Since theta is a vector you need to perform elementwise multiplication:
a = 13;
c = 17;
k = 2*pi/3;
theta = 0:0.0001:2*pi;
d2b = -(a*(cos(theta).*(c^2 - a^2*sin(theta).^2).^(3/2) + a^3.*sin(theta).^4 + a*c^2.*cos(theta).^2 - a*c^2.*sin(theta).^2))./(c^2 - a^2*sin(theta).^2).^(3/2);
figure(3)
plot (theta, d2b);