On the Use of the Subharmonic Resonance as a Method for Filtration

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab M. Abdel-Rahman
Keyword(s):  
Bandpass Filter ◽  
Multiple Scales ◽  
Subharmonic Resonance ◽  
The Other ◽  
Mode Shapes ◽  
Distributed Parameter ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Reduced Order ◽  
Weak Beam

We study the feasibility of employing subharmonic resonance of order one-half to create a bandpass filter. A filter made up of two clamped-clamped microbeam resonators coupled by a weak beam is employed as a test design. We discretize the distributed-parameter system using the Galerkin procedure to obtain a reduced-order model composed of two nonlinear coupled Ordinary Differentiation Equations (ODEs). It accounts for geometric and electric nonlinearities as well as the coupling between these two fields. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We use these equations to determine closed-form expressions for the static and dynamic deflections of the structure. The basis functions in the discretization are the linear undamped global mode shapes of the unactuated structure. We found that it is impractical to use the proposed filter structure for subharmonic resonance-based filtering since it cannot produce a single-valued response for small excitation amplitudes. On the other hand, it is feasible to use cascaded uncoupled resonators to build a bandpass filter by operating one in the softening domain and the other in the hardening domain.

A Subharmonic Resonance-Based MEMS Filter

2007 ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab Abdel-Rahman
Keyword(s):  
Multiple Scales ◽  
Subharmonic Resonance ◽  
Mode Shapes ◽  
Center Frequency ◽  
Distributed Parameter ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Reduced Order ◽  
Filter Performance ◽  
Mems Filter

We present a novel micromechanical filter exploiting the subharmonic resonance of order one-half to obtain a center frequency twice the fundamental frequency of the primary resonators, an ideal stopband, and a sharp roll-off. The filter is made up of two clamped-clamped microbeam resonators connected by a coupling beam. We discretize the distributed-parameter system using the Galerkin procedure to obtain a reduced-order model composed of two nonlinear coupled ODEs. It accounts for geometrical and electrical nonlinearities as well as the coupling between these two fields. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We use these equations to determine closed-form expressions for the static and dynamic deflections of the filter. The basis functions in the discretization are the linear undamped global mode shapes of the unactuated filter. The filtering mechanism is based on the exploitation of the interval where the trivial response to subharmonic excitations is unstable. We found criteria to tune the effective nonlinearities of the filter to realize a bandpass filter of an ideal stopband rejection and a sharp roll-off. When these criteria are not met, multivalued responses appear and distort the filter performance.

A Study of Subharmonic Excitation of Mechanically Coupled Microbeams for Filtration

2008 ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab M. Abdel-Rahman
Keyword(s):  
Bandpass Filter ◽  
Multiple Scales ◽  
Mode Shapes ◽  
Distributed Parameter ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Single Structure ◽  
Subharmonic Excitation ◽  
The Subject ◽  
Coupled Beams

We study the feasibility of employing subharmonic resonance of order one-half to create a bandpass filter using two clamped-clamped microbeam resonators connected by a weak coupling beam. We discretize the distributed-parameter system using the Galerkin procedure to obtain a reduced-order model composed of two nonlinear coupled ODEs. It accounts for geometric and electric nonlinearities as well as the coupling between these two fields. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We use these equations to determine closed-form expressions for the static and dynamic deflections of the structure. The basis functions in the discretization are the linear undamped global mode shapes of the unactuated structure. We found that we can not produce a single-valued response for small excitation amplitudes. So that, it is impractical to use a single structure made of two mechanically coupled beams excited subharmonically in filtration. But we can use a pair of structures to build a bandpass filter by operating one in the softening domain and the other in the hardening domain and, more importantly, implementing processing logic and hardware schemes. However, the complications brought about by mechanically coupling of two microbeams can be avoided by using a pair of uncoupled beams. This makes the fabrication and modeling processes much easier. Using subharmonic excitation with mechanically uncoupled microbeams to realize bandpass filters is the subject of the next work.

A Discretization Approach to Modeling Capacitive MEMS Filters

2007 ◽  
Author(s):  
Bashar K. Hammad ◽  
Ali H. Nayfeh ◽  
Eihab Abdel-Rahman
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Boundary Value ◽  
Mode Shapes ◽  
Algebraic Equations ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Wide Range

We present a reduced-order model and closed-form expressions describing the response of a micromechanical filter made up of two clamped-clamped microbeam capacitive resonators coupled by a weak microbeam. The model accounts for geometrical and electrical nonlinearities as well as the coupling between them. It is obtained by discretizing the distributed-parameter system using the Galerkin procedure. The basis functions are the linear undamped global mode shapes of the unactuated filter. Closed-form expressions for these mode shapes and the coressponding natural frequencies are obtained by formulating a boundary-value problem (BVP) that is composed of five equations and twenty boundary conditions. This problem is transformed into solving a system of twenty linear homogeneous algebraic equations for twenty constants and the natural frequencies. We predict the deflection and the voltage at which the static pull-in occurs by solving another boundary-value problem (BVP). We also solve an eigenvalue problem (EVP) to determine the two natural frequencies delineating the bandwidth of the actuated filter. Using the method of multiple scales, we determine four first-order nonlinear ODEs describing the amplitudes and phases of the modes. We found a good agreement between the results obtained using our model and the published experimental results. We found that the filter can be tuned to operate linearly for a wide range of input signal strengths by choosing a DC voltage that makes the effective nonlinearities vanish.

scholarly journals Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7279
Author(s):  
Jin Wei ◽  
Tao Yu ◽  
Dongping Jin ◽  
Mei Liu ◽  
Dengqing Cao ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Dynamic ◽  
Natural Frequencies ◽  
Great Influence ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Orthogonality Relations ◽  
Tip Mass

A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

Forced Vibrations of Slacked Carbon Nanotube Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis
Keyword(s):  
Perturbation Method ◽  
Multiple Scales ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Beam Model ◽  
Harmonic Load ◽  
Arch Model ◽  
Order Model ◽  
Reduced Order ◽  
Model Equations

In this paper, we present an investigation of the dynamics of electrically actuated carbon nanotubes (CNTs) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear arch model is used to simulate the motion of the slacked CNT. A reduced-order model using a multimode Galerkin procedure based on the mode shapes of the straight un-actuated CNTs is derived. The reduced-order model equations are integrated numerically with time to reveal the steady-state response of the CNT when actuated by a DC load superimposed to an AC harmonic load. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNT. Results of the perturbation method are verified with those obtained by numerically integrating the reduced-order model equations. The effective nonlinearity of the CNT is calculated as function of the slack and the DC load while using a beam model for the CNTs showing a softening dominant behavior.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

Application of partial eigenvalue assignment techniques to dampen electromechanical oscillations in multi-machine power systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Erick Baleeiro da Silva ◽  
José Mário Araújo
Keyword(s):  
Power Systems ◽  
The Other ◽  
Mode Shapes ◽  
Eigenstructure Assignment ◽  
Power System Stabilizers ◽  
Control Effort ◽  
Electromechanical Oscillations ◽  
Oscillation Modes ◽  
Partial Controllability

AbstractIn this study, a methodology for partial eigenstructure assignment (PEVA) is applied to dampen electromechanical oscillations in electrical multi-machine power systems. The approach is anchored in allocating a small number of undesirable eigenvalues, for example, which are poorly damped, preserving the other eigenvalues in the system - the so-called no-spillover spectrum. The new position of the selected eigenvalues is carried out based on the partial controllability analysis of the system, in order to minimize the control effort. Simulation examples using a system with 68 buses, 16 generators and five areas showed that the presented methodology is efficient in dampening the local and inter-area oscillation modes when compared to the classic power system stabilizers (PSS). The quality of the solution is illustrated through computer simulations, eigenvalues tables and mode-shapes.

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