Only do B Pre-measured experimental data:Using the experimental data given below, complete the lab report as detailed in the deliverable.Beam dimensions - breadth=0.0254m, depth=0.0032m, length=0.410m.Damped natural frequencyU11@d2@d3wn = azExperimentally measuredvalue (Hz)12.0290.84214.7Deliverable(a) Mathematical modelling of the cantilever beam: Theoretically model the cantilever beam,using the physical measurements of the cantilever beam, as one degree of freedom system.Calculate the first natural frequency of the beam.EIPALA(b) Research Euler-Bernoulli beam theory and utilising the physical measurements of thecantilever beam. Calculate the first three natural frequencies of your experimental systemusing Euler Bernoulli beam theory.Theoretical details:The fixed-free cantilever beam system is an example of a continuous distribution of mass systemand can have many natural frequencies. Euler Bernoulli beam theory yields a formula [1] tocalculate the natural frequencies of your experimental system.Node, distance from fixed endof the beam (m)E-Young's modulus for mild steel = 210GPaL-Length of the beamA- the cross-sectional area of the beamp - the density for the beam, for mild steel = 7850Kgm-³an - is a constant, for a fixed-free beamWhere I is the second moment of area [2]1=bd²b-breadth of the beamd-depth of the beam0.3350.187, 0.350[1]a₁ = 1.875 a₂ = 4.694 a3 = 7.855[2] Task DescriptionUse the lab details below and the table of results to complete the assignment. You are provided withthe pre-measured experimental data.Background:Systems that oscillate continuously tend to be problematic for engineers. These vibrations can lead toloss of function in electronic components, failure due to fatigue, discomfort and long-term healthproblems such as vibration white finger. It is important to factor a vibration analysis into the designprocess, particularly when designing components that mount near or on vibrating parts such asmotors or engines.Relevant Theory:This theory requires the beam to be represented as a lumped mass with equivalents stiffness/dampingmodel as shown below.OscilloscopeBeamShakerChargeAmplifierAccelerometerThe shaker transmits a constant sinusoidaly varying force into the beam. The amplitude of this forceis set by the signal generator and should remain fixed at all times. The frequency of the force is alsoset by the signal generator and can be varied during the experiment. The vibrations are measured bythe accelerometer. This reading can be integrated electronically by the charge amplifier to givevelocity or position measurements.Experimental Methods - identifying natural Frequencies and mode shapes:Frequency sweep can be performed using the signal generator to identify the first three "modal"frequencies where the amplitudes of vibration increased significantly. The shape of the beam at eachfrequency can be defined by plotting a sinusoid curve through the "nodes" (where there is nomovement) and the "peaks".

Euler-Bernoulli Beam Theory : Linear theory of elasticity is simplified in Euler-Bernoulli beam…

Pre-measured experimental data: Using the experimental data given below, complete the lab report as detailed in the deliverable. Beam dimensions - breadth=0.0254m, depth=0.0032m, length=0.410m. Damped natural frequency @dl @d2 @d3 Experimentally measured value (Hz) 12.02 90.84 214.7 Node, distance from fixed end of the beam (m) 0.335 0.187, 0.350 Deliverable (a) Mathematical modelling of the cantilever beam: Theoretically model the cantilever beam, using the physical measurements of the cantilever beam, as one degree of freedom system. Calculate the first natural frequency of the beam. (b) Research Euler-Bernoulli beam theory and utilising the physical measurements of the cantilever beam. Calculate the first three natural frequencies of your experimental system using Euler Bernoulli beam theory.

Pre-measured experimental data: Using the experimental data given below, complete the lab report as detailed in the deliverable. Beam dimensions - breadth=0.0254m, depth=0.0032m, length=0.410m. Damped natural frequency @dl @d2 @d3 Experimentally measured value (Hz) 12.02 90.84 214.7 Node, distance from fixed end of the beam (m) 0.335 0.187, 0.350 Deliverable (a) Mathematical modelling of the cantilever beam: Theoretically model the cantilever beam, using the physical measurements of the cantilever beam, as one degree of freedom system. Calculate the first natural frequency of the beam. (b) Research Euler-Bernoulli beam theory and utilising the physical measurements of the cantilever beam. Calculate the first three natural frequencies of your experimental system using Euler Bernoulli beam theory.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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