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The coupled acoustic field of fully elastic plate model is described by the modal analysis method. The acoustic potential energy resonance peaks of the fully elastic plate model are significantly more than that of the one elastic plate model due to the influence of the vibration of multi elastic plates. The acoustic field characteristics of the fully elastic plate model are analyzed when the primary excitation source is applied on the different elastic plates. The results show that the coupled acoustic field of the fully elastic plate model is dominated by the structural mode of the elastic plate with primary excitation, and the acoustic mode of the enclosure, and the structural-acoustic coupling between the plate and the enclosure; the structure modes of the other elastic plates have less effects on the acoustic field in the enclosure except the first ones of them.

In order to understand the dynamics of the tripod sliding universal joint, its dynamic equations were established and then the effects of the joint angle, the rotating radius and mass of the slide rods, the lengths of the input and output shafts and the frequency of the input shaft on its dynamics were investigated. The increase in the mass or rotating radius of the slide rods enhances the amplitudes of all dynamic curves and so does the frequency of the input shaft. Increasing length of the output shaft weakens the amplitudes of the forces and torques at the revolute and spherical pairs as well as the amplitude of the load torque but this length hardly affects the amplitudes of the forces at the tripod arm and the holes of the input shaft. The forces at the holes of the input shaft hardly depend on the joint angle whereas the amplitudes of the remaining dynamic curves increase with the increase of the joint angle. The amplitudes of two torques of the revolute pair increase with increasing length of the input shaft but the remaining forces (torques) are almost independent of its length.

This paper presents a new approach to the modeling of squeeze-film damping for electrically actuated microbeams under the effect of a static deflection. The approach utilizes the compressible Reynolds equation coupled with the equation governing the beam deflection. Two squeeze-film damping models for a cantilever microbeam and a fixed–fixed microbeam are derived, respectively. The pressure in the air gap is represented by the product of an assumed parabolic function along the beamwidth and a cosine series along the beam length. Compared with the previous models, the present models account for the static deflection due to the electric load; thus the present models can be used for general purpose design, analysis and optimization of microbeam-based devices. The accuracy of the present models is verified by comparing their results with the experimental results available in the literature.

Predicting air damping is crucial in the design of high Q microelectromechanical systems. In the past, air damping of rigid microbeam in free space at molecular regime is usually estimated using the free molecular model proposed by Christian (Vacuum 16:175–178, 1966), air damping of flexible microbeam is estimated using the model proposed by Blom (J Vac Sci Technol B 10:19–26, 1992). The relation between the two models is Q Blom = 3Q Christian. In this paper, a general proof is presented that shows the Christian’s model is valid for the air damping of flexible microbeam in free space at molecular regime. By comparing with the experimental results available in the literatures (Blom et al. in J Vac Sci Technol B 10:19–26, 1992; Yasumura et al. in J Micromech Syst 9:117–125, 2000), we conclude that the Christian’s model is the best choice in predicting the air damping of flexible microbeam in free space at the molecular regime.

Predicting thermoelastic damping is crucial for the design of high Q micromechanical resonators. In the past, for microresonators which consist of a proof mass and a network of suspension beams, some experiments showed that Zener's model [Phys. Rev. 52 (1937) 230; Phys. Rev. 53 (1938) 90] and Lifshitz and Roukes' model [Phys. Rev. B 61 (2000) 5600] can give a reasonable prediction, and others experiments showed that the two models fail to give a reasonable prediction. Few works give a reasonable and detailed explanation for this phenomenon. In this paper, a general proof is presented that shows Lifshitz and Roukes' model is valid for microresonators with a proof mass support by a network of suspension beams if all suspension beams are operated at pure bending vibration and all suspension beams have the same thickness. The accuracy of Lifshitz and Roukes' model is verified by comparing its results with the experimental results available in the literature.