Bashar K. Hammad

Natural Frequencies and Mode Shapes of Mechanically Coupled Microbeam Resonators with an Application to Micromechanical Filters

We present a methodology to calculate analytically the mode shapes and corresponding frequencies of mechanically coupled microbeam resonators. To demonstrate the methodology, we analyze a mechanical filter composed of two beams coupled by a weak beam. The boundary-value problem (BVP) for the linear vibration problem of the coupled beams depends on the number of beams and the boundary conditions of the attachment points. This implies that the system of linear homogeneous algebraic equations becomes larger as the array of resonators becomes complicated. We suggest a method to reduce the large system of equations into a smaller system. We reduce the BVP composed of five equations and twenty boundary conditions to a set of three linear homogeneous algebraic equations for three constants and the frequencies. This methodology can be simply extended to accommodate any configuration of mechanically coupled arrays. To validate our methodology, we compare our analytical results to these obtained numerically using ANSYS. We found that the agreement is excellent. We note that the weak coupling beam splits the frequency of the single resonator into two close frequencies. In addition, the effect of the coupling beam location on the natural frequencies, and hence the filter behavior, is investigated.

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

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 distributedparameter 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. DOI: 10.1115/1.4003031

Characterization of a Tunable MEMS RF Filter

We present a reduced-order analytical model to describe the response of a tunable MEMS RF filter to an input signal whose frequency is in the neighborhood of the passband. It extends our earlier model by allowing for the application of independent DC voltages in addition to an AC input signal. The model is obtained by discretizing the distributed-parameter system using a Galerkin procedure. It consists of two second-order nonlinearly coupled ordinary-differential equations. Using the method of multiple scales, we determine four first-order nonlinear ordinary-differential equations describing the amplitudes and phases of the modes. We found that mismatch between the natural frequencies of the resonators modifies the global modes significantly, leading to localization of the response in either the input or the output beam. We found that the filter can be tuned to operate linearly for a wide range of VAC by choosing a DC voltage that makes the effective nonlinearities vanish. Amplifying the input signal VAC to improve the filter performance creates multi-valued responses beyond a threshold in the case of non-zero effective nonlinearities.Copyright

A Study of Subharmonic Excitation of Mechanically Coupled Microbeams for Filtration

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.Copyright

Nonlinear Feedback Control and Dynamics of an Electrostatically Actuated Microbeam Filter

This work is concerned with the modeling, nonlinear dynamic analysis and control design of an electrostatically actuated clamped-clamped microbeam filter. The model accounts for the mid-plane stretching and nonlinear form of the electrostatic force actuated along the microbeam span. A reduced-order model is constructed, using the method of multiple scales, to examine the microsystem static and dynamics behaviors. To improve the microbeam behavior, a nonlinear feedback controller is proposed. The main control objective is to make it behave like commonly known one-degree-of-freedom self-excited oscillators, such as the van der Pol and Rayleigh oscillators, which depict attractive filtering features. We present a novel control design that regulates the pass band of the fixed-fixed microbeam and derive analytical expressions that approximate the nonlinear resonance frequencies and amplitudes of the periodic solutions when the microbeam is subjected to one-point and fully-distributed feedback forces.Copyright

Simulation of a MEMS RF Filter

We simulate the motions in a MEMS bandpass Radio-Frequency (RF) filter. The filter model is obtained by discretizing the Lagrangian of the distributed-parameter system using a Galerkin procedure. The Euler-Lagrange equations are then used to obtain a two-degree-of-freedom model consisting of two non-linearly coupled ordinary-differential equations of motion. We use the model to study the transmission characteristics of a bandpass filter made up of two coupled resonators. Three distinct response regimes, separated by two critical amplification levels Vcr1 and Vcr2 , are identified in the filter response. For amplification levels up to Vcr1 , the pass signal is artifact free. Two types of artifacts due to the filter dynamics appear and distort the signal for amplification levels beyond Vcr1 .Copyright

Analysis of integration of remote laboratories for renewable energy courses at Jordan universities

MUREE project aims at the development of courses for training specialists about renewable energy production by combining face-to-face learning with on-line attendance. In this sense, remote laboratories are nowadays essential for distance education, even more within MUREE project, since Jordan students are not able to use face-to-face traditional laboratories due to their different physical location. These remote laboratories can be employed by instructors within their virtual classrooms, so that students can carry out their on-line experiments from anywhere and at anytime. For MUREE project, remote laboratories are seen as pedagogical elements that must be fully-integrated into a the learning/teaching process. Therefore, this work focuses its attentions toward the integration of remote laboratories into Learning Management Systems (LMSs) and, additionally, discusses the advantages and disadvantages of this approach.

A case study of service learning and civic engagement for mechatronics engineering students through a course project

This paper presents a case study of integrating a service learning project into an undergraduate Mechatronics engineering course titled “Building Automation” for the first time at the Hashemite University in Jordan. The project requires students to visit hospitals to learn about a variety of building systems that they have come across during their course lectures. After grasping the operating principles of building systems available in hospitals, students are required to brainstorm and suggest innovative ideas on how to reduce energy consumption based on tips and hints provided by the instructor and specialized consultants in the field of energy. Students achievement in this project was obtained, through their academic supervisor, their energy consultants, their community partners (hospital personnel), and students reflection on their experience. This paper presents qualitative analysis of integrating service learning and civic engagement in this course, explained the benefits, challenges, and recommendations for future implementation.

MICRO CANTILEVER ELECTROSTATIC ENERGY HARVESTER

In this paper, we present a SDOF model of an energy harvester made up of microcantilever beams with tip mass. We investigate performance utilizing electrostatic actuation mechanism resulted from an electret layer patterned underneath the tip mass. The excitation force is transferred to cantilever beams through the vibration of the fixed end, i.e. the base of the beam. The model accounts for the mechanical and electric parameters as well as the coupling between them, and it includes design parameters by lumping them into nondimensional quantities, thereby allowing an easier understanding of their effects and the interaction between the mechanical and electric forces. We study the static behavior of deflection and electric charge as a function of the DC static voltage. In addition, we simulate the dynamic response, generate the frequency-response curves for a variety of conditions, and notice nonlinear effects.

Analysis of out-of-plane Micro-Power Generators

Out-of-plane Micro-Power Generators (MPG) are investigated to identify their optimal design and operating conditions. Those MPGs employ a variable capacitor, an electret layer embedded between its electrodes, and an inertial mass carried by a movable electrode. Using a linear model, we study the impact of varying the capacitor gap, load resistance, and electret voltage on the output power. In addition, we analyze the effect of squeeze-film damping on the MPG performance. We find that the linear model breaks down as the excitation level increases. A nonlinear model is developed to capture the MPG response and estimate its output power in closed-form.