1
Write and solve the loss-factor matrix
Use f = 1000 Hz, η1 = 0.02, η2 = 0.06, η12 = 0.012, η21 = 0.006 and input power P1 = 1 W, P2 = 0 W. The SEA system is ω C E = P.
CA07 exercise · Energy-balance exercise
Two-Subsystem SEA Model
Assemble and solve a two-subsystem SEA loss-factor matrix, vary damping/coupling parameters and convert subsystem energy into averaged response quantities.
45–75 minLinked to Statistical Energy AnalysisDashboard progress enabled
Aim
Solve a two-subsystem SEA balance
This exercise treats a plate–cavity-like system with input power into subsystem 1 and energy transfer to subsystem 2. The unknowns are mean subsystem energies, not local pressure/displacement fields.
2
Interpret the parameters
Damping loss factors describe energy dissipation within a subsystem. Coupling loss factors describe energy transfer between subsystems.
What does η12 mainly control?
Python exercise
Run the two-subsystem SEA model
The code solves the SEA equations over frequency and plots subsystem energies.
Expected observation
The directly excited subsystem stores more energy; the second subsystem receives energy through coupling.
Teaching note
Change η12, η21, η1 and η2 to see the sensitivity of SEA predictions to loss factors.
Written submission
Validity of SEA
When is SEA appropriate?
State two conditions that make SEA more credible and one situation where SEA is risky.
Saved automatically in this browser draft.
Submit solution
Classroom submission workflow
When a student is logged in, the submission is stored in Supabase and becomes visible to the supervisor grading page across devices. Local browser storage remains as fallback.
Supabase not configured
Checking login...
Draft status
0%
0 checks · 0 answers · 0 runs
Student identity
Enter temporary identity until login is active.