scholarly journals Nonlinear Dynamics of an Internally Resonant Base-Isolated Beam under Turbulent Wind Flow

2021 ◽  
Vol 11 (7) ◽  
pp. 3213
Author(s):  
Simona Di Nino ◽  
Daniele Zulli ◽  
Angelo Luongo
Keyword(s):  
Nonlinear Dynamics ◽  
Base Isolation ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Multiple Scale ◽  
Wind Flow ◽  
Isolation System ◽  
Turbulent Wind ◽  
The Mean ◽  
Limit Cycle Amplitude

A base isolation system, aimed to passively control the nonlinear dynamics of an internally resonant tower, exposed to turbulent wind flow, is studied. A continuous visco-elastic beam, constrained at the bottom end by a nonlinear visco-elastic device and free at the top end, is considered. All the nonlinearities, structural, inertial and aeroelastic, these latter computed via the quasi-static theory, are accounted in the model. The interaction between self- and parametric excitations, triggered by the mean wind velocity and the turbulent component, respectively, are analyzed. The Multiple Scale Method is applied to the partial differential equations of motion, to investigate critical and post-critical behaviors, when two modes in internal 1:3 resonance are involved in the response. The first mode is found to lead the phenomenon, while the second mode is marginally involved. The effectiveness of the visco-elastic nonlinear isolation system is assessed, both in increasing the mean wind bifurcation value and in reducing the limit-cycle amplitude. The contribution of structural nonlinearities is found to weakly affect the response.

scholarly journals Nonlinear dynamics of a base-isolated beam under turbulent wind flow

2021 ◽  
Author(s):  
Simona Di Nino ◽  
Angelo Luongo
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Perturbation Methods ◽  
Wind Flow ◽  
Viscoelastic Beam ◽  
Static Theory ◽  
Isolation System ◽  
Turbulent Wind ◽  
Nonlinear Viscoelastic ◽  
Mechanical Performances

AbstractA homogeneous continuous viscoelastic beam, describing the dynamics of a base-isolated tower, exposed to a uniformly distributed turbulent wind flow, is studied. The beam is constrained at the bottom end by a nonlinear viscoelastic device, and it is free at the top end. Aeroelastic forces are computed by the quasi-static theory. The steady component of wind is responsible for a Hopf bifurcation, and the turbulent component induces parametric excitation. The interaction between the two bifurcations is investigated. Critical and post-critical behavior is analyzed by perturbation methods. The mechanical performances of the structure are discussed to assess the effectiveness of the viscoelastic isolation system.

scholarly journals Nonlinear Aeroelastic in-Plane Behavior of Suspension Bridges under Steady Wind Flow

2020 ◽  
Vol 10 (5) ◽  
pp. 1689 ◽  
Author(s):  
Simona Di Nino ◽  
Angelo Luongo
Keyword(s):  
Elastic Beam ◽  
Suspension Bridge ◽  
Multiple Scale ◽  
Continuous Model ◽  
Suspension Bridges ◽  
Wind Flow ◽  
Aeroelastic System ◽  
Natural Modes ◽  
Structural Nonlinearities ◽  
Limit Cycle Amplitude

The nonlinear aeroelastic behavior of suspension bridges, undergoing dynamical in-plain instability (galloping), is analyzed. A nonlinear continuous model of bridge is formulated, made of a visco-elastic beam and a parabolic cable, connected each other by axially rigid suspenders, continuously distributed. The structure is loaded by a uniform wind flow which acts normally to the bridge plane. Both external and internal damping are accounted for the structure, according to the Kelvin-Voigt rheological model. The nonlinear aeroelastic effects are evaluated via the quasi-static theory, while structural nonlinearities are not taken into account. First, the free dynamics of the undamped bridge are addressed, and the natural modes determined. Then, the nonlinear equations ruling the dynamics of the aeroelastic system, close to the bifurcation point, are tackled by the Multiple Scale Method. This is directly applied to the partial differential equations, and provides the finite-dimensional bifurcation equations. From these latter, the limit-cycle amplitude and its stability are evaluated as function of the mean wind velocity. A case study of suspension bridge is analyzed.

INFLUENCE OF HIGH INITIAL ISOLATOR STIFFNESS ON THE SEISMIC RESPONSE OF A BASE-ISOLATED BENCHMARK BUILDING

2011 ◽  
Vol 11 (06) ◽  
pp. 1201-1228 ◽  
Author(s):  
AJAY SHARMA ◽  
R. S. JANGID
Keyword(s):  
Degrees Of Freedom ◽  
Base Isolation ◽  
Near Field ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Time History ◽  
Base Shear ◽  
Isolation System ◽  
Base Displacement ◽  
Floor Acceleration

The influence of high initial isolator stiffness on the response of a base-isolated benchmark building is investigated. The base-isolated building is modeled as a three-dimensional linear-elastic structure having three degrees-of-freedom at each floor level. The time-history analysis of this building is carried out by solving the governing equations of motion using Newmark-beta method along with an iterative predictor–corrector approach. The force–deformation behavior of the isolation system is modeled by a bilinear law, which can be effectively used to model all isolation systems in practice. Three near-field earthquakes with bidirectional ground motions are considered. Structural response parameters such as absolute top floor acceleration, base shear, and base displacement are chosen for investigating the effects of high initial isolator stiffness. It was observed that the high initial isolator stiffness of the isolation system excites the higher modes in the base-isolated building and increases the top floor acceleration. Such a phenomenon can be detrimental to the sensitive instruments placed in the isolated structure. On the other hand, both the base displacement and base shear reduce marginally due to increase in the initial isolator stiffness. Further, the influences of high initial isolator stiffness are found to dependent on the period and characteristic strengths of the base isolation system.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

scholarly journals Influence of Elastomeric Bearings in Tension on the Seismic Performance of Base-Isolated r.c. Buildings

2020 ◽  
Vol 11 (1) ◽  
pp. 82
Author(s):  
Fabio Mazza ◽  
Mirko Mazza
Keyword(s):  
Base Isolation ◽  
Nonlinear Models ◽  
Vertical Component ◽  
Computer Code ◽  
Nonlinear Phenomena ◽  
Isolation System ◽  
Elastomeric Bearings ◽  
Near Fault ◽  
Base Isolation System ◽  
Near Fault Earthquakes

Elastomeric bearings are commonly used in base-isolation systems to protect the structures from earthquake damages. Their design is usually developed by using nonlinear models where only the effects of shear and compressive loads are considered, but uncertainties still remain about consequences of the tensile loads produced by severe earthquakes like the near-fault ones. The present work aims to highlight the relapses of tension on the response of bearings and superstructure. To this end, three-, seven- and ten-storey r.c. framed buildings are designed in line with the current Italian seismic code, with a base-isolation system constituted of High-Damping-Rubber Bearings (HDRBs) designed for three values of the ratio between the vertical and horizontal stiffnesses. Experimental and analytical results available in literature are used to propose a unified nonlinear model of the HDRBs, including cavitation and post-cavitation of the elastomer. Nonlinear incremental dynamic analyses of the test structures are carried out using a homemade computer code, where other models of HDRBs considering only some nonlinear phenomena are implemented. Near-fault earthquakes with comparable horizontal and vertical components, prevailing horizontal component and prevailing vertical component are considered as seismic input. Numerical results highlight that a precautionary estimation of response parameters of the HDRBs is attained referring to the proposed model, while its effects on the nonlinear response of the superstructure are less conservative.

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