Simulation of a MEMS RF Filter

2005 ◽  
Author(s):  
Eihab M. Abdel-Rahman ◽  
Bashar K. Hammad ◽  
Ali H. Nayfeh
Keyword(s):  
Equations Of Motion ◽  
Distributed Parameter ◽  
Parameter System ◽  
Transmission Characteristics ◽  
Coupled Resonators ◽  
Lagrange Equations ◽  
Filter Model ◽  
Rf Filter ◽  
Two Degree Of Freedom ◽  
Filter Response

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.

Dynamic Behavior of Vehicles Travelling on Bridges

1993 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Mehrdaad Ghorashi
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parameter System ◽  
Moving Vehicle ◽  
Lumped Parameter ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

Abstract An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.

Transient Vibration of Gyroscopic Systems With Unsteady Superposed Motion

1995 ◽  
Author(s):  
J. A. Wickert
Keyword(s):  
Equations Of Motion ◽  
Mathematical Structure ◽  
Time Dependent ◽  
Distributed Parameter ◽  
Rotating Shaft ◽  
Transient Vibration ◽  
Modal Amplitude ◽  
Technical Interest ◽  
Gyroscopic Systems ◽  
Two Degree Of Freedom

Abstract The equations of motion for a gyroscopic system with unsteady superposed motion are derived for the prototypical problem in which motion of an oscillating particle is measured relative to a non-inertial frame. The resulting coefficient matrices are time-dependent, and skew-symmetric acceleration terms are present both as Coriolis acceleration and as a component of net stiffness. Such mathematical structure is also demonstrated in the context of other unsteady gyroscopic systems, including flexible media that translate with time-dependent speed. Following the asymptotic approach of Krylov, Bogoliubov and Mitropolsky, a perturbation method is developed for the case in which the superposed motion varies slowly when viewed on the time scale of the natural periods of oscillation. First-order approximations for the modal amplitude and phase are obtained in closed form. The method is illustrated through two examples of technical interest: a two degree-of-freedom model of a rotating shaft, and a distributed parameter model of a moving tape.

Bending-Bending Mode of a Rotating Tapered-Twisted Turbomachine Blade Including Rotatory Inertia and Shear Deformation

1969 ◽  
Vol 91 (4) ◽  
pp. 1017-1024 ◽  
Author(s):  
R. M. Krupka ◽  
A. M. Baumanis
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Torsional Vibrations ◽  
Parameter System ◽  
Field Equations ◽  
Lagrange Equations ◽  
Rotatory Inertia ◽  
Lumped Parameter ◽  
Bending Mode ◽  
Definition Of

This paper presents the effect on natural frequency and mode shape of the inclusion of terms that are present in the general equations of motion to describe phenomena associated with Rotatory Inertia and Shear Deformation. The coupling that exists between the flexural and torsional vibrations is not considered. Carnegie’s formulation of the Lagrange Equations of motion is used and the set of field equations solved using Myklestad’s adaptation of the Holzer method. The definition of the lumped parameter system used and the derivation of the associated discrete “difference equations,” which are utilized in the computer approach to the boundary value problem considered, constitute an extension of the Carnegie work.

Numerical Study of One Dimensional Pipe Flow Under Pump Cavitation Surge

2017 ◽  
Author(s):  
Motohiko Nohmi ◽  
Satoshi Yamazaki ◽  
Shusaku Kagawa ◽  
Byungjin An ◽  
Donghyuk Kang ◽  
...  
Keyword(s):  
Pipe Flow ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Gain Factor ◽  
Distributed Parameter ◽  
Piping System ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Lumped Parameter ◽  
System Calculation

Pump cavitation surge is highly coupled phenomenon with unsteady cavitation inside a pump and system dynamics of the pipe flow surrounding the pump. The piping system flow dynamics can be calculated under two kinds of assumptions; lumped parameter system (LPS) and distributed parameter system (DPS). In the lumped parameter system, the equations of motion of water columns inside pipes are calculated upstream and downstream of the pump. In the distributed parameter system, wave propagations along the pipes are calculated. In this study a simple system that consists of an upstream tank, an upstream pipe, a pump with cavitation, a downstream pipe and a downstream tank is analyzed by using two methods. Cavitation inside the pump is featured in the lumped parameters of cavitation compliance and mass flow gain factor. In the lumped parameter system case, equations of motion are calculated numerically by Runge-Kutta methods. In the distributed parameter system case, wave propagations are calculated by Method of Characteristics. From the comparison of two method results, appropriate criterion for practical piping system calculation is discussed.

Modeling and Boundary Control of a Hanging Cable Immersed in Water

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Michael Böhm ◽  
Miroslav Krstic ◽  
Sebastian Küchler ◽  
Oliver Sawodny
Keyword(s):  
Differential Equation ◽  
Wave Equations ◽  
Equations Of Motion ◽  
Distributed Parameter ◽  
Stream Velocity ◽  
Water Stream ◽  
Varying Coefficients ◽  
Feedforward Controller ◽  
Spatially Varying ◽  
Two Degree Of Freedom

A nonlinear distributed parameter system model governing the motion of a cable with an attached payload immersed in water is derived. The payload is subject to a drag force due to a constant water stream velocity. Such a system is found, for example, in deep sea oil exploration, where a crane mounted on a ship is used for construction and thus positioning of underwater parts of an offshore drilling platform. The equations of motion are linearized, resulting in two coupled, one-dimensional wave equations with spatially varying coefficients and dynamic boundary conditions of second order in time. The wave equations model the normal and tangential displacements of cable elements, respectively. A two degree of freedom controller is designed for this system with a Dirichlet input at the boundary opposite to the payload. A feedforward controller is designed by inverting the system using a Taylor-series, which is then truncated. The coupling is ignored for the feedback design, allowing for a separate design for each direction of motion. Transformations are introduced, in order to transform the system into a cascade of a partial differential equation (PDE) and an ordinary differential equation (ODE), and PDE backstepping is applied. Closed-loop stability is proven. This is supported by simulation results for different cable lengths and payload masses. These simulations also illustrate the performance of the feedforward controller.

scholarly journals Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 115
Author(s):  
Andriy Chaban ◽  
Marek Lis ◽  
Andrzej Szafraniec ◽  
Radoslaw Jedynak
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Fitness Function ◽  
Least Square ◽  
Distributed Parameter ◽  
Parameter Method ◽  
Analytical Mechanics ◽  
Parameter System ◽  
Rotational Systems ◽  
Elastic Elements

Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

2021 ◽  
pp. 107754632199358
Author(s):  
Ali Fasihi ◽  
Majid Shahgholi ◽  
Saeed Ghahremani
Keyword(s):  
Energy Harvester ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

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