Discrete dynamic viscoelastic systems and vibration analysis of an engine supported on viscoelastic mounts

• Main Author: Muravyov, Alexander
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/7435

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.