Abstract:Abstract.A novel formulation for the rocking motion of a rigid block on a rigid foundation is presented in this work. The traditional piecewise equations are replaced by a single ordinary differential equation. In addition, damping effects are no longer introduced by means of a coefficient of restitution but understood as the presence of impulsive forces. The agreement with the classical formalism is very good for both free rocking regime and harmonic forcing excitation.
“…1 46,53,54,59,60] to cite a few. In parallel, the field of impact dynamics has witnessed an intense activity in the past 25 years; see, e.g., [8-10, 15, 18-20, 29, 31, 38, 48, 52, 66] and references therein.…”
mentioning
confidence: 99%
“…They found good agreements between their simulations and their experiments. Pena and Prieto et al [42,43,46] performed many experiments and also proposed a new model for rocking. It is noteworthy that in their experiments that Pena et al [42] found better matching between the above value of r and the experimental values, which differ by much smaller percentage than in [7,45].…”
This paper concerns the dynamics of planar rocking blocks, which are mechanical systems subject to two unilateral constraints with friction. A recently introduced multiple impact law that incorporates Coulomb friction is validated through comparisons between numerical simulations and experimental data obtained elsewhere by other authors. They concern the free-rocking motion with no base excitation, and motions with various base excitations for the study of the onset of rocking and of the overturning phenomenon. The comparisons made for free-rocking and for the onset of rocking demonstrate that the proposed impact model allows one to correctly predict the block motions. Especially the free-rocking experiments can be used to fit the impact law parameters (restitution and friction coefficients, block width). The free-rocking fitted parameters are then used in the excited-base cases.
“…1 46,53,54,59,60] to cite a few. In parallel, the field of impact dynamics has witnessed an intense activity in the past 25 years; see, e.g., [8-10, 15, 18-20, 29, 31, 38, 48, 52, 66] and references therein.…”
mentioning
confidence: 99%
“…They found good agreements between their simulations and their experiments. Pena and Prieto et al [42,43,46] performed many experiments and also proposed a new model for rocking. It is noteworthy that in their experiments that Pena et al [42] found better matching between the above value of r and the experimental values, which differ by much smaller percentage than in [7,45].…”
This paper concerns the dynamics of planar rocking blocks, which are mechanical systems subject to two unilateral constraints with friction. A recently introduced multiple impact law that incorporates Coulomb friction is validated through comparisons between numerical simulations and experimental data obtained elsewhere by other authors. They concern the free-rocking motion with no base excitation, and motions with various base excitations for the study of the onset of rocking and of the overturning phenomenon. The comparisons made for free-rocking and for the onset of rocking demonstrate that the proposed impact model allows one to correctly predict the block motions. Especially the free-rocking experiments can be used to fit the impact law parameters (restitution and friction coefficients, block width). The free-rocking fitted parameters are then used in the excited-base cases.
“…Several approaches for the design of a rocking structure have also been proposed [18,19]. Prieto and Lourenço [20] described the impact effect of a rocking rigid block on a rigid base using the D'Alembert principle. Attention was seldom paid to the footing response, especially the contact force at the interface between the footing and the underlying soil.…”
Section: Introductionmentioning
confidence: 99%
“…Only a limited number of analytical studies on the impact mechanism due to uplift have been conducted. Prieto and Lourenço [20] described the impact effect of a rocking rigid block on a rigid base using the D'Alembert principle. They pointed out that the impacts make the total energy of a rocking block no longer equal to the sum of kinetic and potential energy.…”
“…Some authors have used the simple model of Housner to investigate analytically and numerically the rocking response of rigid blocks subjected to a seismic action as well as their stability [2,3,4,5], while others have defined a new formulation to unify the piecewise equation describing the rocking motion [6] or developed numerical tools based on the Discrete Element Method (DEM) to model the rigid block [7].…”
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