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Signum values and domain of z per segment Table 1 A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895

Table 1 Signum values and domain of z per segment Table 1 A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895

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Fig. 1. Bouc-Wen model. It has been shown in formal mathematical manner that the parameters of Bouc-Wen model are functionally redundant; there exists a multiplicity of parameter vectors that produce an identical response for a given
Fig. 1. Bouc-Wen model. It has been shown in formal mathematical manner that the parameters of Bouc-Wen model are functionally redundant; there exists a multiplicity of parameter vectors that produce an identical response for a given
Fig. 2. Response of Bouc-Wen model under cyclic excitation.
Fig. 2. Response of Bouc-Wen model under cyclic excitation.
Fig. 3. Steady-state response of hysteretic spring under symmetric wave T-periodic excitation. A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895 where z, is the unknown maximum value of hysteretic parameter z. There exist several analytical expressions of z4 for specific values of n and (f—y). In general, however, numerical evaluation must be employed. In similar manner, as in the preceding section, the Van Wijngaarden—Dekker—Brent method [13] is employed which converges rapidly. If root bracketing with z4 € [0, 1 — ¢] fails, then full yield is assumed and z, is taken equal to unity. ws aoe ase ae: 1 . a 3 1 1 1°: a r — 1 1
Fig. 3. Steady-state response of hysteretic spring under symmetric wave T-periodic excitation. A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895 where z, is the unknown maximum value of hysteretic parameter z. There exist several analytical expressions of z4 for specific values of n and (f—y). In general, however, numerical evaluation must be employed. In similar manner, as in the preceding section, the Van Wijngaarden—Dekker—Brent method [13] is employed which converges rapidly. If root bracketing with z4 € [0, 1 — ¢] fails, then full yield is assumed and z, is taken equal to unity. ws aoe ase ae: 1 . a 3 1 1 1°: a r — 1 1
Thus, based on the derived complementary areas, Eq. (14) assumes the form: Eq. (21) can be employed for both partially and fully yielding systems. Particularly for the latter case, parameters kGp and ky, can be provided by simple approximate functions. These are derived using standard
Thus, based on the derived complementary areas, Eq. (14) assumes the form: Eq. (21) can be employed for both partially and fully yielding systems. Particularly for the latter case, parameters kGp and ky, can be provided by simple approximate functions. These are derived using standard
Fig. 4. (a) Parameter k@p as a function of n, y (b) Parameter kj, as a function of n (full yield). A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895 Table 2 Parameter kj, for various values of n (full yield)
Fig. 4. (a) Parameter k@p as a function of n, y (b) Parameter kj, as a function of n (full yield). A.E. Charalampakis, V.K. Koumousis / Journal of Sound and Vibration 309 (2008) 887-895 Table 2 Parameter kj, for various values of n (full yield)
Fig. 5. Dissipated energy as a function of displacement amplitude (f = 0.1, y = 0.9).
Fig. 5. Dissipated energy as a function of displacement amplitude (f = 0.1, y = 0.9).
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