1 given the two beams aluminum and steel 0125x 1x 20 with

Question

1) Given the two beams (Aluminum and steel) (0.125"X 1"X 20"), with the following material properties: For Steel E = 206.8 (10^9) Pa and ρ = 0.7830 kg/cm. E= 30X10^6 psi, ρ =0.00074 lb/ft 

For Aluminum: E = 73 (10^9) Pa and ρ = 0.2750 kg/cm

E=10.6(10^6) psi and ρ = 0.00026 lb/ft

The resonant frequencies for a simple cantilever beam is given by

w= natural frequency in cycles per second

E = modulus of elasticity of the material in psi

I = moment of inertia in inches4

L =length in inches

ρ = mass per unit length , for steel =0.284/(12*32) =0.00074 lb/ft or 0.7830 kg/cm

For aluminum ρ = 0.1/(12*32) =0.00026 lb/ft or .275kg/cm Cn = coefficient for the different resonant modes ( C1 = 3.52, C 2 = 22.4, C 3 = 61.7 )

Calculate the first three natural frequencies using the above equation.

2) Are the number of degrees of freedom of a system and the number of its norm al modes related? If so, how?

3) How can a normal mode be recognized physically?

4) What data will you record during the lab?

5) What observations will you make?

6) What do you expect to happen when you drive a system at one of its natural frequencies?

Attachment:- 319562_3_ibrahem--1- (1).xlsx

Answer 1

By considering the material properties of Aluminum and steel (illustrated in the assignment), please answer the following questions by solving each part using appropriate concepts and formulas. 1) Provided the two beams (Aluminum and steel) (0.125"X 1"X 20"), having given material properties. Compute the first three natural frequencies employing the above equation. 2) Are number of degrees of freedom of a system and the number of its normal modes connected? If so, illustrated how? 3) Illustrate how can a normal mode be identified physically? 4) Illustrate what data will you record throughout the lab? 5) Illustrate what observations will you make? 6) Illustrate what do you expect to occur whenever you drive a system at one of its natural frequencies?