PSI - Issue 29

138 Michela Monaco et al. / Procedia Structural Integrity 29 (2020) 134–141 Michela Monaco et al. / Structural Integrity Procedia 00 (2019) 000 – 000 ( ) + ̈ 1 ( )) = −sgn( ̇ 1 ( )) (13) The analysis of thedynamic system begins with the evaluation of the type ofmotion rela ted to the base acceleration. Three possible patterns of motion have been examined (Figure 4): a) rocking of the top block with pedestal a t rest with respect to the ground; b) slidingmotionof thecomplex statue-pedestal as one rigid body and c) combined motion pa tterns: rockingof thestatue and slidingof the pedestal. The conditions for the activationof themotion a) are given by: { ̈ ( ) < ( ̇ ( )) ̈ 2 ( ) ℎ > . (14) The time is the instant a twhich: ̈ 2 ( ) ℎ = (15) It corresponds to the change of motion to range b), whose conditions for the activationare given by: { ̈ ( ) > ( ̇ ( )) ̈ 2 ( ) ℎ < . (16) The ba lance of friction force with inertia forces corresponds to the time in which: ̈ ( ) = ( ̇ ( )) (17) The conditions for the activationof themotion c) are given by: { ̈ ( ) > ( ̇ ( )) ̈ 2 ( ) ℎ > . (18) In genera l, the motion a) lasts until the ground accelerationdo not overcome the static friction force. ̈ ( ) − 2 ( ( )){ ( − | ( )|) ̇ 2 ( )− ( − | ( )|) ̈( )} ≥ ( ( )) (19) The transitionofmotion froma) to c) occurs when (19) holds. 3. The case study The Na tionalArchaeologicalMuseumof Paestumhas recentlyplanneda newlayout of theRomancollection, and some of themarble statues will be placed in the entranceof the exhibit room. A picture of the marble statue considered in this paper and that of its new layout, with the new position of the sta tue, is reported in Fig. 2. The sta tue, found presumably in the Forumarea, is unfortunately acephalous. The toga is the symbol of the Romancitizenship thatwas granted in 71 A.C. to the veterans byEmperorVespasian togetherwith the Paestum lands. The statuerepresents perhaps oneof theveterans settled in Paestumafter 71 A.C. (Torelli, 1999). 5 ( ̈