On the eigencharacteristics of a cantilevered visco-elastic beam carrying a tip mass and its representation by a spring-damper-mass system

2007 ◽  
Vol 301 (1-2) ◽  
pp. 420-426 ◽  
Author(s):  
M. Gürgöze ◽  
A.N. Doğruoğlu ◽  
S. Zeren
Keyword(s):  
Elastic Beam ◽  
Mass System ◽  
Tip Mass

scholarly journals Energy Harvesting in a Nonlinear Cantilever Piezoelastic Beam System Excited by Random Vertical Vibrations

2014 ◽  
Vol 14 (08) ◽  
pp. 1440018 ◽  
Author(s):  
Marek Borowiec ◽  
Grzegorz Litak ◽  
Michael I. Friswell ◽  
Sondipon Adhikari
Keyword(s):  
Power Generation ◽  
Energy Harvester ◽  
Elastic Beam ◽  
Stochastic Force ◽  
Beam System ◽  
Voltage Output ◽  
Single Well ◽  
Vertical Vibrations ◽  
Ambient Excitation ◽  
Tip Mass

The vertical elastic beam with vertical ambient excitation is proposed as an energy harvester. The beam has a tip mass and piezoelectric patches which transduce the bending strains induced by the stochastic force caused by vertical kinematic forcing into electrical charge. We focus on the region with a fairly large amplitude of voltage output where the beam overcomes the potential barrier. Increasing the noise level allows the transition from single well oscillations to inter-well stochastic jumps with more power generation.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

scholarly journals Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Mudasir Younis ◽  
Deepak Singh ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Graph Theory ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Nonlinear Problems ◽  
Point Theory ◽  
Open Problems ◽  
Mass System ◽  
Fixed Point Result

The purpose of this article is twofold. Firstly, combining concepts of graph theory and of fixed point theory, we will present a fixed point result for Kannan type mappings, in the framework of recently introduced, graphical b-metric spaces. Appropriate examples of graphs validate the established theory. Secondly, our focus is to apply the proposed results to some nonlinear problems which are meaningful in engineering and science. Some open problems are proposed.

ENERGY HARVESTING IN PIEZOELASTIC SYSTEMS DRIVEN BY RANDOM EXCITATIONS

2013 ◽  
Vol 13 (07) ◽  
pp. 1340006 ◽  
Author(s):  
M. BOROWIEC ◽  
G. LITAK ◽  
M. I. Friswell ◽  
S. F. Ali ◽  
S. Adhikari ◽  
...  
Keyword(s):  
Noise Level ◽  
Large Amplitude ◽  
Energy Harvester ◽  
Elastic Beam ◽  
Horizontal Displacement ◽  
Beam System ◽  
Piezoelectric Layers ◽  
Single Well ◽  
Beam Motion ◽  
Tip Mass

The inverted elastic beam is proposed as an energy harvester. The beam has a tip mass and piezoelectric layers which transduce the bending strains induced by the stochastic horizontal displacement into electrical charge. The efficiency of this nonlinear device is analyzed, focusing on the region of stochastic resonance where the beam motion has a large amplitude. Increasing the noise level allows the motion of the beam system to escape from single well oscillations and thus generate more power.

Full Beam Formulation of a Rotating Beam-Mass System

1994 ◽  
Vol 116 (1) ◽  
pp. 93-99 ◽  
Author(s):  
B. Fallahi ◽  
S. H.-Y. Lai ◽  
R. Gupta
Keyword(s):  
Nonlinear Term ◽  
Cross Coupling ◽  
Automatic Generation ◽  
Shape Functions ◽  
Rotating Beam ◽  
Mass System ◽  
Computational Implementation ◽  
Geometric Stiffening ◽  
Rigid Body Motions ◽  
Tip Mass

In this study a comprehensive approach for modeling flexibility for a beam with tip mass is presented. The method utilizes a Timoshenko beam with geometric stiffening. The element matrices are reported as the integral of the product of shape functions. This enhances their utility due to their generic form. They are utilized in a symbolic-based algorithm for the automatic generation of the element matrices. The time-dependent terms are factored after assembly for better computational implementation. The effect of speed and tip mass on cross coupling between the elastic and rigid body motions represented by Coriolis, normal and tangential accelerations is investigated. The nonlinear term (geometric stiffening) is modeled by introducing a tensor which plays the same role as element matrices for the linear terms. This led to formulation of the exact tangent matrix needed to solve the nonlinear differential equation.

On the Dynamics and Multiple Equilibria of an Inverted Flexible Pendulum With Tip Mass on a Cart

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Ojas Patil ◽  
Prasanna Gandhi
Keyword(s):  
Dynamic Model ◽  
Multiple Equilibria ◽  
Chaotic Behavior ◽  
Elastic Beam ◽  
Superior Performance ◽  
Flexible Link ◽  
Equilibrium Solutions ◽  
Lagrange Formulation ◽  
Compact Design ◽  
Tip Mass

Flexible link systems are increasingly becoming popular for advantages like superior performance in micro/nanopositioning, less weight, compact design, lower power requirements, and so on. The dynamics of distributed and lumped parameter flexible link systems, especially those in vertical planes are difficult to capture with ordinary differential equations (ODEs) and pose a challenge to control. A representative case, an inverted flexible pendulum with tip mass on a cart system, is considered in this paper. A dynamic model for this system from a control perspective is developed using an Euler Lagrange formulation. The major difference between the proposed method and several previous attempts is the use of length constraint, large deformations, and tip mass considered together. The proposed dynamic equations are demonstrated to display an odd number of multiple equilibria based on nondimensional quantity dependent on tip mass. Furthermore, the equilibrium solutions thus obtained are shown to compare fairly with static solutions obtained using elastica theory. The system is demonstrated to exhibit chaotic behavior similar to that previously observed for vibrating elastic beam without tip mass. Finally, the dynamic model is validated with experimental data for a couple of cases of beam excitation.

Response variations of a cantilever beam–tip mass system with nonlinear and linearized boundary conditions

2018 ◽  
Vol 25 (3) ◽  
pp. 485-496 ◽  
Author(s):  
Vamsi C. Meesala ◽  
Muhammad R. Hajj
Keyword(s):  
Boundary Conditions ◽  
Cantilever Beam ◽  
Nonlinear Boundary ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Boundary Conditions ◽  
Distributed Parameter ◽  
Governing Equations ◽  
Mass System ◽  
Tip Mass

The distributed parameter governing equations of a cantilever beam with a tip mass subjected to principal parametric excitation are developed using a generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. The discretized governing equation considering the nonlinear boundary conditions assumes a simpler form. We solve the distributed parameter and discretized equations separately using the method of multiple scales. Through comparison with the direct approach, we show that accounting for the nonlinear boundary conditions boundary conditions is important for accurate prediction in terms of type of bifurcation and response amplitude.

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