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A mathematical analysis IS presented of the reduction of package stresses by mtroductng an on-chip decouphng zone Different configurations of the zones are compared, using the fimte-element method (FEM) and analytical models A reductton of several orders of magnitude 1s obtamed when a deep and thm axqmmetncal corrugation wtth a V-shaped cross sectlon (a V-zone) IS apphed as the decoupling zone Approximate expressions for the stiffness and the force reduction are derived The application of a membrane pressure sensor wrth a V-zone as decoupling zone IS evaluated It IS shown that the sensltwity of the sensor IS not reduced by the ad&bon of the V-zone

This paper deals with a theoretical and experimental investigation on a rigid, rectangular plate oscillating in the proximity of a fixed surface. The plate is suspended by springs. The airloads generated by the oscillating motion of the plate are determined. Due to the fact that the plate is rigid, the system is modelled as a 1-DOF system. The influence of the surrounding air is detected by changes in the plate's natural frequency and damping. For the behaviour of the air in the gap between the plate and the fixed surface an analytical solution is presented. This solution includes the effects of inertia, viscosity, compressibility and thermal conductivity. It is shown that the main parameters governing the motion of the air in the gap are the shear wave number, the reduced frequency, the narrowness of the gap and the aspect ratio of the plate. With these parameters the validity of several simplifications can easily be demonstrated and solutions, given in the literature, can be put in perspective. Special experiments were carried out with an oscillating solar panel in order to verify the analytical model. The analytical results and the experimental results show fair agreement. The solutions shows that for low shear wave numbers the effects of viscosity cannot be discarded.

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Various computational methods have been studied with respect to their suitability for obtaining very accurate solutions of plate vibration problems, especially for the higher modes. Because of the interest in the higher modes, also higher order effects such as transverse shear deformation and rotational inertia are considered. The Rayleigh-Ritz method with global trial functions appeared to be a suitable choice. To reach a high convergence rate in order to obtain accurate solutions, the complementary boundary conditions formulated by Baruh and Tadikonda should be satisfied. This can be accomplished when polynomials are used as trial functions. When the polynomials are not properly chosen, the algorithm is not numerically stable. It is shown that orthogonalization of the polynomials by means of the Gram-Schmidt process results in a numerical stable process. For free-free boundary conditions, these orthogonal polynomials are the well known Legendre polynomials. For other boundary conditions the resulting polynomials are very similar to the Legendre polynomials. Because of the very high convergence rates, these methods are suitable for obtaining accurate solutions. The numerical stability guarantees that also the higher modes can be calculated.