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Presented in this paper is a micro-resonant acceleration sensor based on the frequency shift of quartz double ended tuning fork (DETF). The structure is silicon substrate having a proof mass supported by two parallel flexure hinges as doubly sustained cantilever, with a resonating DETF located between the hinges. The acceleration normal to the chip plane induces an axial stress in the DETF beam and, in turn, a proportional shift in the beam resonant frequency. Substrate is manufactured by single-crystal silicon for stable mechanical properties and batch-fabrication processes. Electrodes on the four surfaces of DETF beam excite anti-phase vibration model, to balance inner stress and torque and imply a high quality factor. The sensor is simply packaged and operates unsealed in atmosphere for measurements. The tested natural frequency is 36.9 kHz and the sensitivity is 21 Hz/g on a nominally ±100 g device, which is in good agreement with analytical calculation and finite element simulation. The output frequency drifting is less than 0.5 Hz (0.0014% of steady output) within 1 h. The nonlinearity is 0.0019%FS and hysteresis is 0.0026%FS. The testing results confirm the feasibility of combining quartz DETF and silicon substrate to achieve a micro-resonant sensor based on simple processing for digital acceleration measurements.

The error estimates for moving least-square approximation, which is the method for obtaining the shape function in element-free Galerkin method, are presented in Sobolev space Wk,p(Ω) for high dimensional problems. Then on the basis of element-free Galerkin method for potential problems, the error estimates for element-free Galerkin method for potential problems, in which the essential boundary conditions are enforced by penalty methods, are obtained. The error estimates we present in this paper have optimal order when the nodes and shape functions satisfy certain conditions. From the error analysis, it is shown that the error bound of the potential problem is directly related to the radii of the weight functions. Two numerical examples are also given to verify the conclusions in this paper.

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In this paper, the finite point method is used to obtain the solution of a one-d imensional inverse heat conduction problem with a source parameter, and the corr esponding discrete equations are obtained. Compared with the numerical methods b ased on mesh, the finite point method only needs the scattered nodes instead of meshing the domain of the problem. The finite point method is a meshless method in which the moving least-square approximation is used to form the meshless appr oximation functions. And the collocation method is used to discretize the govern ing partial differential equations. The finite point method has the advantages o f simpler numerical procedures, lower computation cost and arbitrary nodes. The result of a numerical example is presented to show the method is effective.