ME242 Mechanical Systems Laboratory Tabletop Poster Presentations

Transcription

1 ME242 Mechanical Systems Laboratory Tabletop Poster Presentations Daniel. S. Stutts, Ph.D. Associate Professor of Mechanical Engineering and Office: 282 Toomey URL: Ph: Wednesday, February 12, 2014

2 Overview Ideas for Final Experiment Basic Requirements (see ME242 Intro PPT and Experimental Planning and Design Guidelines Prototype Final Experiment Proposal Format (what you must prepare for) Content (what to show) Structure (how to show it) Example

3 Ideas For 4 th Experiment See the ME242 Website: Talk to faculty who work in an area you are interested in. Guidelines for experimental planning and design: Experimental Planning and Design.pdf (referenced on previous slide) Purchasing procedures and limitations

4 Basic Requirements for 4 th Lab 1. Must contain an experimental component i.e. measurement of a system property or properties 2. Must be based on sound physical principles A. Must test a hypothesis (statistically) B. Or must validate a mathematical model best if all experimental hypotheses can be reduced to mathematical models. This is usually easier than option A. C. In either A or B, you must cite at least one publication from the primary literature e.g. a peer-reviewed journal article. Refer to the latest draft of the ME242 Text for more details.

5 Example Proposal Dynamic Vibration Absorber Proposal

6 Format Format Considerations 48 by 36 poster developed on PowerPoint, and obtained from library ($10 for nonlaminated version) Link to library poster information Two groups will share a 6 foot table with whatever you want on it that can Multiple presenters and browsing general audience Will leave poster up all day, so it should be sufficiently self-explanatory.

7 Content Who you are make sure to put your names on your poster! What you were trying to accomplish How you did it Results Conclusions and recommendations References (Bibliography)

8 Content continued Show ALL key equations in your derivations within the limits of available space. Be sure to include enough theory and derivations for the audience to see what you did. If you cannot fit your derivation on your poster, then provide the details in a handout.

9 Structure 1. Comparison of model to experiment a. Linear top-down, right to left flow of results and conclusions culminating with comparison of model to data b. Bi-radial: in the middle, who you are, followed by results and conclusions. Development on either side.

10 Structure 2. Before and After Treatment Statistical Analysis a. Semi-bi-lateral: Introduction on left, followed by before treatment in the middle, and after on the right side. b. Bi-radial: Introduction etc. in middle with before and after treatment on the left and right respectively.

11 Other Considerations Make sure the font is large enough to be easily read! Wear business-formal attire i.e. men wear suit or sport coat, slacks, and a tie. Only death or incapacitation should prevent you from attending the presentation!

12 Other formats and Structures There are many ways to layout a poster presentation. The keys are: Make the font legible Make the flow logical, and what you did as obvious as possible to the uninitiated. Make sure ALL presenters know what they are talking about!

13 Project Description The Effect of a Localized Mass Non-Uniformity on a Longitudinally Vibrating Piezoelectric Rod Husain Shekhani Faculty Advisor: Dr. Daniel S. Stutts Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology Funded by Opportunities for Undergraduate Research (OURE) In this project the effects of a localized (point) mass nonuniformity located arbitrarily on a longitudinally vibrating piezoelectric rod is explored. The project consisted of analytical development and experimental verification. In the analytical modes, the point-mass non-uniformity is accounted for using the receptance method. Expressions for the natural frequencies, modes, and the forced solution for the non-uniform rod and corresponding impedance are developed in closed form. The model is experimentally verified using impedance data from piezoelectric rods with attached concentrated masses. The modeling approach detailed in this paper is potentially useful in the design of piezoelectric transformers and health monitoring of piezoelectric sensors and devices, as well as other piezoelectric applications. Experimental Setup Analytical Results Natural Frequency Mode Shapes M =0.3 m Goals Develop and simulate the analytical parameters of interest Confirm the accuracy of the analytical models using experimental impedance testing Predict and observe the occurrence of even modes of vibration on the perturbed piezoelectric rod structure Point- Mass Proper:es Placement (a) Mass (M) Mode Number L % % % 0.10 L % % % Placement of the Point Mass (a) 0.15 L 0.20 L 0.25 L % % % % % 0.00% % % % Rod B 0.30 L 0.31 m Experimental Results Impedance Trace-Rod A Mode Shapes of a Uniform Vibrating in its Longitudinal Direction with Free BC s System of Interest Rod A 0.26 L 0.31 m 0.40 L % % % 0.50 L 0.00% % 0.00% Percent Difference of Combined System Natural Frequency Based the Placement of the Localized Point-Mass (M =0.3 m) Forced Response M = 0.3 m Governing Equations Piezoelectric Constitutive Equations: Equation of Motion: Piezoelectric Forcing Term : Definition of Receptance: Combined System Mode Shape: nπ nπ L L n,c 2 nπ 2 n =1 c L Frequency equation for the combined mass-piezoelectric rod system: n,c 2 u T =Y e E ( x, t ) x YA a = 0.2 L Uniform Rod Perturbed Rod Percent Natural Frequency Natural Frequency Difference (khz) (khz) % Off-Resonance Forced Response Resonance Forced Response Modal Participation Ae V (δ ( x x ) δ ( x x2 ))e jωt h deflection at location a harmonic force at location a receptance Analytical Models U ( x) = 2 ρla cos( (Y ( U (a) a) cos( x) ) ) ρω 1 =0 Mωc Effect of Varying the Mass Experimental Results Impedance Trace-Rod B a = 0.2 L u D =e + ε 31E ( x, t ) x Effect of Varying the Position u u M δ (x a) ρ A = f (x, t) x t f ( x, t ) = Impedance Trace M = 0.3 m Variable definitions M = mass of the point-mass m = mass of the rod a = placement of the point-mass L = length of the rod Conclusions Reducing the loss parameter enables the model to capture the second resonance-anti-resonance frequencies Analytical Models Cont. 1) The receptance method was shown to accurately predict the natural frequencies of the Impedance Formulation: 2 2) Adding a mass non-uniformity was shown to excite the even modes of vibration 3) Future studies will investigate stiffness non-uniformities as well as combinations of both mass and stiffness non-uniformities 2 Y (ω ) = Re{Y (ω )} + Im{Y (ω )} combined system, as seen from the impedance measurements Re{Y (ω )} = Im{Y (ω )} = be31 ω X c (U n,c ( x1 ) U n,c ( x2 ) )sin(φc ) V0 c =1 be31 ω X c (U n,c ( x1 ) U n,c ( x2 ) )cos(φc ) c0ω V0 c =1 Z (ω ) = 1 Y (ω )

14 ME242 4th Lab Ideas Ideas page

15 Dynamic Absorber/Tuned Mass Damper

16 Transient Heat Conduction/Convection

17 Schematic of Conductive Rod 1 Control feedback thermocouple 2 Movable thermocouple

18 Boundary Temp Control Schematic

19 Rationale: Heat Transfer Experiment To compare and validate three mathematical models of transient 1D conduction: Assume infinite conduction rod Assume finite conduction rod Account for 1D convection The performance of each will be compared on three materials: copper, aluminum, and stainless steel.

20 Rationale Continued: Controls Experiment To predict and verify temperature control stability limits in terms of: Gain Feedback delay For more information see: Dr. Stutts' Notes on Stability Analysis Using Frequency- Based Methods