The solution to a problem with an impact or excitation model having more than two masses and/or any number of non-linear energy absorbers becomes too complex to solve in a closed form. Then, numerical evaluation and integration techniques are necessary to solve for the dynamic responses. Models such as the two non-isomorphic (with different structural configuration) hybrid or standard solid models, the combination of two hybrid models, and special cases with point masses will be treated first in closed-form. The purpose of the closed-form analysis is to investigate the dynamic responses of two dynamically equivalent hybrid models. In a multi-mass. | CHAPTER 5 RESPONSE PREDICTION BY NUMERICAL METHODS INTRODUCTION The solution to a problem with an impact or excitation model having more than two masses and or any number of non-linear energy absorbers becomes too complex to solve in a closed form. Then numerical evaluation and integration techniques are necessary to solve for the dynamic responses. Models such as the two non-isomorphic with different structural configuration hybrid or standard solid models the combination of two hybrid models and special cases with point masses will be treated first in closed-form. The purpose of the closed-form analysis is to investigate the dynamic responses of two dynamically equivalent hybrid models. In a multi-mass model the unloading characteristics of a spring element is as important as the loading characteristics. The unloading of one mass in a model may produce loading of the neighboring masses thereby affecting the total system model responses. Power curve loading and unloading simulation with hysteresis energy loss and permanent deformation will be covered. To help solve some dynamic models quickly a lumped-parameter model CRUSH II 1 coupled with animation will be utilized. The force-deflection formulas of some simple structures are listed for ease of determining the spring stiffness for the modeling. Some lumped-parameter models for the full frontal side and frontal offset impacts are described. The basic concepts of splitting a simple spring-mass model for the frontal offset impact and the model validation are also presented. HYBRID MODEL A STANDARD SOLID MODEL There are two types of hybrid models Hybrid 1 and 2 shown in Figs. and respectively. v12 ak V 2 a XT VY o Fig. Hybrid Model 1 a xt- W Fig. Hybrid Model 2 2002 by CRC Press LLC A hybrid model is a combination of Maxwell and Kelvin models. It has three elements two springs and one damper. These three elements are connected in such a way that the two hybrid models are structurally and .
