By Paulo Flores, Hamid M. Lankarani
This e-book analyzes a number of compliant touch strength versions in the context of multibody dynamics, whereas additionally revisiting the most concerns linked to basic touch mechanics. specifically, it offers quite a few touch strength types, from linear to nonlinear, from merely elastic to dissipative, and describes their parameters. Addressing the various numerical equipment and algorithms for touch difficulties in multibody platforms, the e-book describes the gross movement of multibody structures through the use of a two-dimensional formula in line with absolutely the coordinates and employs varied touch versions to symbolize contact-impact occasions. effects for chosen planar multibody mechanical structures are offered and applied to debate the most assumptions and approaches followed all through this paintings. the fabric supplied the following shows that the prediction of the dynamic habit of mechanical structures related to contact-impact strongly is dependent upon the alternative of touch strength version. in brief, the e-book offers a entire source for the multibody dynamics neighborhood and past on modeling touch forces and the dynamics of mechanical structures present process contact-impact events.
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Extra resources for Contact Force Models for Multibody Dynamics
2011) and Gharib and Hurmuzlu (2012) present a close behavior. For these models, the hysteresis damping factor increases asymptotically with the decrease of the coefﬁcient of restitution, meaning that they can perform satisfactorily for perfectly inelastic contacts. It must be pointed out that the contact force models analyzed in this study do only hold if viscoelasticity is not the only dissipative process during the contact event. For the cases where friction, plastic deformation, brittle failure, fracture, adhesion, among other effects, have to be considered, there are more appropriate models to simulate the bodies in contact.
This is clear by observing the nonsymmetrical nature of the contact force plot. 10) is valid for impact velocities lower than the propagation velocity pﬃﬃﬃﬃﬃﬃﬃﬃﬃ of elastic waves across the two bodies, that is, d_ ðÀÞ 10À5 E=q, where E is the Young’s modulus and ρ is the material mass density (Love 1944). The quantity pﬃﬃﬃﬃﬃﬃﬃﬃﬃ E=q, velocity of wave propagation, is the larger of two propagation velocities of the elastic deformation waves in the colliding bodies. Shivaswamy (1997) studied theoretically and experimentally the impact between bodies and demonstrated that at low impact velocities, the hysteresis damping is the prime factor for energy dissipation.
This is clear by observing the nonsymmetrical nature of the contact force plot. 5 6 Contact force [kN] Penetration Contact force Contact force [kN] Penetration [µm] 40 4 2 0 0 10 20 30 40 Penetration [µm] Fig. 7 Externally colliding spheres modeled by Flores et al. 5 43 Other Dissipative Contact Force Models In this section, several dissipative contact force modelsproposed over the last decades are briefly presented (Alves et al. 2015). It is known that the contact process between two solid spherical bodies can be represented as a spring and a damper, as illustrated in Fig.
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