Abstract: This paper deals with nonlinear vibration analysis
using finite element method for frame structures consisting of elastic
and viscoelastic damping layers supported by multiple nonlinear
concentrated springs with hysteresis damping. The frame is supported
by four nonlinear concentrated springs near the four corners. The
restoring forces of the springs have cubic non-linearity and linear
component of the nonlinear springs has complex quantity to represent
linear hysteresis damping. The damping layer of the frame structures
has complex modulus of elasticity. Further, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled differential equations using normal coordinate corresponding
to linear natural modes. Comparing shares of strain energy of the
elastic frame, the damping layer and the springs, we evaluate the
influences of the damping couplings on the linear and nonlinear impact
responses. We also investigate influences of damping changed by
stiffness of the elastic frame on the nonlinear coupling in the damped
impact responses.
Abstract: This paper describes dynamic analysis using proposed
fast finite element method for a shock absorbing structure including a
sponge. The structure is supported by nonlinear concentrated springs.
The restoring force of the spring has cubic nonlinearity and linear
hysteresis damping. To calculate damping properties for the structures
including elastic body and porous body, displacement vectors as
common unknown variable are solved under coupled condition. Under
small amplitude, we apply asymptotic method to complex eigenvalue
problem of this system to obtain modal parameters. And then
expressions of modal loss factor are derived approximately. This
approach was proposed by one of the authors previously. We call this
method as Modal Strain and Kinetic Energy Method (MSKE method).
Further, using the modal loss factors, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled equations using normal coordinate corresponding to linear
natural modes. This transformation yields computation efficiency. As
a numerical example of a shock absorbing structures, we adopt double
skins with a sponge. The double skins are supported by nonlinear
concentrated springs. We clarify influences of amplitude of the input
force on nonlinear and chaotic responses.