tailieunhanh - Vibration Analysis and Control New Trends and Developments Part 9

Tham khảo tài liệu 'vibration analysis and control new trends and developments part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 190 Vibration Analysis and Control - New Trends and Developments The error function erf x and the unit step function u x are defined as follows. 6 u x 1 x 0 7 u x 0 x 0 8 The basic expression obtained here for pre-strained wires is a modified form of the model suggested by wilde et al 12 which is used for predicting the tensile behaviour of SMA materials. This mathematical expression describes the mechanical response of materials showing hysteresis. . . .7 - a n ơ E f- 9 where o is the one dimensional stress and e is the one-dimensional strain p is the one dimensional back stress E elastic modulus Y the yield stress and n the constant controlling the sharpness of the transition from elastic to plastic states. The modified Cozzarelli model suggested by Wilde et al represents the hardening of the material after the transition from austenite to martensite is completed. Here in this case for pre strained wires for maximum energy dissipation the hardening branch has not been considered which requires additional terms containing further unit step functions. The model is rate and temperature independent. The requirement of zero residual strain at the end of the loading process motivated the selection of the particular form of back stress through the unit step function. The coefficients ft and c are material constants controlling the recovery of the elastic strain during unloading. Since the stress and strain were found to be independent of the rate the time differential can be eliminated. Hence equation 2 and 3 can be used for predicting the behaviour after many cycles by appropriately changing the values of n and the starting stress value which follows the trend as in fig. 15. The material constants for the wires tested were obtained as ft C n a . Using Equations 2 and 3 the curves are fitted. Fig. 15 gives the fitted curve for the maximum energy dissipation for the material tested. 8. Various seismic response mitigation strategies Earthquake .