to matrix methods, transfer functions for harmonic response, impulse response, and step response, convolution integrals for response to arbitrary inputs, principle frequencies and modes, applications to critical speeds, measuring instruments, isolation, torsional systems, introduction to nonlinear problems.

### Topics Covered:

Dynamics of Single Degree Of Freedom (SDOF) systems; Dynamics of Multiple Degree Of Freedom (MDOF) systems; Damping; Fundamentals of analytical dynamics; Numerical techniques for the response of dynamical systems; Dynamics of continuous systems; Analytical and approximate solutions of continuous systems; Intro to the dynamics of discrete nonlinear systems and perturbation techniques; Static and dynamic reduction.

### Prerequisites:

Undergraduate class in Rigid Body Dynamics and Differential Equations.

40/60

### Homework:

There will be 6-8 homeworks in the class, you are given 1-2 weeks to finish them. They are typically 3-4 problems and may require coding in Matlab or Python for some problems.

### Textbooks:

#### Required:

"Mechanical Vibrations: A Lecturebook", Chuck Krousgrill and Jeff Rhoads.

### Computer Requirements:

Matlab or Numerical Package in Python