  Jammed particulate systems, such as granular media, colloids, and foams,
interact via one-sided forces that are nonzero only when particles overlap. We
find that systems with one-sided repulsive interactions possess no linear
response regime in the large system limit ($N\rightarrow \infty$) for all
pressures $p$ (or compressions $\Delta \phi$), and for all $N$ near jamming
onset $p\rightarrow 0$. We perform simulations on 2D frictionless bidisperse
mechanically stable disk packings over a range of packing fractions $\Delta
\phi = \phi-\phi_J$ above jamming onset $\phi_J$. We apply perturbations with
amplitude $\delta$ to the packings along each eigen-direction from the
dynamical matrix and determine whether the response of the system evolving at
constant energy remains in the original eigenmode of the perturbation. For
$\delta > \delta_c$, which we calculate analytically, a single contact breaks
and fluctuations abruptly spread to all harmonic modes. As $\delta$ increases
further all discrete harmonic modes disappear into a continuous frequency band.
We find that $<\delta_c >\sim \Delta \phi/N^{\lambda}$, where $1 > \lambda >
0.5$, and thus jammed particulate systems are inherently nonharmonic with no
linear vibrational response regime as $N\rightarrow \infty$ over the full range
of $\Delta \phi$, and as $\Delta \phi \rightarrow 0$ at any $N$.
