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Implementing Applied Dynamics

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Novel Teaching Methods In Engineering Technology

Tagged Division

Engineering Technology

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Paper Authors

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Michael Spektor Oregon Institute of Technology


Walter W. Buchanan P.E. Texas A&M University

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Walter W. Buchanan is a Professor at Texas A&M University. He is a Fellow and served on the Board of Directors of both ASEE and NSPE, is a past president of ASEE and the Massachusetts Society of Professional Engineers, and is a registered P.E. in six states. He is a past member of the Executive Committee of ETAC of ABET and is on the editorial board of the Journal of Engineering Technology.

Michael B. Spektor
Michael Spektor holds a degree of a mechanical engineer from Kiev Polytechnic University and a Ph.D. degree from Kiev Construction University. He is a former Professor and Department Chair of the Department of Mechanical and Manufacturing Engineering Technology at Oregon Institute of Technology. He launched and for many years was until retirement the director of the Bachelor's degree completion program in manufacturing engineering technology at Boeing (Seattle). In addition to his work in the USA, he has worked in industry and in higher education in Israel and former USSR. He is the author of numerous scientific papers and two books in the area of Dynamics published recently by Industrial Press.

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Lawrence J. Wolf P.E. Oregon Institute of Technology

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Professor Wolf received his DSc in structural engineering at Washington University, St. Louis. As associate professor at Purdue University Calumet, he headed the department of Manufacturing Engineering Technology. He went on to become the dean of the College of Technology at the University of Houston Then he moved to Oregon Tech to become the president of OIT. He maintains his professorship but has been retired from the presidency since 1998. Industrially Wolf has been an engineer with Chevron, Monsanto, McDonnell Douglas, and Boeing, and a visiting scientist in residence at the Brookhaven National Laboratory. He teaches mechanical design and takes active interest in product lifecycle management software, including CATIA in full-associativity and functionality. He advises senior projects and masters theses. Professor Wolf is a life member and fellow of both the ASEE and the ASME. He is a fellow of ABET. He holds active PE registrations in Missouri and Oregon. His international activities have included Saudi Arabia, Iran, Norway, Nigeria, Singapore and Japan.

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The programs in mechanical engineering and related fields do not provide adequate training to enable graduates to conduct analytical investigations of actual problems in dynamics. An analytical approach to the improvement and development of mechanical systems allows the purposeful control of the parameters and in the same time saves time and resources. The analytical investigation in applied dynamics comprises the following three steps: 1) Composing the differential equation of motion of the system and determining the initial conditions of motion; 2) Solving the differential equation of motion for the initial conditions of motion; 3) Analyzing the solution according to the goal of the investigation.

As it is well known, the differential equation of motion consists of loading factors: forces or moments. Active loading factors cause the motion, while resisting loading factors oppose the motion. The left side of the differential equation of motion consists of the sum of resisting loading factors including the force or moment of inertia, while the right side of the equation includes the sum of active loading factors (in the absence of active factors the right side of the equation equals zero). This looks simple, however sometimes it becomes not that simple when confronting a real-life engineering problem. On the beginning, the investigator, based on the information of the problem, should figure out the characteristics of the loading factors that are applied to the system. Obviously, insignificant loading factors could be ignored. It should be emphasized that the results of the investigation depend upon the measure of accuracy that the differential equation reflects the working process of the system.

The engineering programs do not offer a straightforward universal methodology of solving linear differential equations of motion. However, as it is known, the Laplace Transform allows solving any linear differential equation of motion or a system of two linear differential equations of motion for a two-degree-of-freedom system. The Laplace Transform methodology comprises the following three steps: 1) Converting the differential equation of motion into a corresponding algebraic equation of motion based on Laplace Transform Pairs that are represented in tables. There is no need to memorize the fundamentals of Laplace Transform in order to use the tables that are available in numerous publications; 2) Solving the obtained algebraic equation of motion for the displacement in the Laplace domain. 3) Inverting the obtained solution in the second step into the time domain. This inversion is also based on the Laplace Transform Pairs and actually represents the solution of the differential equation of motion.

The solution represents the law of motion of the system or its displacement as a function of time. The analysis of the solution includes taking the first and second derivatives of the displacement in order to determine the velocity and acceleration. By applying conventional mathematical actions to the obtained parameters of motion, it is possible to determine the role of the parameters of the system in achieving the goal of the investigation.

Spektor, M., & Buchanan, W. W., & Wolf, L. J. (2016, June), Implementing Applied Dynamics Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26204

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