% A flat, free-edged plate held at its center, struck near the rim: a flat
% cymbal or gong. Units are SI.
%
% The plate's stiffness comes from bending triplets (three beads in a row
% resist bending, sys.bends), not from tension: the springs carry no load
% at rest and only resist stretching. Stretching is what makes the plate
% nonlinear, once the motion is comparable to the plate's effective
% thickness, about a*sqrt(kb/k) (here 4 mm). The center is clamped by
% pinning the middle bead and its six neighbours; with a single pinned bead
% the plate could tilt and spin freely.

R = 0.2;           % radius (m)
a = 0.012;         % bead spacing (m)
sigma = 8.9;       % mass per area (kg/m^2), about 1 mm of bronze
kb = 7e5;          % bending stiffness of each triplet (N/m); sets the pitch
thick = 0.1;       % kb/k: larger is "thicker", nonlinear only at larger motion

[pos, tri, rim, trip] = bp_hexdisk(R, a);
E = bp_edges(tri);

sys.pos = pos;
sys.mass = sigma * (sqrt(3)/2) * a^2;
sys.pinned = bp_near(pos, [0 0 0], 1.05 * a);       % the mount
sys.springs = bp_springs(pos, E, kb / thick, 0);    % no tension at rest
sys.bends = [trip, kb * ones(size(trip, 1), 1)];
sys = bp_decay(sys, [100 2.5; 5000 1.2]);

% A stick on the edge: a sharp 0.3 ms push on the beads within 2 cm of the
% rim point. The plate is mildly nonlinear at this force (14% from the
% small-strike reference by 0.3 s); at 4x it differs by 14% within 10 ms
% and 93% by 0.3 s. A longer, softer push mostly rocks the plate on its
% mount.
hit.t = 0;
hit.beads = bp_near(pos, [0.18 0 0], 0.02);
hit.force = [0 0 -150];      % peak force per bead (N)
hit.duration = 3e-4;
sys.hits = hit;

sys.listen = struct('beads', bp_near(pos, [-0.1 0.06 0], 0), 'dir', [0 0 1]);
sys.duration = 2.5;

fprintf('%d beads, %d springs, %d bending triplets, %d struck\n', ...
    size(pos, 1), size(E, 1), size(trip, 1), numel(hit.beads));