Abstract: The present
work investigates the general theory of
vibrations of an elastic body through the
analytical studies by using a dynamical
system. Also, some applications can be applied
in L2-space,
seismology, and coherent process.
Consider the
following Cauchy problem for system of m non-homogeneous
differential equations in a Banach space E
with initial
data
where
(2)
um
is the displacement at time t.
(3) v
is the volume expansion of the elastic body.
(4)
m
> 0, l
> 0 are elastic constants.
(5)
r
is the
density of the elastic body.
(6)
a
is the
velocity of propagation of plane waves of
distortion.
(7)
is the velocity of propagation of plane waves
of dilatation.
(8)
f0m(a,
b),
and g0m(a,
b)
are arbitrary functions.
