Lie group analysis of non-linear dynamic of micro structures under electrostatic field

Changizi, M. Amin; Stiharu, Ion

doi:10.3233/jcm-150546

Cited by 3 publications

(7 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There is no close form analytical formulation in the best of our knowledge to express the solution of the non-linear equation (6) [11]. The micro dimensions of the involved structures contribute to the stiffness of the ODE.…”

Section: Theorymentioning

confidence: 99%

“…For this reason, no analytical solution for this ODE can be formulated. One can show that there is no transformation of scaling or rotation symmetry for (6) [11]. This equation has a singularity (where…”

Section: Theorymentioning

confidence: 99%

“…An infinitesimal transformation is applied as an operator on itself and, both functions ξ and η defined in (9), must satisfy the following equality [11]: η xx + (2η xy − ξ xx )ý +(η yy − 2ξ xy )ý2 − ξ yy ý3 + (η y − 2ξ x − 3ξ y ý)ω = ω x + ηω y + ((η x − ξ x )ý− ξ y ý2) ω ý (12) Subsequently, ξ and η can be calculated by decomposed [3][4][5][6] into a system of partial differential equations. The following Lie symmetries which including rotation, translation and scaling was considered to calculate ξ and η. ξ = C 1 + C 2 x + C 3 y η = C 4 + C 5 x + C 6 y (13)…”

Section: Theorymentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Changizi¹,

Stiharu²

2017

IJMEM

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Changizi¹,

Stiharu²

2017

IJMEM

Self Cite

View full text Add to dashboard Cite

show abstract

“…This represents the classical problem [1][2][3]. This case is verified assuming that the bottom beam is extremely thick (2m).…”

Section: Single Beam Pull-in Voltagementioning

confidence: 99%

“…The operation of micro-cantilever structures under the influence of different types of electric fields has been investigated. Modelling of the phenomenon as well as experimental works were reported [2,3,4]. The differential equation that describes the dynamic behaviour of the microsystem consisting of a micro-cantilever beam close to a rigid substrate charged at different potentials can lead to evaluate the pull-in voltage.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Analysis of Pull-in Voltage of Twin Micro-Cantilever Beams with Different Dimensions

Changizi¹,

Sarafrazi²,

Stiharu³

2017

Proceedings of the 4th International Conference of Control, Dynamic Systems, and Robotics (CDSR'17)

Self Cite

View full text Add to dashboard Cite

-Micro-cantilevers are micromechanical structures that are being used in detection and sensing as MEMS. The easy usage and the relatively simple fabrication of micro-cantilever beams make them stand as suitable candidates for a wide variety of engineering applications. Dynamic capability of micro-cantilever beams to withstand considerable impacts and even various static loadings make them useful in applications as AFM, inertial sensors, or flow applications. Specific configurations with micro cantilever beams could be used for more advanced applications such as liquid viscosity measurement. The main objective of this research is to investigate the nonlinear dynamic behaviour of two parallel micro cantilever beams with slightly different geometry under the condition of closed to pull-in voltage. The governing differential equations that model closely the dynamical behaviour microcantilever beams under electrostatic field are used in the formulation. The model is based on discreet 2 degree of freedom mass-springdamping. The electrostatic loading induces the dynamical behaviour of two parallel micro cantilever beams expressed in two differential equations that are nonlinear and stiff. A specific algorithm that optimizes the integration steps which is named ISODE is used to perform the computation. The time response and phase diagram to the step-voltage for the mass-spring-damper system is derived numerically and the pull-in voltage of the system is evaluated.

show abstract

Viscosity Measurement for Picoliter Liquid Volumes

Changizi¹,

Stiharu

2021

Nano Scaled Structural Problems

View full text Add to dashboard Cite

The chapter introduces the reader to the fluid-related problems associated with discrete small volumes. The sizes that might be reasonable by now in the scientific community—micrometers, nanometers—affect the fluids by a power of three as fluids mainly consist of spherical particles. Specific physical quantities that characterize the fluids are virtually impossible to measure when the droplets of the fluids are micrometer-sized droplets and in the femtograms weight range. Devices capable of reaching to those ranges are scarce and the influences of the environmental conditions at such levels become extremely significant. One example of such particles is liposomes—volumes of organic matter in the nanometer size range which embed useful chemicals and which can target specific tissues within the human body.

show abstract

Lie group analysis of non-linear dynamic of micro structures under electrostatic field

Cited by 3 publications

References 55 publications

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Nonlinear Analysis of Pull-In Voltage of Twin Micro-Cantilever Beams

Nonlinear Analysis of Pull-in Voltage of Twin Micro-Cantilever Beams with Different Dimensions

Viscosity Measurement for Picoliter Liquid Volumes

Contact Info

Product

Resources

About