Structural Dynamics EXAM

1) Qualitative Responses

Write the general equation, u(t), of the solution for the following cases:

a. Un-damped Free Vibration System

b. Damped Free Vibration System

c. Harmonic Vibration of Un-damped System

d. Damped Harmonic Vibration System

e. Duhamel's Integral (without damping)

f. Duhamel's Integral (with damping)

g. True or False (circle one). The natural period, T_n, of a structure depends on the applied loads. Please explain WHY to support your answer.

2) Equations of Motion

The system below consists of two masses (each with a weight of 100 pounds) and two springs having different stiff nesses shown below. There is no damping. A projectile that weighs 1 pound is traveling at 1000 in/sec., and suddenly strikes mass #1 and becomes fully embedded.

a. Draw a free-body diagram (FBD) and kinetic diagram (KD) for the system.

b. Determine the mass matrix.

c. Determine the stiffness matrix.

d. Write the equation of motion for this system.

3) Matrix Structural Analysis

For P1.14 in Chopra's text (3^rd edition-pinned-pinned, top beam not rigid), determine the stiffness matrix only. State the degrees-of-freedom you selected.

4) Harmonic Excitation. For the single-story building shown in the diagram below, determine the following:

a. Natural circular frequency, ω_n

b. Damped natural circular frequency, ω_D

c. Natural period, T_n

d. Natural frequency in Hertz, f_n

e. Damping ratio, ζ

f. Determine the displacement response (be sure to specifically evaluate for your constants, A, B, etc.) if the building, which is at rest, is subjected to a harmonic force of p(t) = p_ocosω_t

g. What is the maximum displacement for the steady-state response?

5) Response to Arbitrary and Pulse Excitations.

For the triangular pulse shown below, SHOW ALL OF YOUR WORK to:

a. Determine the TOTAL displacement response for an un-damped SDOF system subjected to a symmetrical triangular pulse by considering the superposition of three ramp functions shown below:

b. Determine the maximum deformation due to this triangular pulse?

Attachment:- Assignment File.rar