Analytical Modal Analysis of Thin-Film Flat Lenses

2003 ◽  
Author(s):  
L. Moxey ◽  
H. Hamidzadeh
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Dynamic Response ◽  
Modal Analysis ◽  
Closed Form ◽  
Material Properties ◽  
Mathieu Equation ◽  
Free Vibrations ◽  
Vibration Response ◽  
Closed Form Solutions

Dynamics of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin film membranes were mathematically modeled using Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters such as material properties, membrane pre strain and the geometry on the dynamic response of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin film lenses.

Analytical modal analysis of thin-film flat lenses

2005 ◽  
Vol 219 (1) ◽  
pp. 55-59 ◽  
Author(s):  
H R Hamidzadeh ◽  
L Moxey
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Dynamic Response ◽  
Modal Analysis ◽  
Closed Form ◽  
Material Properties ◽  
Mathieu Equation ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Closed Form Solutions

The free vibrations of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin-film membranes were mathematically modelled using the Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case, when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters, such as material properties, membrane pre-strain rate, and the geometry, on natural frequency and mode shapes of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin-film lenses.

An Improved Analytical Model for Deflections of a Circular Multi-Layer Piezoelectric Actuator

2005 ◽  
Author(s):  
Mandar Deshpande ◽  
Laxman Saggere
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Piezoelectric Actuator ◽  
Plate Theory ◽  
Analytical Models ◽  
Sensors And Actuators ◽  
Closed Form Solutions ◽  
Design And Optimization ◽  
Closed Form Analytical Solution ◽  
Model Correlation

Models for simple closed-form analytical solutions for accurately predicting static deflections of circular thin-film piezoelectric microactuators are very useful in design and optimization of a variety of MEMS sensors and actuators utilizing piezoelectric actuators. While closed-form solutions treating actuators with simple geometries such as cantilevers and beams are available, simple analytical models treating circular bending-type actuators commonly used in MEMS applications are generally lacking. This paper presents a closed-form analytical solution for accurately estimating the deflections and the volume displacements of a circular multi-layer piezoelectric actuator under combined voltage and pressure loading. The model for the analytical solution presented in this paper, which is based on classical laminated plate theory, allows for inclusion of multiple layers and non-uniform diameters of various layers in the actuator including bonding and electrode layers, unlike other models previously reported in the literature. The analytical solution presented is validated experimentally as well as through a finite element solution and excellent experiment-model correlation within 1% variation is demonstrated. General guidelines for optimization of circular piezoelectric actuator are also discussed. The utility of the model for design optimization of a multi-layered piezoelectric actuator is demonstrated through a numerical example wherein the dimensions of a test actuator are optimized to improve the displaced volume by three-fold under combined voltage and resisting pressure loads.

Modal Analysis of Multi-Stepped Distributed-Parameter Rotor-Bearing Systems Using Exact Dynamic Elements

2001 ◽  
Vol 123 (3) ◽  
pp. 401-403 ◽  
Author(s):  
Seong-Wook Hong ◽  
Jong-Heuck Park
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Complete Analysis ◽  
Distributed Parameter ◽  
Analysis Method ◽  
Closed Form Solutions ◽  
Analysis Scheme ◽  
Rotor Bearing ◽  
The Matrix ◽  
Transcendental Functions

Although the exact dynamic elements have been suggested by the authors [1] and proved to be useful for the dynamic analysis of distributed-parameter rotor-bearing systems, difficulty remains in computation because of the presence of transcendental functions in the matrix. This paper proposes a complete analysis scheme for the exact dynamic elements, a generalized modal analysis method, to obtain exact and closed form solutions of time and frequency domain responses for multi-stepped distributed-parameter rotor-bearing systems. A numerical example is provided for validating the proposed method.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

Closed form solutions for the dynamic response of Euler–Bernoulli beams with step changes in cross section

2006 ◽  
Vol 295 (1-2) ◽  
pp. 214-225 ◽  
Author(s):  
Michael A. Koplow ◽  
Abhijit Bhattacharyya ◽  
Brian P. Mann
Keyword(s):  
Dynamic Response ◽  
Closed Form ◽  
Cross Section ◽  
Closed Form Solutions

Dynamic Response of an Electro-Rheological Sandwich Beam with Different Elastic Layers Subjected to Simultaneous Impact Loads

2012 ◽  
Vol 232 ◽  
pp. 117-121 ◽  
Author(s):  
M. Sepehrinour ◽  
M. Nezami
Keyword(s):  
Analytical Solution ◽  
Electric Field ◽  
Dynamic Response ◽  
Material Properties ◽  
Transverse Vibration ◽  
Sandwich Beam ◽  
Impact Loads ◽  
Governing Equations ◽  
Simultaneous Impact ◽  
Elastic Layers

Dynamic response of an electro-rheological sandwich beam subjected to simultaneous Impact loads will be considered. Analytical solution will be used to draw FRF diagram of the beam for different electric field. Upper and lower layers of the beam have different material properties. Coupled governing equations derived from Hamilton Principle will be solved in frequency domain to find transverse vibration of the beam.

Dynamic Response of a Timoshenko Beam to a Moving Force

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
Paweł Śniady
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Constant Velocity ◽  
Free Vibrations ◽  
Dynamical Response ◽  
Transverse Displacement ◽  
Closed Form Solutions ◽  
Simply Supported ◽  
Moving Force

We consider the dynamical response of a finite, simply supported Timoshenko beam loaded by a force moving with a constant velocity. The classical solution for the transverse displacement and the rotation of the cross section of a Timoshenko beam has a form of a sum of two infinite series, one of which represents the force vibrations (aperiodic vibrations) and the other one free vibrations of the beam. We show that one of the series, which represents aperiodic (force) vibrations of the beam, can be presented in a closed form. The closed form solutions take different forms depending if the velocity of the moving force is smaller or larger than the velocities of certain shear and bar velocities.

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