| Summary: | An analysis of linear dynamic viscoelastic discrete systems is presented, and its application to
the vibration of an engine supported on viscoelastic mounts is discussed.
A new procedure is developed which allows exact (closed form) homogeneous solutions
in the time domain to be derived for a dynamic system consisting of isotropic viscoelastic
components, for which the relaxation kernels are represented as a sum of exponentials. The
developed procedure (which is given a name "substitution method") for determination of
closed form solutions is extended to the solution of boundary value problems. The application
of the substitution method is also extended to the case of periodic loading. Based on this
method, a numerical investigation of free and forced vibration responses of some viscoelastic
systems is presented.
Several approximation techniques are developed in this study which allow the parameters
of the relaxation kernels (represented as a sum of exponentials) to be determined from experimental
data. Also a numerical procedure for determination of complex moduli of isotropic
viscoelastic materials is developed, in which certain experimental data related to the material
specimen are required as input information.
A hereditary (viscoelastic) stiffness matrix-operator is obtained by replacement of the
elastic constants in the elastic stiffness matrix by the corresponding viscoelastic operators, or
by complex moduli (for steady-state response problems). Comparison of experimental results
(in terms of steady-state responses) with the numerical ones is presented.
The sufficient conditions of diagonalization of discrete viscoelastic systems are formulated
in this study.
Analysis of the conditions of overdamping of a simple viscoelastic single-degree-of-freedom system is conducted, and new results concerned with this analysis are demonstrated.
A particular case of a dynamic viscoelastic system (an internal combustion engine on
elastomeric mounts) is given special consideration. A new dynamic model of an enginemount
system is developed where rotating and reciprocating parts lead to the mass matrix and
velocity matrix (matrix-coefficient at the velocity vector) as periodic functions of time. The
derivation of the equations of motion on the basis of Lagrange's equations is demonstrated.
An analysis of parametric resonance phenomena for some examples of engine-mount systems
is conducted. A method for steady-state response calculations for the case of time-dependent
(periodic) matrices in the equation of motion is developed and some numerical results are
presented.
An optimization problem is posed and solved with the associated constraints and the
objective function reflecting the optimum criteria of the performance of an engine-mount
system. As a result, the optimum parameters of the mount material are determined.
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