A MEMS Tunable Capacitor With Dual Deformation Modes and High Tunability and Linearity

MEMS tunable capacitors have applications in tunable filters and RF circuits where high tunability and Q-factor are desired. Conventional parallel-plate tunable capacitors have a highly nonlinear capacitance-voltage (C-V) response and limited tunability of up to 50% due to fundamental limitation and structural instability. In this work, we present a novel design idea for a parallel-plate tunable capacitor that increases the tuning ratio and provides a smoother (more linear) response. The design uses two modes of deformation, rigid-body displacement of a curved moving electrode before pull-in and deforming the plate after pull-in, and exploits nonlinear structural stiffness to improve the linearity (and the tunability) of the tunable parallel-plate capacitor. The capacitor structure is designed such that when actuation voltage is applied, first the beams holding the moving electrode deform, and capacitance increase similar to conventional design up to pull-in. After the pull-in, the top electrode (which has a curved geometry) is deformed and further increases the capacitance, as the voltage increases. The design may provide an overall simulated tunability of more than 380%, and also has a more linear C-V response. The design is modeled and simulated using ANSYS coupled-field multiphysics solver and the effect of different design parameters are investigated. The simulation results show much high tunability and better linearity than conventional parallel-plate capacitors.

Combining Finite Element and Analytical methods to Contact Problems of 3D Structure on Soft Foundation

The computational efficiency and nonconvergence of the iteration are two main difficulties in contact problems, especially in the creep of the foundation. This paper proposes a method to analyze the structural soft foundation system affected by time. The methodology is an explicit method, combining the finite element method with the analytical method. The creep deformation of soft foundation is obtained based on Laplace transforms. The structural deformation contains the statically determinate structural deformation and rigid body displacement, solved by the finite method. The contact forces are calculated by the deformation coordination equations and equilibrium equations. The methodology is validated through augmented Lagrangian (AL) method. The results can clearly illustrate the local disengagement phenome, greatly overcome the nonconvergence of the iteration, and significantly improve computing efficiency.

Coupling Vibration of Tapered Rod

In rod's free vibration, its easy to obtain normal modes. However, if there is rigid body displacement, the problem will be much more complex. To solve these kinds of problems, single flexible body dynamics is needed. As the first part of the paper, considering rods rigid body displacement, the free vibration of tapered rod is discussed. By solving partial differential equation of rods free vibration, normal frequencies of tapered rod are obtained. As the second part of the paper, coupling vibration is discussed, in which process quasi-variational principle as the most important tool is used. Finally, first-order frequency of coupled vibration of rod is represented.

On the Identities for Elastostatic Fundamental Solution and Nonuniqueness of the Traction BIE Solution for Multiconnected Domains

In this paper, the four integral identities satisfied by the fundamental solution for elastostatic problems are reviewed and slightly different forms of the third and fourth identities are presented. Two new identities, namely the fifth and sixth identities, are derived. These integral identities can be used to develop weakly singular and nonsingular forms of the boundary integral equations (BIEs) for elastostatic problems. They can also be employed to show the nonuniqueness of the solution of the traction (hypersingular) BIE for an elastic body on a multiconnected domain. This nonuniqueness is shown in a general setting in this paper. It is shown that the displacement (singular) BIE does not allow any rigid-body displacement terms, while the traction BIE can have arbitrary rigid-body translation and rotation terms, in the BIE solutions on the edge of a hole or surface of a void. Therefore, the displacement solution from the traction BIE is not unique. A remedy to this nonuniqueness solution problem with the traction BIE is proposed by adopting a dual BIE formulation for problems with multiconnected domains. A few numerical examples using the 2D elastostatic boundary element method for domains with holes are presented to demonstrate the uniqueness properties of the displacement, traction and the dual BIE solutions for multiconnected domain problems.

Optimal Shear Key Interval for Offshore Shallow Foundations

Embedment of offshore shallow foundations is typically achieved by ‘skirts’, i.e. thin vertical plates that protrude from the underside of a foundation top plate and penetrate the seabed confining a soil plug. Skirted shallow foundations are often idealized as a solid, rigid element for geotechnical analysis of the foundation, on the assumption that sufficient skirts, or ‘shear keys’ will be provided to ensure that the deformable soil plug displaces as a rigid body. Should too few shear keys be provided, failure mechanisms involving deformation within the soil plug may occur, leading to a reduction in load-carrying capacity. There is currently no formal guidance regarding the optimal spacing of shear keys to ensure rigid body displacement of the soil plug. The absence of guidance may lead to unconservative designs if the number of shear keys is under estimated to save on fabrication or to conservative designs if additional shear keys are provided to minimize the risk associated with the uncertainty. Either case is undesirable and clear benefit is to be gained from a better understanding of shear key spacing. This paper presents guidance on the minimum number of shear keys required to achieve optimal capacity of square and rectangular skirted foundations (i.e. equivalent to that of a solid rigid foundation) under undrained generalized six degree-of-freedom loading in soft soils with linearly increasing shear strength with depth.

Finite Displacement Screw Operators With Embedded Chasles’ Motion

Rigid body displacement can be presented with Chasles’ motion by rotating about an axis and translating along the axis. This motion can be implemented by a finite displacement screw operator in the form of either a 3 × 3 dual-number matrix or a 6 × 6 matrix that is executed with rotation and translation as an adjoint action of the Lie group. This paper investigates characteristics of this finite displacement screw matrix and decomposes the secondary part that is the off diagonal part of the matrix into the part of an equivalent translation due to the effect of off-setting the rotation axis and the part of an axial translation. The paper hence presents for the first time the axial translation matrix and reveals its property, leading to discovery of new results and new formulae. The analysis further reveals two new traces of the matrix and presents the relationship between the finite displacement screw matrix and the instantaneous screw, leading to the understanding of Chasles’ motion embedded in a rigid body displacement. An algebraic and geometrical interpretation of the finite displacementscrew matrix is thus given, presenting an intrinsic property of the matrix in relation to the finite displacement screw. The paper ends with a case study to verify the theory and illustrate the principle.