Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion

Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.

Ground-motion simulation for the MW6.1 Ludian earthquake on 3 August 2014 using the stochastic finite-fault method

The stochastic finite-fault simulation method was applied to synthesize the horizontal ground acceleration seismograms produced by the MW6.1 Ludian earthquake on August 3,2014.For this purpose,we produced first a total of 200 kinematic source models for the Ludian event,which are characterized by the heterogeneous slip on the conjugated ruptured fault and the slip-dependent spreading of the rupture front.The results indicated that the heterogeneous slip and the spatial extent of the ruptured fault play dominant roles in the spatial distribution of ground motions in the near-fault area.The peak ground accelerations(PGAs)and 5%-damped pseudospectral accelerations(PSAs)at periods shorter than 0.5 s estimated on the resulting synthetics generally match well with the observations at stations with Joyner-Boore distances(RJB)greater than 20 km.The synthetic PGVs and PSAs at periods of 0.5 s and 0.75 s are in good agreement with predicted medians by the Yu14 model(Yu et al.,2014).However,the synthetic results are generally much lower than the predicted medians by BSSA14 model(Boore et al.,2014).Moreover,the ground motion variability caused by the randomness in the source rupture process was evaluated by these synthetics.The standard deviations of PSAs on the base-10 logarithmic scale,Sigma[log10(PSA)],are closely dependent on either the spectral period or the RJB.The Sigma[log10(PSA)]remains a constant approximately 0.55 at periods shorter than 0.1 s,and then increase continuously up to^0.13 as the period increases from 0.1 to 2.0 s.The Sigma[log10(PSA)]values at periods of 0.1‒2.0 s show the downward tendency as the RJB values increase.However,the Sigma[log10(PSA)]​values at periods shorter than 0.1 s decrease as the RJB values increase up to^50 km,and then increase with the increasing RJB.Furthermore,we found that the ground-motion variability shows the significant dependence on the azimuth.

An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.