Analytical solutions for the stiffness and damping coefficients of squeeze films in MEMS devices with perforated back plates

Closed-form expressions for the stiffness and the damping coefficients of a squeeze film are derived for MEMS devices with perforated back plates. Two kinds of perforation configurations are considered—staggered and matrix or non-staggered configuration. The analytical solutions are motivated from the observation of repetitive pressure patterns obtained fromnumerical (FEM) solutions of the compressible Reynolds equation for the two configurations using ANSYS. A single pressure pattern is isolated and further subdivided into circular pressure cells. Circular geometry is used based on observed symmetry. Using suitable boundary conditions, the Reynolds equation is analytically solved over the pressure cells. The complex pressure obtained is used to identify the stiffness and damping offered by the pressure cells. The stiffness and damping forces due to pressure cells within a pattern are added up separately. In turn, the stiffness and damping due to all the patterns are summed up resulting in the stiffness and damping forces due to the entire squeeze film. The damping and spring forces thus obtained analytically are compared with those obtained from the FEM simulations in ANSYS. The match is found to be very good. The regime of validity and limitations of the analytical solutions are assessed in terms of design parameters such as pitch to air gap, hole length to diameter and pitch to hole radius ratios. The analysis neglects inertial effects. Hence, the results are presented for low values of Reynolds number

Additives in Wood Products : Today and Future Development

Most wood products include additives. They may be preservatives to protect the wood against biological degradation or against fire, coatings for protection or to give the wood a more favourable aesthetic appearance, non-wood materials to improve the performance of the product and overcome weaknesses in the wood material, or plastics in combinations with wood residues to create new types of wood–plastic combinations. The global wood industry is, for example the largest user of adhesives; about 80 % of all wood and wood-based products involve some form of bonding and 70 % of the total volume of adhesives produced is consumed in the woodworking industry. Wood can thus be regarded as a composite consisting of wood-based materials combined with other materials to form an aggregate material. An example is plywood, in which veneers are joined with adhesive to form a flat panel. Other types of wood composites include various board products, structural composite timber and, furniture and joinery components, all including some form of bonding with adhesive. This situation obviously influences the way in which we should relate to wood products and their environmental impacts. This chapter gives a state-of-the-art presentation of different additives currently being used in wood products. This information is necessary for further studies on the influence that these additives have on the service life and on environmental aspects, and the limitations which they may impose on the reuse, recycling and upgrading of wood productsGodkänd; 2016; 20160401 (andbra)</p