Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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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 U11 @d2 @d3 wn = az Experimentally measured value (Hz) 12.02 90.84 214.7 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. EI PALA (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. Node, distance from fixed end of the beam (m) E-Young's modulus for mild steel = 210GPa L-Length of the beam A- the cross-sectional area of the beam p - the density for the beam, for mild steel = 7850Kgm-³ an - is a constant, for a fixed-free beam Where I is the second moment of area [2] 1=bd² b-breadth of the beam d-depth of the beam 0.335 0.187, 0.350 [1] a₁ = 1.875 a₂ = 4.694 a3 = 7.855 [2]
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Transcribed Image Text: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 U11 @d2 @d3 wn = az Experimentally measured value (Hz) 12.02 90.84 214.7 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. EI PALA (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. Node, distance from fixed end of the beam (m) E-Young's modulus for mild steel = 210GPa L-Length of the beam A- the cross-sectional area of the beam p - the density for the beam, for mild steel = 7850Kgm-³ an - is a constant, for a fixed-free beam Where I is the second moment of area [2] 1=bd² b-breadth of the beam d-depth of the beam 0.335 0.187, 0.350 [1] a₁ = 1.875 a₂ = 4.694 a3 = 7.855 [2]
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. Oscilloscope Beam 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".
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Transcribed Image Text: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. Oscilloscope Beam 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".
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Step 3 : Calculation of natural frequencies
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