i need help with part (C). ive also already done part (A) and (B) but i would appreciate it if you can show the calvulat

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i need help with part (C).
ive also already done part (A) and (B) but i would appreciate it if you can show the calvulations needed to answer both of those questions, i just want to check the answers i have. Theres no need to provide the answers for any of them moreso how i would answer them.

I Need Help With Part C Ive Also Already Done Part A And B But I Would Appreciate It If You Can Show The Calvulat 1 (58.56 KiB) Viewed 24 times

I Need Help With Part C Ive Also Already Done Part A And B But I Would Appreciate It If You Can Show The Calvulat 2 (58.56 KiB) Viewed 24 times

I Need Help With Part C Ive Also Already Done Part A And B But I Would Appreciate It If You Can Show The Calvulat 3 (47.86 KiB) Viewed 24 times

I Need Help With Part C Ive Also Already Done Part A And B But I Would Appreciate It If You Can Show The Calvulat 4 (68.41 KiB) Viewed 24 times

Task Description Use the lab details below and the table of results to complete the assignment. You are provided with the pre-measured experimental data. Background: Systems that oscillate continuously tend to be problematic for engineers. These vibrations can lead to loss of function in electronic components, failure due to fatigue, discomfort and long-term health problems such as vibration white finger. It is important to factor a vibration analysis into the design process, particularly when designing components that mount near or on vibrating parts such as motors or engines. Relevant Theory: This theory requires the beam to be represented as a lumped mass with equivalents stiffness/damping model as shown below. wwwwwww Oscilloscope Bear Shaker = Charge Amplifier Accelerometer The shaker transmits a constant sinusoidaly varying force into the beam. The amplitude of this force is set by the signal generator and should remain fixed at all times. The frequency of the force is also set by the signal generator and can be varied during the experiment. The vibrations are measured by the accelerometer. This reading can be integrated electronically by the charge amplifier to give velocity 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 each frequency can be defined by plotting a sinusoid curve through the "nodes" (where there is no movement) and the "peaks"
Pre-measured experimental data: Using the experimental data given below, complete the lab report as detailed in the deliverable. Beam dimensions - breadth=0.025m, depth=0.003m, length=0.435m. Damped natural frequency Experimentally measured value (Hz) 12 78.75 212.5 Wadl Wdd2 @dd3 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. w₁ = a (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. Theoretical details: The fixed-free cantilever beam system is an example of a continuous distribution of mass system and can have many natural frequencies. Euler Bernoulli beam theory yields a formula [1] to calculate the natural frequencies of your experimental system. EI PAL Node, distance from fixed end of the beam (m) E-Young's modulus for mild steel = 210GPa 0.35 0.21, 0.39 L-Length of the beam A- the cross sectional area of the beam p-the density for the beam, for mild steel = 7850Kgm³ an-is a constant, for a fixed-free beam a₁ 1.875 a 4.694 as 7.855
Where I is the second moment of area [2] 1 = bd³ 12 b-breadth of the beam d-depth of the beam (c) Euler-Bernoulli beam theory can also be used to determine the theoretical mode shapes associated with these natural frequencies. As a self-directed study, you should investigate the relevant equations to describe the mode shapes associated with these natural frequencies and calculate the first three mode shapes (shape of the cantilever beam as it vibrates) associated with each of these natural frequencies. (d) Describe the methodology of finite element model of the cantilever beam using SolidWorks. (e) Model the cantilever beam using SolidWorks and extract the first three natural frequencies and their associated transverse mode shapes for the cantilever beam. Assume the beam is in a fixed-free constrained condition. You should also utilise the following information: E-Young's modulus for mild steel = 210GPa p- the density for the beam, for mild steel = 7850Kgm-³ (f) Compare the experimental, Theoretical and FE results showing the relationship between each set of results - experimental, theoretical and FE method. (Be clear and concise). (g) Discuss the accuracy and precision of your results. Discuss any errors, limitation and any recommendation on how to improve the results. (h) Draw together the most important results and their significances