ON THE EFFECT OF AN ATTACHED SPRING-MASS SYSTEM ON THE FREQUENCY SPECTRUM OF LONGITUDINALLY VIBRATING ELASTIC RODS CARRYING A TIP MASS

1999 ◽  
Vol 227 (2) ◽  
pp. 471-477 ◽  
Author(s):  
H. EROL ◽  
M. GÜRGÖZE
Keyword(s):  
Frequency Spectrum ◽  
Elastic Rods ◽  
Mass System ◽  
Tip Mass

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.

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.

Tuning of a Piezoelectric Harvester by Means of a Cantilever Spring-Mass System

2018 ◽  
Author(s):  
Alberto Doria ◽  
Cristian Medè ◽  
Giulio Fanti ◽  
Daniele Desideri ◽  
Alvise Maschio ◽  
...  
Keyword(s):  
High Frequency ◽  
Natural Frequencies ◽  
Coupled System ◽  
Vibration Absorber ◽  
Main Resonance ◽  
Dynamic Vibration Absorber ◽  
Mass System ◽  
High Frequency Resonance ◽  
Tip Mass ◽  
Piezoelectric Harvester

The possibility of improving the performance of a piezoelectric harvester by means of a cantilever dynamic vibration absorber (CDVA) is investigated. The CDVA cancels the original mode of vibration of the harvester and generates two new modes. Some prototypes are developed using a mathematical model for predicting the natural frequencies of the coupled system. Impulsive tests were performed on prototypes. Experimental results show that a small CDVA can lower the main resonance frequency of an harvester of the same extent as a larger tip mass. The measured voltage shows also an high frequency resonance peak, which can be exploited for collecting energy. A multi-physics numerical model is developed for performing modal analysis and stress analysis. Numerical results show that the stress inside the piezoelectric material of the harvester with CDVA results smaller than the stress inside the harvester with a tip mass tuned to the same frequency.

Dynamic analysis of the flexible hub-beam system based on rigid-flexible coupling mechanism

2020 ◽  
Vol 234 (3) ◽  
pp. 536-545
Author(s):  
Xiaowei Guo ◽  
Xin Yang ◽  
Fuqiang Liu ◽  
Zhangfang Liu ◽  
Xiaolin Tang
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Flexible Beam ◽  
Coupling Mechanism ◽  
Mass System ◽  
Typical Structure ◽  
Concentrated Load ◽  
Flexible Coupling ◽  
Beam System ◽  
Tip Mass

The flexible hub-beam system is a typical structure of the rigid-flexible coupling dynamic system. In this paper, the dynamic property of the flexible hub-beam system is investigated. First, based on the dynamic analysis of the flexible beam in the flexible hub-beam system, the dynamic model of a flexible hub-beam-tip mass system is established and researched. Second, the dynamic response of the flexible beam under different external loads, including end concentrated load, end sinusoidal load, and uniform load, is analyzed and calculated. Finally, the influence of magnitude, direction, and type of load on the dynamic response of the flexible beam is also discussed. This research can provide a novel strategy for controlling the maximum stress of the structural components to be lower than the yield stress of the material, and flexible components remain in the linear elastic range even under the condition of high-speed rotation.

Exact Frequency Analysis of a Rotating Cantilever Beam With Tip Mass Subjected to Torsional-Bending Vibrations

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Masoud Ansari ◽  
Ebrahim Esmailzadeh ◽  
Nader Jalili
Keyword(s):  
Frequency Analysis ◽  
Time Domain ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Bending Vibrations ◽  
Resonant Condition ◽  
Mass System ◽  
Coupled Equations ◽  
Tip Mass ◽  
Gyroscopic Systems

An exact frequency analysis of a rotating beam with an attached tip mass is addressed in this paper while the beam undergoes coupled torsional-bending vibrations. The governing coupled equations of motion and the corresponding boundary condition are derived in detail using the extended Hamilton principle. It has been shown that the source of coupling in the equations of motion is the rotation and that the equations are linked through the angular velocity of the base. Since the beam-tip-mass system at hand serves as the building block of many vibrating gyroscopic systems, which require high precision, a closed-form frequency equation of the system should be derived to determine its natural frequencies. The frequency analysis is the basis of the time domain analysis, and hence, the exact frequency derivation would lead to accurate time domain results, too. Control strategies of the aforementioned gyroscopic systems are mostly based on their resonant condition, and hence, acquiring knowledge about their exact natural frequencies could lead to a better control of the system. The parameter sensitivity analysis has been carried out to determine the effects of various system parameters on the natural frequencies. It has been shown that even the undamped systems undergoing base rotation will have complex eigenvalues, which demonstrate a damping-type behavior.

scholarly journals Nonlinear Dynamic Behavior of a Flexible Structure to Combined External Acoustic and Parametric Excitation

2006 ◽  
Vol 13 (4-5) ◽  
pp. 233-254 ◽  
Author(s):  
Paulo S. Varoto ◽  
Demian G. Silva
Keyword(s):  
Dynamic Response ◽  
Dynamic Behavior ◽  
Parametric Excitation ◽  
Accurate Determination ◽  
Longitudinal Axis ◽  
Equation Of Motion ◽  
Driving Mechanism ◽  
Lumped Mass ◽  
Mass System ◽  
Tip Mass

Flexible structures are frequently subjected to multiple inputs when in the field environment. The accurate determination of the system dynamic response to multiple inputs depends on how much information is available from the excitation sources that act on the system under study. Detailed information include, but are not restricted to appropriate characterization of the excitation sources in terms of their variation in time and in space for the case of distributed loads. Another important aspect related to the excitation sources is how inputs of different nature contribute to the measured dynamic response. A particular and important driving mechanism that can occur in practical situations is the parametric resonance. Another important input that occurs frequently in practice is related to acoustic pressure distributions that is a distributed type of loading. In this paper, detailed theoretical and experimental investigations on the dynamic response of a flexible cantilever beam carrying a tip mass to simultaneously applied external acoustic and parametric excitation signals have been performed. A mathematical model for transverse nonlinear vibration is obtained by employing Lagrange’s equations where important nonlinear effects such as the beam’s curvature and quadratic viscous damping are accounted for in the equation of motion. The beam is driven by two excitation sources, a sinusoidal motion applied to the beam’s fixed end and parallel to its longitudinal axis and a distributed sinusoidal acoustic load applied orthogonally to the beam’s longitudinal axis. The major goal here is to investigate theoretically as well as experimentally the dynamic behavior of the beam-lumped mass system under the action of these two excitation sources. Results from an extensive experimental work show how these two excitation sources interacts for various testing conditions. These experimental results are validated through numerically simulated results obtained from the solution of the system’s nonlinear equation of motion.

Sign in / Sign up

Export Citation Format

Share Document