Development Of GUI In MATLAB For Experimental Modal .

MKSSS’s Cummins College of Engineeringfor Women, PuneDevelopment of GUI in MATLABfor Experimental Modal Analysis ofTransverse Vibrations in 2D DomainMitali Vaidya, Puja More, Varsha Nemane, Nishita Deshmukh,Dr. Gautam Chandekar*Department of Mechanical Engineering,MKSSS’s Cummins College of Engineering,Karve Nagar, Pune- 411 052.*.Corresponding Author (email gautam.chandekar@cumminscollege.in )

Introduction to Modal Analysis MODAL ANALYSIS- Modal analysis is the process of determining theinherent dynamic characteristics of a system in forms of naturalfrequencies, damping factors and mode shapes, and using them toformulate a mathematical model for its dynamic behaviour. NATURAL FREQUENCY- Natural frequency is the frequency of freevibration of the system . It is a constant for given system. MODE SHAPE- Mode Shape is a characteristic displacement pattern,which may be real or complex and corresponds to a naturalfrequency.22-Apr-16Department of Mechanical Engineering2

1-D Domain22-Apr-16Department of Mechanical Engineering3

Validating Data with 1-D Domain Boundary Condition : Fixed-Free (Cantilever Beam) Methodology : Finding analytical natural frequencies and modeshapes from Equations of Motion using MATLAB. Finding experimental natural frequencies and modeshapes using MATLAB. Verifying the experimental results by comparing withanalytical results.22-Apr-16Department of Mechanical Engineering4

Methodology for 1-D Domain22-Apr-16Department of Mechanical Engineering5

Results Obtained for Beam22-Apr-16Department of Mechanical Engineering6

Results Obtained for Beam22-Apr-16Department of Mechanical Engineering7

Results Obtained for Beam22-Apr-16Department of Mechanical Engineering8

Results Obtained for BeamFor animation of mode shapes, please watch attachedvideos in ‘BEAM MODESHAPES AVI’ folder.22-Apr-16Department of Mechanical Engineering9

2-D Domain22-Apr-16Department of Mechanical Engineering10

Analytical Solution for 2–D Domain Boundary Condition : Simply Supported on all the four sides Analytical Governing Equation:W(x,y) ere:A-Amplitude of Vibrationa-Length of the plateb-Width of the plate(Reference : Vibrations of Continuous Media by S. S. Rao)22-Apr-16Department of Mechanical Engineering11

Analytical Mode Shapes Obtained For 2-D Domain Using MATLAB.First Mode Shape(fn 437Hz)22-Apr-16Department of Mechanical Engineering12

Analytical Mode Shapes Contd.Second Mode Shape(fn 1093Hz)22-Apr-16Department of Mechanical Engineering13

Analytical Mode Shapes Contd.Third Mode Shape(fn 1093Hz)22-Apr-16Department of Mechanical Engineering14

Analytical Mode Shapes Contd.Fourth Mode Shape(fn 1748Hz)For animation of mode shapes, please watch attached videos in‘Animation Plate AVI’ folder.22-Apr-16Department of Mechanical Engineering15

Analytical Solution for 2–D Domain Boundary Condition : SS-F-SS-FWhere : SS-Simply supportedF-Free Analytical Governing Equation:Xm sin(xα);Yn (ẟ1(λ2 1b)) (cosh(y.ẟ2).(λ2-α2(1- μ)) cos(y.ẟ1).(λ2 )2)(ẟ1sinh(y.ẟ2).(λ2 α2(1-μ)) ẟ2sin(y.ẟ1).(λ2-α2(1-μ))))Z A.Xm.Yn(Reference : Vibrations of Continuous Media by S. S. Rao)22-Apr-16Department of Mechanical Engineering16

Analytical Mode ShapesFirst Mode Shape22-Apr-16Department of Mechanical Engineering17

Analytical Mode Shapes Contd.Second Mode Shape22-Apr-16Department of Mechanical Engineering18

Analytical Mode Shapes Contd.Third Mode Shape22-Apr-16Department of Mechanical Engineering19

Analytical Mode Shapes Contd.Fourth Mode Shape22-Apr-16Department of Mechanical Engineering20

Methodology for 2–D Domain22-Apr-16Department of Mechanical Engineering21

Experimental Setup for 2D PlatePlateFFTAnalyzerL-AnglesMesh Grid22-Apr-16ImpactHammerAccelerometerDepartment of Mechanical Engineering22

Experimental Setup for 2D PlateContd Accelerometer22-Apr-16Department of Mechanical Engineering23

Experimental Setup for 2D Plate(SS-F-SS-F Boundary Condition)Mesh GridPlateL-Angles22-Apr-16Department of Mechanical Engineering24

Experimental Setup for 2D PlateContd Plate Dimensions: 300*300*8 mm Plate material: Mild Steel (E 210 GPa) Boundary Conditions: Set 1: SS-SS-SS-SSSet 2: SS-F-SS-F A grid of 9*9 (81) points for Set 1, and 11*11 (121) points for Set2, has been made, with fixed numbering for each point.22-Apr-16Department of Mechanical Engineering25

Experimental Setup for 2D PlateContd A tri-axial Delta Tronaccelerometer is attached at aparticular point using beeswax(Make:B&K,Type:4524)22-Apr-16 ICP Impact hammermodel 086C03 hasbeen used to excite atall the points definedon the grid, so as toobtain requiredreadings.(Make: PCBPIEZOTRONICS)Department of Mechanical Engineering26

Experimental Setup for 2D PlateContd RT Photon software hasbeen used for analysis. The real time data obtainedfrom the Data AcquisitionSystem (FFT Analyzer) is thenused in the MATLAB code. Make:B&K22-Apr-16Department of Mechanical Engineering27

Experimental Mode ShapesFirst Mode Shape22-Apr-16Department of Mechanical Engineering28

MODAL ANALYSIS- Modal analysis is the process of determining the inherent dynamic characteristics of a system in forms of natural frequencies, damping factors and mode shapes, and using them to formulate a mathematical model for its dynamic behaviour. NATURAL FREQUENCY- Natural frequency is the frequency of free vibration of the system .