Journal of Micromechanics and Microengineering, 2004
Many MEMS devices employ parallel plates for capacitive sensing and actuation. The desire to get ... more Many MEMS devices employ parallel plates for capacitive sensing and actuation. The desire to get a significant change in capacitance has been pushing the need to reduce the gap between the moving plate and the fixed plate. With fabrication processes making rapid strides, it is now possible to push the gap to be so small that it becomes comparable to
In this paper, we investigate the effect of vacuum sealing the backside cavity of a Capacitive Mi... more In this paper, we investigate the effect of vacuum sealing the backside cavity of a Capacitive Micromachined Ultrasonic Transducer (CMUT). The presence or absence of air inside the cavity has a marked effect upon the system parameters, such as the natural frequency, damping, and the pull-in voltage. The presence of vacuum inside the cavity of the device causes a reduction in the effective gap height which leads to a reduction in the pull-in voltage. We carry out ANSYS simulations to quantify this reduction. The presence of vacuum inside the cavity of the device causes stress stiffening of the membrane, which changes the natural frequency of the device. A prestressed modal analysis is carried out to determine the change in natural frequency due to stress stiffening. The equivalent circuit method is used to evaluate the performance of the device in the receiver mode. The lumped parameters of the device are obtained and an equivalent circuit model of the device is constructed to determine the open circuit receiving sensitivity of the device. The effect of air in the cavity is included by incorporating an equivalent compliance and an equivalent resistance in the equivalent circuit.
MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant... more MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant frequency of the final fabricated structure can be a denting factor for its suitability towards a desired application. There are numerous factors which alter the designed resonant frequency of the fabricated resonator such as the metal layer deposited on top of the beam and the residual stresses present in the fabricated structure. While the metal coating, which acts as electrode, increases the stiffness and the effective mass of the composite structure, the residual stress increases or decreases the net stiffness if it is a tensile or compressive type respectively. In this paper, we investigate both these cases by taking two different structures, namely, the micro cantilever beam with gold layer deposited on its top surface and the MEMS gyroscope with residual stresses. First, we carry out experiments to characterize both these structures to find their resonant frequencies.
One of the critical design considerations in dynamic microelectromechanical systems (MEMS) device... more One of the critical design considerations in dynamic microelectromechanical systems (MEMS) devices is the structural natural frequency of the sensing or actuation element. Most dynamic MEMS devices employ planar geometry using an assembly of beams and plates for the structural elements. Most often the goal is to place the first resonant frequency at a desired value. Since the frequency depends on mass and stiffness of the structure, designing for frequency usually requires FEM analysis of the structure. FEM calculations are intensive, depend on many subtle modelling assumptions, and require huge number of simulations to build intuition. Since the design space for such structures is fairly high dimensional, tuning the frequency of the first-cut design can be a fairly intensive optimization computation. Here, we present a lumped parameter spring-mass model for a typical microstructure consisting of a plate and beams and show how the higher dimensional geometric design space can be partitioned to effect desired frequency changes in the structure linearly with the chosen design variables. In particular, four sets of design variables are considered and their effective range and sensitivity for linear tuning of the natural frequency is presented. We include the effect of residual stress on stiffness and show how the values of residual stress affect the tuning of the natural frequency with respect to the selected design variables. All results are compared with FEM calculations and a table is presented for cross comparison of efficacy of the different design variables. The goal is to present a simple analysis that can be easily followed by MEMS designers with any background and build their intuition for such designs.
Journal of Micromechanics and Microengineering, 2005
Closed-form expressions for the stiffness and the damping coefficients of a squeeze film are deri... more 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 from numerical (FEM) solutions of the compressible Reynolds equation for the two configurations
Nature has evolved a beautiful design for small-scale vibratory rategyro in the form of dipteran ... more Nature has evolved a beautiful design for small-scale vibratory rategyro in the form of dipteran halteres that detect body rotations via Coriolis acceleration. In most Diptera, including soldier fly, Hermetia illucens, halteres are a pair of special organs, located in the space between the thorax and the abdomen. The halteres along with their connecting joint with the fly's body constitute a mechanism that is used for muscle-actuated oscillations of the halteres along the actuation direction. These oscillations lead to bending vibrations in the sensing direction (out of the haltere's actuation plane) upon any impressed rotation due to the resulting Coriolis force. This induced vibration is sensed by the sensory organs at the base of the haltere in order to determine the rate of rotation. In this study, we evaluate the boundary conditions and the stiffness of the anesthetized halteres along the actuation and the sensing direction. We take several crosssectional SEM (scanning electron microscope) images of the soldier fly haltere and construct its three dimensional model to get the mass properties. Based on these measurements, we estimate the natural frequency along both actuation and sensing directions, propose a finite element model of the haltere's joint mechanism, and discuss the significance of the haltere's asymmetric cross-section. The estimated natural frequency along the actuation direction is within the range of the haltere's flapping frequency. However, the natural frequency along the sensing direction is roughly double the haltere's flapping frequency that provides a large bandwidth for sensing the rate of rotation to the soldier flies.
This paper deals with a group theoretic approach to the finite element analysis of linear free vi... more This paper deals with a group theoretic approach to the finite element analysis of linear free vibrations of shells with dihedral symmetry. Examples of such shell structures are cylindrical shells, conical shells, shells with circumferential stiffeners, corrugated shells, spherical shells, etc. The group theoretic approach is used to exploit the inherent symmetry in the problem. For vibration analysis, the group
A simple supported elasto-plastic beam is modeled as a single degree of freedom oscillator with b... more A simple supported elasto-plastic beam is modeled as a single degree of freedom oscillator with bilinear hysteresis. Kinematic hardening is used as a problem parameter and an explicit map is obtained for plastic cycles under free vibrations. This map is analyzed and a bifurcation ...
High quality factor of dynamic structures at micro and nano scale is exploited in various applica... more High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels
The dynamic response of a single-degree-of-freedom elasto-plastic oscillator with kinematic harde... more The dynamic response of a single-degree-of-freedom elasto-plastic oscillator with kinematic hardening is analyzed in this paper under two kinds of periodic impulse forcing: (a) direct and (b) parametric. In the first case, impulses of constant amplitude are applied periodically to the system and the resulting motion is analyzed using eigenvalues of the linearized Poincare map, and a boundary curve separating
Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this p... more Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this paper. A bilinear hysteretic model is used to represent the material non-linearity. The coefficient of kinematic hardening is used as a problem parameter in the equations of motion. By solving the governing equations on each branch of the hysteretic cycle and matching the transition conditions, an iterative
The squeeze-film damping in perforated structures is modelled using a modified Reynolds equation ... more The squeeze-film damping in perforated structures is modelled using a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green's function. The solution thus obtained adds an additional term to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting = 0, one recovers Blech's formulae. We compute the squeeze film forces using these new formulae and compare the computed forces with the solution of 3D Navier-Stokes equation solved using ANSYS for different perforation ratios (ratio of hole to cell dimensions). The results match very well. The approximate limit of maximum frequencies under which the formulae give reasonable results is also discussed. Although the main result is derived for a rigid plate under transverse motion, we discuss the effect of flexibility of the structure by deriving results for a flexible plate under a specified set of boundary conditions and comparing the results with that of a suitably modified rigid plate result. For small amplitude motion, the results show that a suitably modified rigid plate model can capture the effect of flexibility through a simple scaling factor.
A MEMS varactor using torsional beams for actuation is proposed. Analytical expression for electr... more A MEMS varactor using torsional beams for actuation is proposed. Analytical expression for electrostatic torque developed is derived. The structure is compared with existing structures for dynamic range and actuation voltage. It is demonstrated that the proposed varactor outperforms the other structures in terms of wide dynamic range and lower actuation voltage, coupled with ease of fabrication. A methodology to choose the dimensions of varactor beams and plates has been outlined.
MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant... more MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant frequency of the final fabricated structure can be a denting factor for its suitability towards a desired application. There are numerous factors which alter the designed resonant frequency of the fabricated resonator such as the metal layer deposited on top of the beam and the residual stresses present in the fabricated structure. While the metal coating, which acts as electrode, increases the stiffness and the effective mass of the composite structure, the residual stress increases or decreases the net stiffness if it is a tensile or compressive type respectively. In this paper, we investigate both these cases by taking two different structures, namely, the micro cantilever beam with gold layer deposited on its top surface and the MEMS gyroscope with residual stresses. First, we carry out experiments to characterize both these structures to find their resonant frequencies.
In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor tha... more In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor that uses in-plane motion for both actuation and sensing. The design criterion for the rate sensor is based on a high sensitivity and low bandwidth. The required sensitivity of the yaw rate sensor is attained by using the inplane motion in which the dominant damping mechanism is the fluid loss due to slide film damping i.e. two-three orders of magnitude less than the squeeze-film damping in other rate sensors with out-of-plane motion. The low bandwidth is achieved by matching the drive and the sense mode frequencies. Based on these factors, the yaw rate sensor is designed and finally realized using surface micromachining. The inplane motion of the sensor is experimentally characterized to determine the sense and the drive mode frequencies, and corresponding damping ratios. It is found that the experimental results match well with the numerical and the analytical models with less than 5% error in frequencies measurements. The measured quality factor of the sensor is approximately 467, which is two orders of magnitude higher than that for a similar rate sensor with out-of-plane sense direction.
In this work, the natural frequencies and mode shapes of polygonal ducts are obtained by a finite... more In this work, the natural frequencies and mode shapes of polygonal ducts are obtained by a finite element analysis via a group theoretic approach. We show that the group theoretic techniques provide a natural setting for the solution of the problem via optimum utilization of the ...
Journal of Micromechanics and Microengineering, 2008
... Ashok Kumar Pandey1 and Rudra Pratap2,3 ... Technion-Israel Institute of Technology, Haifa, I... more ... Ashok Kumar Pandey1 and Rudra Pratap2,3 ... Technion-Israel Institute of Technology, Haifa, Israel 2 CranesSci MEMS Lab, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnataka, India E-mail: [email protected] and [email protected] ...
Journal of Micromechanics and Microengineering, 2007
... Ashok Kumar Pandey and Rudra Pratap CranesSci MEMS Lab, Department of Mechanical Engineering,... more ... Ashok Kumar Pandey and Rudra Pratap CranesSci MEMS Lab, Department of Mechanical Engineering, Indian Institute of Science, Bangalore-560012, Karnataka, India E-mail: [email protected] and [email protected] ...
Journal of Micromechanics and Microengineering, 2004
Many MEMS devices employ parallel plates for capacitive sensing and actuation. The desire to get ... more Many MEMS devices employ parallel plates for capacitive sensing and actuation. The desire to get a significant change in capacitance has been pushing the need to reduce the gap between the moving plate and the fixed plate. With fabrication processes making rapid strides, it is now possible to push the gap to be so small that it becomes comparable to
In this paper, we investigate the effect of vacuum sealing the backside cavity of a Capacitive Mi... more In this paper, we investigate the effect of vacuum sealing the backside cavity of a Capacitive Micromachined Ultrasonic Transducer (CMUT). The presence or absence of air inside the cavity has a marked effect upon the system parameters, such as the natural frequency, damping, and the pull-in voltage. The presence of vacuum inside the cavity of the device causes a reduction in the effective gap height which leads to a reduction in the pull-in voltage. We carry out ANSYS simulations to quantify this reduction. The presence of vacuum inside the cavity of the device causes stress stiffening of the membrane, which changes the natural frequency of the device. A prestressed modal analysis is carried out to determine the change in natural frequency due to stress stiffening. The equivalent circuit method is used to evaluate the performance of the device in the receiver mode. The lumped parameters of the device are obtained and an equivalent circuit model of the device is constructed to determine the open circuit receiving sensitivity of the device. The effect of air in the cavity is included by incorporating an equivalent compliance and an equivalent resistance in the equivalent circuit.
MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant... more MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant frequency of the final fabricated structure can be a denting factor for its suitability towards a desired application. There are numerous factors which alter the designed resonant frequency of the fabricated resonator such as the metal layer deposited on top of the beam and the residual stresses present in the fabricated structure. While the metal coating, which acts as electrode, increases the stiffness and the effective mass of the composite structure, the residual stress increases or decreases the net stiffness if it is a tensile or compressive type respectively. In this paper, we investigate both these cases by taking two different structures, namely, the micro cantilever beam with gold layer deposited on its top surface and the MEMS gyroscope with residual stresses. First, we carry out experiments to characterize both these structures to find their resonant frequencies.
One of the critical design considerations in dynamic microelectromechanical systems (MEMS) device... more One of the critical design considerations in dynamic microelectromechanical systems (MEMS) devices is the structural natural frequency of the sensing or actuation element. Most dynamic MEMS devices employ planar geometry using an assembly of beams and plates for the structural elements. Most often the goal is to place the first resonant frequency at a desired value. Since the frequency depends on mass and stiffness of the structure, designing for frequency usually requires FEM analysis of the structure. FEM calculations are intensive, depend on many subtle modelling assumptions, and require huge number of simulations to build intuition. Since the design space for such structures is fairly high dimensional, tuning the frequency of the first-cut design can be a fairly intensive optimization computation. Here, we present a lumped parameter spring-mass model for a typical microstructure consisting of a plate and beams and show how the higher dimensional geometric design space can be partitioned to effect desired frequency changes in the structure linearly with the chosen design variables. In particular, four sets of design variables are considered and their effective range and sensitivity for linear tuning of the natural frequency is presented. We include the effect of residual stress on stiffness and show how the values of residual stress affect the tuning of the natural frequency with respect to the selected design variables. All results are compared with FEM calculations and a table is presented for cross comparison of efficacy of the different design variables. The goal is to present a simple analysis that can be easily followed by MEMS designers with any background and build their intuition for such designs.
Journal of Micromechanics and Microengineering, 2005
Closed-form expressions for the stiffness and the damping coefficients of a squeeze film are deri... more 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 from numerical (FEM) solutions of the compressible Reynolds equation for the two configurations
Nature has evolved a beautiful design for small-scale vibratory rategyro in the form of dipteran ... more Nature has evolved a beautiful design for small-scale vibratory rategyro in the form of dipteran halteres that detect body rotations via Coriolis acceleration. In most Diptera, including soldier fly, Hermetia illucens, halteres are a pair of special organs, located in the space between the thorax and the abdomen. The halteres along with their connecting joint with the fly's body constitute a mechanism that is used for muscle-actuated oscillations of the halteres along the actuation direction. These oscillations lead to bending vibrations in the sensing direction (out of the haltere's actuation plane) upon any impressed rotation due to the resulting Coriolis force. This induced vibration is sensed by the sensory organs at the base of the haltere in order to determine the rate of rotation. In this study, we evaluate the boundary conditions and the stiffness of the anesthetized halteres along the actuation and the sensing direction. We take several crosssectional SEM (scanning electron microscope) images of the soldier fly haltere and construct its three dimensional model to get the mass properties. Based on these measurements, we estimate the natural frequency along both actuation and sensing directions, propose a finite element model of the haltere's joint mechanism, and discuss the significance of the haltere's asymmetric cross-section. The estimated natural frequency along the actuation direction is within the range of the haltere's flapping frequency. However, the natural frequency along the sensing direction is roughly double the haltere's flapping frequency that provides a large bandwidth for sensing the rate of rotation to the soldier flies.
This paper deals with a group theoretic approach to the finite element analysis of linear free vi... more This paper deals with a group theoretic approach to the finite element analysis of linear free vibrations of shells with dihedral symmetry. Examples of such shell structures are cylindrical shells, conical shells, shells with circumferential stiffeners, corrugated shells, spherical shells, etc. The group theoretic approach is used to exploit the inherent symmetry in the problem. For vibration analysis, the group
A simple supported elasto-plastic beam is modeled as a single degree of freedom oscillator with b... more A simple supported elasto-plastic beam is modeled as a single degree of freedom oscillator with bilinear hysteresis. Kinematic hardening is used as a problem parameter and an explicit map is obtained for plastic cycles under free vibrations. This map is analyzed and a bifurcation ...
High quality factor of dynamic structures at micro and nano scale is exploited in various applica... more High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels
The dynamic response of a single-degree-of-freedom elasto-plastic oscillator with kinematic harde... more The dynamic response of a single-degree-of-freedom elasto-plastic oscillator with kinematic hardening is analyzed in this paper under two kinds of periodic impulse forcing: (a) direct and (b) parametric. In the first case, impulses of constant amplitude are applied periodically to the system and the resulting motion is analyzed using eigenvalues of the linearized Poincare map, and a boundary curve separating
Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this p... more Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this paper. A bilinear hysteretic model is used to represent the material non-linearity. The coefficient of kinematic hardening is used as a problem parameter in the equations of motion. By solving the governing equations on each branch of the hysteretic cycle and matching the transition conditions, an iterative
The squeeze-film damping in perforated structures is modelled using a modified Reynolds equation ... more The squeeze-film damping in perforated structures is modelled using a modified Reynolds equation that includes compressibility and rarefaction effect. This equation is linearized and transformed to the standard two-dimensional diffusion equation using a simple mapping function. The analytical solution is then obtained using Green's function. The solution thus obtained adds an additional term to the damping and spring force expressions derived by Blech for compressible squeeze flow through non-perforated plates. This additional term contains several parameters related to perforations and rarefaction. Setting = 0, one recovers Blech's formulae. We compute the squeeze film forces using these new formulae and compare the computed forces with the solution of 3D Navier-Stokes equation solved using ANSYS for different perforation ratios (ratio of hole to cell dimensions). The results match very well. The approximate limit of maximum frequencies under which the formulae give reasonable results is also discussed. Although the main result is derived for a rigid plate under transverse motion, we discuss the effect of flexibility of the structure by deriving results for a flexible plate under a specified set of boundary conditions and comparing the results with that of a suitably modified rigid plate result. For small amplitude motion, the results show that a suitably modified rigid plate model can capture the effect of flexibility through a simple scaling factor.
A MEMS varactor using torsional beams for actuation is proposed. Analytical expression for electr... more A MEMS varactor using torsional beams for actuation is proposed. Analytical expression for electrostatic torque developed is derived. The structure is compared with existing structures for dynamic range and actuation voltage. It is demonstrated that the proposed varactor outperforms the other structures in terms of wide dynamic range and lower actuation voltage, coupled with ease of fabrication. A methodology to choose the dimensions of varactor beams and plates has been outlined.
MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant... more MEMS resonators are designed for a fixed resonant frequency. Therefore, any shift in the resonant frequency of the final fabricated structure can be a denting factor for its suitability towards a desired application. There are numerous factors which alter the designed resonant frequency of the fabricated resonator such as the metal layer deposited on top of the beam and the residual stresses present in the fabricated structure. While the metal coating, which acts as electrode, increases the stiffness and the effective mass of the composite structure, the residual stress increases or decreases the net stiffness if it is a tensile or compressive type respectively. In this paper, we investigate both these cases by taking two different structures, namely, the micro cantilever beam with gold layer deposited on its top surface and the MEMS gyroscope with residual stresses. First, we carry out experiments to characterize both these structures to find their resonant frequencies.
In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor tha... more In this paper, we present the design and characterization of a vibratory yaw rate MEMS sensor that uses in-plane motion for both actuation and sensing. The design criterion for the rate sensor is based on a high sensitivity and low bandwidth. The required sensitivity of the yaw rate sensor is attained by using the inplane motion in which the dominant damping mechanism is the fluid loss due to slide film damping i.e. two-three orders of magnitude less than the squeeze-film damping in other rate sensors with out-of-plane motion. The low bandwidth is achieved by matching the drive and the sense mode frequencies. Based on these factors, the yaw rate sensor is designed and finally realized using surface micromachining. The inplane motion of the sensor is experimentally characterized to determine the sense and the drive mode frequencies, and corresponding damping ratios. It is found that the experimental results match well with the numerical and the analytical models with less than 5% error in frequencies measurements. The measured quality factor of the sensor is approximately 467, which is two orders of magnitude higher than that for a similar rate sensor with out-of-plane sense direction.
In this work, the natural frequencies and mode shapes of polygonal ducts are obtained by a finite... more In this work, the natural frequencies and mode shapes of polygonal ducts are obtained by a finite element analysis via a group theoretic approach. We show that the group theoretic techniques provide a natural setting for the solution of the problem via optimum utilization of the ...
Journal of Micromechanics and Microengineering, 2008
... Ashok Kumar Pandey1 and Rudra Pratap2,3 ... Technion-Israel Institute of Technology, Haifa, I... more ... Ashok Kumar Pandey1 and Rudra Pratap2,3 ... Technion-Israel Institute of Technology, Haifa, Israel 2 CranesSci MEMS Lab, Department of Mechanical Engineering, Indian Institute of Science, Bangalore, Karnataka, India E-mail: [email protected] and [email protected] ...
Journal of Micromechanics and Microengineering, 2007
... Ashok Kumar Pandey and Rudra Pratap CranesSci MEMS Lab, Department of Mechanical Engineering,... more ... Ashok Kumar Pandey and Rudra Pratap CranesSci MEMS Lab, Department of Mechanical Engineering, Indian Institute of Science, Bangalore-560012, Karnataka, India E-mail: [email protected] and [email protected] ...
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