530_343lecture05

# 530_343lecture05 - ME 530.343 Design and Analysis of...

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ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 5 – Mass-Spring Systems and Equivalent Mechanical Systems Wednesday, February 11, 2009 1 Today’s Objectives Purpose of today’s lecture: Degrees of freedom Identify equivalent systems: m eq ¨ x + b eq ˙ x + k eq x = f eq Springs and dampers in series and in parallel Reading: Palm Chapter 4.1, 4.2, 4.4, 4.5 (ignore Laplace transform examples for now) 2 Degrees of Freedom To begin modeling any dynamic system, you first know how many degrees of freedom there are in the system. This will tell you: How many equations of motion you will finding The size of the matrix equation describing the system (if you need to put it in that form, as we will in the last half of this course) How many and which system variables you will select The number of degrees of freedom is the number of parameters that can be independently varied in a system . Test for simple mass-spring-damper systems: Can you hold one mass in a mechanical system at a constant position, but still move another mass in the system? m m k For complex or continuous systems (e.g., buildings), the concept of (finite) degrees of freedom is not as well defined. You typically want to create a model that has enough degrees of freedom to appro- priately characterize the system’s behavior, but not so many that the computational requirements are too high.

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• Spring '08
• Sun
• k2, World War I submarines of the United Kingdom, equivalent weight, All wheel drive vehicles, Barrow-built ships, B2 X2

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