### Mechanical Vibrations

#### ME 56300 / 3 Cr. (3 Class)

Review of systems with one degree of freedom. Lagrange's equations of motion for multiple-degree-of-freedom systems. 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. Nonlinear problems. Mechanics staff.

**Available Online:** No

**Credit by Exam:** No

**Laptop Required:** No

**Prerequisites/Co-requisites:**

P: ME 27200, ME 27400 and ME 33000 or equivalent.

##### Outcomes

**After completion of this course, the students should be able to:**

- Explain the concept of modes of vibration, and the difference between single-, two- and multi-degree-of-freedom vibrating systems.[a]
- Formulate the equation of motion of a single degree-of-freedom vibration system using Newton's laws of motion. [a]
- Formulate the equations of motion of lumped parameter multi-degree-of-freedom systems using Newton's laws of motion. [a]
- Formulate the equations of motion of a multi-degree of freedom system using Lagrange’s Equations. [a]
- Analytically and numerically predict the dynamic response of a single degree-of-freedom mass-spring-damper system with no force excitation, with harmonic force excitation, and with general force excitation. [a, k]
- Analytically and numerically predict the dynamic response of 2-DOF systems and multi-degree of freedom systems with no force excitation, with harmonic force excitation, and with general force excitation. [a, k]
- Explain the difference between free and forced vibration. [a]
- Predict the dynamic response of vibrating systems with viscous damping and Coulomb damping. [a]
- Analytically predict the dynamic response of cables/strings, beams and membranes. [a]
- Determine the mode shapes and natural frequencies of a multi-degree of freedom system. [a, k]
- Control and reduce vibrations using mass balancing techniques, damping, vibrations isolators and vibration absorbers. [a, k]

Note: The letters within the brackets indicate the general program outcomes of mechanical engineering. See: ME Program Outcomes.