I have a spring-mass system with 200 masses and 199 springs. All masses are 100 tonnes and stiffness 20 MN. The boundary conditions are fixed-free.
I have constructed a lumped mass matrix and stiffness matrix and calculated the lowest natural frequency. Including the boundary conditions I...
I have a piecewise function described by g_1(x) as shown in the figure below. I wish to make a smooth curve, g_2(x), to fit (but not necessarily exactly) g_1(x). The only conditions are:
Both curves must start at (0,0) and end at (a,0).
The area of both curves must be the same.
How do...
I have updated the expression to include time.
I have found a solution for the problem: the analogue model was a summation of terms; when processing this infinite summation was truncated to 5 terms. This caused the phenomenon in the bar which dissappeared when the amount of terms was...
The bar was subject to a base support motion in the form v = -(t-sqrt(a))^2 + a. That motion is what has excited the bar. I can give you more details on this method of excitation if you require.
They are both excited in the same manner.
The excitation is from a base support motion (i.e. a bar with one end fixed and one end free) with a displacement profile u_g = F_g(t) applied to the 'fixed' end (which moves according to u_g).
The horizontal axis is the length of the bar (the left side has the base support motion).
The three images are taken at different time intervals.
The discretised model was created by applying Newton 2 to the mass-spring-mass...etc system (i.e. sum(F)=ma ). These equations were then...
To visualize this I have included the following plots from a video of the velocity of the bar. Why is the discretised bar not the same?
http://www.test1.ausalive.com/images/640_bar2.jpg
[PLAIN]http://www.test1.ausalive.com/images/640_bar3.jpg...
I am doing some study into longitudinal wave dynamics. I am using theoretical models of wave motion in continuous bar and comparing this to numerical analysis using a lumped mass model.
So far I have discovered that the continuous bar vibrations, caused by base support motion (i.e. vibration...