Mathematical Modeling and Analysis of Vibration Characteristics of Smart-Phone

2013 ◽  
Vol 284-287 ◽  
pp. 800-805
Author(s):  
Suk Min Yoon ◽  
Jae Hee Kim ◽  
Jin Ho Kim
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Analysis ◽  
Smart Phone ◽  
Vibration Characteristics ◽  
Linear Actuator ◽  
Vibration Characteristic ◽  
Linear Vibration ◽  
Modeling And Analysis ◽  
Key Technologies

Slimming of a smart phone is one of the key technologies in the current smart-phone industry. Because the vibration actuator is the thickest part of a smart phone, a slim linear vibration actuator has been developed. For the analysis of the vibration characteristic of a smart phone, experiment has been used one of the most popular techniques, but it consumes a lot of cost and time. Accordingly, as an alternative to experiments, mathematical modeling and analysis can be applied. In this paper, a mathematical modeling is created for analysis of the vibration characteristics of a smart-phone applied with a horizontally vibrating linear actuator. In addition, the result of the mathematical analysis is compared with that of the experiment for verification.

scholarly journals Nonlinear Vibration Characteristics of a Flexible Blade with Friction Damping due to Tip-Rub

2011 ◽  
Vol 18 (1-2) ◽  
pp. 105-114 ◽  
Author(s):  
Dengqing Cao ◽  
Xiaochun Gong ◽  
Dong Wei ◽  
Shiming Chu ◽  
Ligang Wang
Keyword(s):  
Nonlinear Vibration ◽  
Piecewise Linear ◽  
Equation Of Motion ◽  
Vibration Characteristics ◽  
Vibration Characteristic ◽  
Linear Vibration ◽  
Friction Damping ◽  
The Galerkin Method ◽  
Three Degree Of Freedom ◽  
Frequency Curves

An approximate approach is proposed in this paper for analyzing the two-dimensional friction contact problem so as to compute the dynamic response of a structure constrained by friction interfaces due to tip-rub. The dynamical equation of motion for a rotational cantilever blade in a centrifugal force field is established. Flow-induced distributed periodic forces and the internal material damping in the blade are accounted for in the governing equation of motion. The Galerkin method is employed to obtain a three-degree-of-freedom oscillator with friction damping due to tip-rub. The combined motion of impact and friction due to tip-rub produced a piecewise linear vibration which is actually nonlinear. Thus, a complete vibration cycle is divided into successive intervals. The system possesses linear vibration characteristic during each of these intervals, which can be determined using analytical solution forms. Numerical simulation shows that the parameters such as gap of the tip and the rotational speed of the blades have significant effects on the dynamical responses of the system. Finally, the nonlinear vibration characteristics of the blade are investigated in terms of the Poincare graph, and the frequency spectrum of the responses and the amplitude-frequency curves.

A Stochastic Hierarchical Population System: Excitement, Extinction and Transition to Chaos

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Irina Bashkirtseva ◽  
Tatyana Perevalova ◽  
Lev Ryashko
Keyword(s):  
Mathematical Modeling ◽  
Food Chain ◽  
Analytical Method ◽  
Three Dimensional ◽  
Biological Parameters ◽  
Top Predator ◽  
Population System ◽  
Modeling And Analysis ◽  
Transition To Chaos ◽  
Random Fluctuations

A problem of the mathematical modeling and analysis of noise-induced transformations of complex oscillatory regimes in hierarchical population systems is considered. As a key example, we use a three-dimensional food chain dynamical model of the interacting prey, predator, and top predator. We perform a comparative study of the impacts of random fluctuations on three key biological parameters of prey growth, predator mortality, and the top predator growth. A detailed investigation of the stochastic excitement, noise-induced transition from order to chaos, and various scenarios of extinction is carried out. Constructive abilities of the semi-analytical method of confidence domains in the analysis of the noise-induced extinction are demonstrated.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

Sign in / Sign up

Export Citation Format

Share Document