  The bulk band topology of symmetry invariant adiabatic systems in the
thermodynamic limit are considered to be determined by the hopping energy. In
this work, we present that in closed classical systems, due to generalized
chiral symmetry broken, the on-site energy cannot always be regarded as
identical and can crucially impact the topological properties of the systems.
Based on a finite one-dimensional chain, we demonstrate that the non-equivalent
on-site energy of bulk lattices affects the topological phases of the bands,
and the on-site energy of end lattices affects the existence of the topological
states. Along these lines, the correspondence with generalized chiral symmetry
in acoustic system is rigorously proposed. Our work provides a new degree of
freedom for topological classical systems, and can be generalized to
higher-dimensions and non-Hermitian conditions.
