Mode-based equivalent multi-degree-of-freedom system for one-dimensional viscoelastic response analysis of layered soil deposit

Discrete models such as the lumped parameter model and the finite element model are widely used in the solution of soil amplification of earthquakes. However, neither of the models will accurately estimate the natural frequencies of soil deposit, nor simulate a damping of frequency independence. This research develops a new discrete model for onedimensional viscoelastic response analysis of layered soil deposit based on the mode equivalence method. The new discrete model is a one-dimensional equivalent multi-degree-of-freedom（MDOF） system characterized by a series of concentrated masses, springs and dashpots with a special configuration. The dynamic response of the equivalent MDOF system is analytically derived and the physical parameters are formulated in terms of modal properties. The equivalent MDOF system is verified through a comparison of amplification functions with the available theoretical solutions. The appropriate number of degrees of freedom（DOFs） in the equivalent MDOF system is estimated. A comparative study of the equivalent MDOF system with the existing discrete models is performed. It is shown that the proposed equivalent MDOF system can exactly present the natural frequencies and the hysteretic damping of soil deposits and provide more accurate results with fewer DOFs.

Simulation study of a magnetocardiogram based on a virtual heart model:effect of a cardiac equivalent source and a volume conductor

In this paper, we present a magnetocardiogram （MCG） simulation study using the boundary element method （BEM） and based on the virtual heart model and the realistic human volume conductor model. The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated. The single dipole source model, the multiple dipoles source model and the equivalent double layer （EDL） source model are analysed and compared with the cardiac equivalent source models. Meanwhile, the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated. The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken, while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source. Therefore, the EDL source is suitable for the study of MCG forward and inverse problems, and more attention should be paid to it in future MCG studies.

Comparison between Equivalent Charge Model and Equivalent Dipole Model on Realistic Head Model

Equivalent source layer （ESL） imaging is an important kind of high-resolution electro- encephalogram （EEG） imaging. It consists of two categories： equivalent dipole layer （EDL） and equivalent charge layer （ECL）. Both of them are assumed to be located on or near the cortical surface and have been proposed as high-resolution imaging modalities or as intermediate steps to estimate the epicortical potential. Here, EDL and ECL based on a realistic head model are presented, both simulations and real data experiment are done to compare these two models. The results show that ECL can provide higher spatial resolution about source location than EDL does.

Tooth Position and Deformation of Flexspline Assembled with Cam in Harmonic Drive Based on Force Analysis

Deformation of the flexspline is the basis of analyzing tooth trajectory and designing tooth profile.Considering the tooth influence on the position of equivalent neutral layer,a piecewise method for calculating the deformation of flexspline assembled with a cam wave generator is presented in this paper.Firstly,a mechanic model of a ring of uniform thickness in contact with a rigid cam is established.The displacements of the ring inside and outside an unknown wrapping angle are determined by the geometric constraints of the cam profile and the equilibrium rela-tionship,respectively.Meanwhile,the wrapping angle is solved according to the boundary conditions.The assembly forces are derived to investigate the circumferential elongation and strain.Then,considering the tooth effects on the neutral layer of flexspline,the tooth is positioned on the equivalent neutral layer,which is the non-elongation layer within one gear pitch but offset from the geometric mid-layer.The equivalent neutral layer is positioned by the empirical formula of the offset ratio,which is summarized by the orthogonal simulation on finite element models of racks.Finally,finite element models of a ring-shaped and a cup-shaped flexspline assembled with elliptical cam are established to verify the effectiveness and accuracy of the piecewise method.The results show that,compared with the geometric method,the tooth positioning deviation calculated by the piecewise method can be reduced by about 70%with a more accurate deformation description from the geometric condition and mechanic condition inside and outside the wrapping angle.

Free vibration of functionally graded sandwich plates in thermal environments

This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to obtain the solution.Two types of sandwich plates are examined in this study:one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets.The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method.The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature.The effects of volume fraction distribution,geometrical parameters,and temperature increments on the free vibration characteristics are discussed in detail.