| """Grounded linear viscous damper, independent SciPy time-domain reference. |
| |
| Apache-2.0. Uses the exported solid-component ROM, not a neural network. |
| """ |
| import numpy as np |
| from scipy.linalg import expm |
| from assembly import solve |
|
|
|
|
| def free_decay(chain, rolls=None, supports=None, node=None, axis=2, c=10000., |
| amplitude=.001, mode_count=12, frames=600, duration=None): |
| """First-mode release; peak coordinate amplitude in metres, c in N s/m. |
| |
| Zero initial velocity, no background damping or imposed forcing. Motion is |
| a linear perturbation about equilibrium; thermal prestress is not included. |
| Returns exact-in-time samples for the selected truncated modal equations. |
| """ |
| node=len(chain) if node is None else node |
| if axis not in (0,1,2) or not 0<=node<=len(chain) or c<0 or not np.isfinite(c): |
| raise ValueError('Invalid grounded damper') |
| if not 0<amplitude<=.01 or mode_count<1 or frames<1:raise ValueError('Invalid release settings') |
| r=solve(chain,rolls=rolls,supports=supports,nmodes=mode_count) |
| w=2*np.pi*r['frequency'];n=len(w) |
| locations=[(abs(m[j,k,0]),a,j,k) for a,m in enumerate(r['mode_displacements']) for j in range(len(m)) for k in range(3)] |
| _,a,j,k=max(locations);probe=r['mode_displacements'][a][j,k] |
| z=np.zeros(n);z[0]=amplitude/probe[0] |
| b=r['modes'][node*6+axis];C=c*np.outer(b,b) |
| A=np.block([[np.zeros((n,n)),np.eye(n)],[-np.diag(w*w),-C]]) |
| T=6/r['frequency'][0] if duration is None else duration |
| if T<=0:raise ValueError('Invalid duration') |
| time=np.linspace(0,T,frames+1);P=expm(A*T/frames);state=np.r_[z,np.zeros(n)];states=[] |
| for _ in time:states.append(state.copy());state=P@state |
| states=np.array(states);q,v=states[:,:n],states[:,n:] |
| energy=.5*np.sum(v*v+(q*w)**2,axis=1) |
| return dict(time=time,signal=q@probe,reference=amplitude*np.cos(w[0]*time), |
| force=-c*(v@b),energy=energy,coordinates=q,velocities=v, |
| probe=dict(component=a,sample=j,axis=k),frequency=r['frequency'], |
| method='scipy matrix exponential of the modal state-space system') |
|
|
