Analysis of the Quality Factor and Response Time of Resonant Biosensor

2016 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Response Time ◽  
Quality Factor ◽  
Governing Equation ◽  
Dynamic Effect ◽  
Equation Of Motion ◽  
Measured Parameter ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Relationship

The relationship between the overall damping and response time of resonant biosensors is investigated in this paper. The governing equation of motion is derived using a single degree-of-freedom model of the resonator considering the dynamic effect of adsorption of the measured parameter. It is shown that the adsorption leads to a damping force on the resonant sensor. If not taken into account, this damping force results in misinter-pretation of the sensor readings.

Vibration of Beam-Type Resonant Biosensors With Time-Varying Mass Density

2019 ◽  
Author(s):  
Pezhman Hassanpour
Keyword(s):  
Governing Equation ◽  
Mass Density ◽  
Dynamic Effect ◽  
Equation Of Motion ◽  
Viscous Damping ◽  
Time Varying ◽  
Absorption Process ◽  
Damping Force ◽  
Total Change ◽  
Beam Type

Abstract This paper investigates the dynamic response of a uniform beam with varying density. The governing equation of motion is derived using the Euler-Bernoulli model of the beam considering the dynamic effect of the change of the beam’s density. The dynamics of a beam-type resonant biosensor is investigated to demonstrate the effect of time-varying beam’s density. In this type of sensors, the density of the resonant beam changes with time due to the nature of absorption process. The absorption is modeled as an asymptotic exponential function of time. It is shown that the adsorption leads to a viscous damping force with a time-varying coefficient. The approximate solution of the governing equation of motion is derived for comparing with the exact solution. The response of the system is presented for several combinations of the system parameters. It is shown that two factors govern the viscous damping effect of the absorption process, namely the time constant of the process and the total change of the mass density over time. In general, a faster absorption process and greater change in mass density lead to more damping in the system. This is significant because a fast absorption rate and greater mass change are desirable design goals while damping is generally considered undesirable.

A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

Estimation of Ship Roll Parameters in Random Waves

1992 ◽  
Vol 114 (2) ◽  
pp. 114-121 ◽  
Author(s):  
J. B. Roberts ◽  
J. F. Dunne ◽  
A. Debonos
Keyword(s):  
Markov Property ◽  
Simulated Data ◽  
Wide Band ◽  
Equation Of Motion ◽  
Roll Motion ◽  
Random Waves ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Ship Roll ◽  
Stochastic Input

The problem of estimating the parameters in an equation of roll motion from roll measurements only, taken in an irregular sea, is discussed. A single degree of freedom equation of motion is assumed, with a wide-band stochastic input and with a linear-in-the-parameters representation of both the damping and restoration terms. A method based on the Markov property of the energy envelope process, associated with the roll motion, is developed which enables all the relevant parameters to be estimated. The method is validated by applying it to some simulated data, for which the true parameters are known.

scholarly journals Simulation Analysis of One Degree of Freedom Motion of Electromagnetic Spherical Joint based on Maxwell

2021 ◽  
Vol 2085 (1) ◽  
pp. 012014
Author(s):  
Haoran Wang ◽  
Fucong Liu ◽  
Sai Lou
Keyword(s):  
Mathematical Model ◽  
Simulation Analysis ◽  
Lagrange Equation ◽  
Degree Of Freedom ◽  
Spherical Joint ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Structure And Motion ◽  
The Mathematical Model ◽  
The Relationship

Abstract In order to improve the stiffness of the spherical joint of the robot, reduce the difficulty of manufacturing and the complexity of the control system, this paper proposed a method of spherical joint and digital drive of the robot based on the electromagnetic principle. Firstly, introduces the structure and motion principle of the spherical joint of the robot, establishes the mathematical model of the spherical joint and establishes the dynamic model according to the second Lagrange equation. after that, the relationship between the number of ampire-turns of the electromagnet on the spherical joint, the attitude Angle of the rotor and the force of the rotor was obtained by simulating the single degree of freedom of the joint based on Ansys maxwell and Matlab, which provided a basis for the realization of the digital drive of the spherical joint.

A New Approach to Nonlinear Oscillations

2001 ◽  
Vol 68 (6) ◽  
pp. 951-952 ◽  
Author(s):  
B. Wu ◽  
P. Li
Keyword(s):  
Governing Equation ◽  
Nonlinear Oscillation ◽  
Harmonic Balance ◽  
Nonlinear Oscillations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
New Approach ◽  
Single Degree ◽  
Method Of Harmonic Balance ◽  
Approximate Formulas

This paper deals with nonlinear oscillation of a general single-degree-of-freedom system. By combining the linearization of the governing equation with the method of harmonic balance, we establish two analytical approximate formulas for the period. These two formulas are valid for small as well as large amplitudes of oscillation.

A minimum transmitted load control method for shock isolation mounts with magnetorheological energy absorbers

2021 ◽  
pp. 1045389X2110643
Author(s):  
Zhongqiang Feng ◽  
Dong Yu ◽  
Zhaobo Chen ◽  
Xudong Xing ◽  
Hui Yan
Keyword(s):  
Control Method ◽  
Selection Criterion ◽  
Soft Landing ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Bingham Number ◽  
Optimal Control Method ◽  
Shock Isolation ◽  
Energy Absorbers ◽  
The Relationship

This paper proposed a minimum transmitted load (MTL) control method for drop-induced shock isolation mounts (SIM) with magnetorheological energy absorbers (MREAs). MTL control method consists of two parts of maximum damping force (MDF) control and one part of constant acceleration (CA) control, which can make the payload stop after fully utilize MREA stroke (soft landing) with minimum transmitted load. The control algorithm of MTL control method is derived in a single-degree-of-freedom (SDOF) system. The relationship between the controllable velocity range of MTL control method and parameters of shock isolation mounts is also derived. An optimal control method selection criterion between Bingham number (BN) control method and MTL control method is developed. The performance of MTL control method and selection criterion are shown by applying to the SIM system with variable drop velocities and system parameters. Results shows that MTL control method has the minimum transmitted load and the selection criterion is feasible.

Nonlinear Oscillators with a Power-Form Restoring Force: Non-Isochronous and Isochronous Case

2013 ◽  
Vol 430 ◽  
pp. 14-21
Author(s):  
Ivana Kovacic
Keyword(s):  
Kinetic Energy ◽  
Constant Coefficient ◽  
Nonlinear Term ◽  
Nonlinear Oscillators ◽  
Equation Of Motion ◽  
Constant Amplitude ◽  
Restoring Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
First Case

This work is concerned with single-degree-of-freedom conservative nonlinear oscillators that have a fixed restoring force, which comprises a linear term and an odd-powered nonlinear term with an arbitrary magnitude of the coefficient of nonlinearity. There are two cases of interest: i) non-isochronous, when the system has an amplitude-dependent frequency and ii) isochronous, when the frequency of oscillations is constant (amplitude-independent). The first case is associated with the constant coefficient of the kinetic energy, while the frequency-amplitude relationship and the solution for motion need to be found. To that end, the equation of motion is solved by introducing a new small expansion parameter and by adjusting the Lindstedt-Poincaré method. In the second case, the condition for the frequency of oscillations to be constant is derived in terms of the expression for the position-dependent coefficient of the kinetic energy. The corresponding solution for isochronous oscillations is obtained. Numerical verifications of the analytical results are also presented.

On Free Vibrations With Combined Viscous and Coulomb Damping

1980 ◽  
Vol 102 (4) ◽  
pp. 283-286 ◽  
Author(s):  
P. H. Markho
Keyword(s):  
Decay Curve ◽  
Closed Form Solution ◽  
Free Vibrations ◽  
Form Solution ◽  
Forced Response ◽  
Experimental Plot ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

A closed-form solution of the governing, nonlinear equation for free vibrations of a single-degree-of-freedom system, without stops, under combined viscous and Coulomb damping is first obtained. This is much less involved than forced-response considerations of the same system (with or without stops) the solution of which problem was first obtained by Den Hartog [1]. This note contains the first derivation, as far as the author is aware of, of the equation for the amplitude decay curve (or envelope) for such a system vibrating freely under no-stop conditions. This equation is presented in a form which enables the components of the damping force to be determined from the system’s experimental plot (or record) of displacement versus time.

Estimation of Hysteretic Energy of MDOF Structures Based on Equivalent SDOF Systems

2007 ◽  
Vol 340-341 ◽  
pp. 435-440
Author(s):  
Hong Nan Li ◽  
Feng Wang ◽  
Zhao Hui Lu
Keyword(s):  
Ground Motions ◽  
Estimation Method ◽  
Degree Of Freedom ◽  
Energy Relation ◽  
Energy Estimation ◽  
Single Degree Of Freedom ◽  
Hysteretic Energy ◽  
Single Degree ◽  
Energy Demands ◽  
The Relationship

It is important for obtaining the relationship between seismic energies of single degree-of-freedom (SDOF) systems and multiple degree-of-freedom (MDOF) structures in engineering. In this paper, the formula of hysteretic energy between the MDOF structures and equivalent SDOF systems is developed. Here is also presented the procedure for estimating hysteretic energy of MDOF structures subjected to severe ground motions employing the energy relation equation based on equivalent SDOF systems. Eight examples for two regular and six irregular MDOF structures show that the procedure to obtain the hysteretic energy demands of MDOF structures may be used as a simple and effective energy estimation method.

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