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Nonlinear coupled moving-load excited dynamics of beam-mass structures

Ghayesh M. H., Farokhi H., Zhang Y., Gholipour A.

Archives of Civil and Mechanical Engineering

2020

Vol. 20, no. 2

207--217

Investigated in this paper is the first on the moving-load-caused nonlinear coupled dynamics of beam-mass systems. A constant value load excites the beam-mass system where its position on the beam-mass system changes periodically. The energy contribution of the moving load is included via a virtual work formulation. The kinetic energy of the mass together with the beam as well as energy stored in the beam after deflection is formulated. Hamilton’s principle gives nonlinear equations of the beam-mass system under a moving load in a coupled transverse/longitudinal form. A weighted-residual-based discretisation gives a 20 degree of freedom which is numerically integrated via continuation/time integration along with Floquet theory techniques. The resonance dynamics in time, frequency, and spatial domains is investigated. As we shall see, torus bifurcations are present for some beam-mass structure parameters as well as travelling waves. A finite element analysis is performed for a simpler linear version of the problem for to-some-extend verifications.

Nonlinear motion characteristics of microarches under axial loads based on modified couple stress theory

Farokhi H., Ghayesh M. H.

Archives of Civil and Mechanical Engineering

2015

Vol. 15, no. 2

401--411

The aim of the present study is to investigate the geometrically nonlinear size-dependent bending as well as resonant behaviour over the bent state of a microarch under an axial load. In particular, an axial load is applied on the system causing the initial curvature to increase by giving rise to a new bent configuration. A distributed harmonic transverse force is then exerted on the microarch and the nonlinear resonant response of the system over the new deflected configuration is investigated. The nonlinear partial differential equation of motion is obtained via Hamilton's principle based on the modified couple stress theory. The equation is discretized into a set of nonlinear ordinary differential equations through use of the Galerkin scheme. The pseudo-arclength continuation technique is then applied to the resultant set of ordinary differential equations. First, for the unforced system in the transverse direction, the axial load is increased and the new deflected configuration of the system is plotted versus the axial compression load; the nonlinear resonant response over the deflected configuration is then investigated through constructing frequency–response and force–response curves.