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On Implementing General Modal Analysis Within The Mathcad® Software Package

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2003 Annual Conference


Nashville, Tennessee

Publication Date

June 22, 2003

Start Date

June 22, 2003

End Date

June 25, 2003



Conference Session

Computed Simulation and Animation

Page Count


Page Numbers

8.886.1 - 8.886.12

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Paper Authors

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Ira Lockwood

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Caleb Chitwood

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Byron Newberry

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 2320

On Implementing General Modal Analysis within the Mathcad® Software Package

B. L. Newberry, C. Chitwood, and I. Lockwood

Oklahoma Christian University

I. Abstract

A general Mathcad 1 model is presented to simulate the suspension dynamics of a small off-road vehicle designed for the SAE Mini-Baja collegiate competition. The model uses the method of Modal Analysis to solve the multiple degree-of-freedom dynamic system. Model variations addressing both front quarter car dynamics (with tire stiffness effects) and half car pitch/heave dynamics are discussed, each subject to arbitrary forcing. The model presented, generated as part of a student project within the senior Machine Vibrations class at Oklahoma Christian University, allows the students to integrate several analytical techniques into a single computational design tool. With the simulation process automated within Mathcad, the student designer is free to concentrate on parametric studies and optimization of the suspension response. Moreover, the presented model allows the designer to consider realistic (i.e. arbitrary) off-road ground profiles. The educational strengths of this integrated Mathcad model are discussed.

II. Background

Most practical dynamic systems incorporate multiple degrees-of-freedom and are subject to complex, if not random, excitation. Hand analysis of such a system in an undergraduate setting is a daunting task. In an effort to reduce the complexity of the analyses, greatly simplified academic models often replace realistic systems. Such academic models, though simpler, are less interesting and fail to expose students to the challenge of more complicated systems.

An approach for analyzing multiple degree-of-freedom dynamic systems, subject to arbitrary excitation, is herein proposed. The proposed model implements the method of Linear Modal Analysis2 within the Mathcad software suite. Modal analysis, as outlined in the next section, requires many calculations to determine the response of the system. As such, it is prohibitive for student to consider design variations via hand calculations using this approach. The ideal balance is for the student, once he or she understands the methodology and required calculation steps, to implement the model within a computational environment that facilitates “what if” experimentation. Mathcad is ideally suited for this task as it allows the analyst to focus on the implementation, not the mathematical manipulations.

Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright © 2003, American Society for Engineering Education

Lockwood, I., & Chitwood, C., & Newberry, B. (2003, June), On Implementing General Modal Analysis Within The Mathcad® Software Package Paper presented at 2003 Annual Conference, Nashville, Tennessee.

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