PSI - Issue 44

A.Di Egidio et al. / Procedia Structural Integrity 44 (2023) 2136–2143 A. Di Egidio, S. Pagliaro, A. Contento / Structural Integrity Procedia 00 (2022) 000–000

2138

3

to a linear rack through a pinion-gear mechanism. The resisting force F ID of the inerter device is (Makris and Kampas, 2016) F ID = m Re ( ¨ u dx − ¨ u sx ) (2) where m Re is the inertance or apparent mass of the inerter, which depends on the geometrical and mechanical charac teristics of the system. For the device of Fig. 1c with two flywheels, the apparent mass m Re reads

R 2 1 ρ 2 1

R 2 ρ 2

2 2

1 R 1 ρ

1 2

1 2

m Re =

m ω 1

m ω 2

(3)

+

2 2

Independently of the total physical mass of the inerter, any value of inertance can be obtained with a su ffi cient number and size of flywheels.

m 2

k , c 2 2

0,00

k , c c c

0,00

m e

m 1

h 2

Chevron m Re

h 1

k , c 1 1

h 1

k , c e e

(a)

R 1

u 2

Flywheel

r 1

u dx ..

u sx ..

r 2

m w 1

Rack

m w 2

R 2

u e

Pinions & gears

u 1

(c)

g x ( t )

(b)

Fig. 1. Mechanical system: (a) geometrical and mechanical characteristics of the system; (b) deformed configuration and Lagrangian parameters (positive directions); (c) Rack-pinion-flywheel supplemental rotational inertia system.

3. Parametric analysis

An extensive parametric analysis is performed to investigate the range of parameters characterizing the coupling devices and external structure for which the coupling improves the dynamic and seismic performances of the frame structure.

3.1. Variable parameters

In this paper, the 2-DOF model of the frame structure describes a 3-D frame structures having the characteristics reported in Table 1. The mass and height of the storeys are assumed to be constant at every level.