I aim to conduct a numerical frequency sweep analysis on a nonlinear, coupled two-degree-of-freedom vibration model and compare the results with the analytical solution. However, I am currently facing two main difficulties:

1. I am unsure how to determine whether the computed response has reached a steady state. If I simply use the maximum value to represent the steady-state amplitude, it can be misleading—since transient responses prior to reaching steady state may yield a higher peak, as seen in the uploaded code.

2. I do not know how to properly select the steady-state result from the previous frequency as the initial condition for the next frequency step.
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This time domain diagram has been drawn, but if you want to draw its outer outline, how should you command it?
saopinjifen1230.mw

The determinant of a 10*10 matrix is solved, but the result is very long, like the numerical way to solve, but did not find the appropriate method, the Analytic solution is very slow, calculated for 5 hours has not been calculated.

question128.mw

Lb1 represents a number of lengths, but I don't want to use a number to replace it now, but directly using eval, the variable in it becomes Lb1, unlike the following values show, how to write it like a number?

For a system of 8 equations, it takes too long for me to solve it by using solve, but I can only give one solution by using fsolve. If I want solutions in other ranges, I need to provide a general range, but I don't know the range, how can I quickly find all the solutions?question1118.mw