Effect of a tip mass on the natural frequencies of a rotating pre-twisted cantilever plate

1980 ◽  
Vol 70 (4) ◽  
pp. 598-601 ◽  
Author(s):  
S. Sreenivasamurthy ◽  
V. Ramamurti
Keyword(s):  
Natural Frequencies ◽  
Cantilever Plate ◽  
Tip Mass

scholarly journals Characteristic Constraint Modes for Component Mode Synthesis

1999 ◽  
Author(s):  
Matthew P. Castanier ◽  
Yung-Chang Tan ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Component Mode Synthesis ◽  
Complex Structures ◽  
Cantilever Plate ◽  
Vibration Transmission ◽  
Stiffness Matrices ◽  
Physical Insight ◽  
Insight Into

Abstract In this paper, a technique is presented for improving the efficiency of the Craig-Bampton method of Component Mode Synthesis (CMS). An eigenanalysis is performed on the partitions of the CMS mass and stiffness matrices that correspond to the so-called constraint modes. The resultant eigenvectors are referred to as “characteristic constraint modes,” since they represent the characteristic motion of the interface between the component structures. By truncating the characteristic constraint modes, a CMS model with a highly-reduced number of degrees of freedom may be obtained. An example of a cantilever plate is considered. It is shown that relatively few characteristic constraint modes are needed to yield accurate approximations of the lower natural frequencies. This method also provides physical insight into the mechanisms of vibration transmission in complex structures.

Wave-Induced Vibrations of an Axial-Loaded Immersed Timoshenko Beam Carrying an Eccentric Tip Mass with Rotary Inertia

2010 ◽  
Vol 54 (01) ◽  
pp. 15-33
Author(s):  
Jong-Shyong Wu ◽  
Chin-Tzu Chen
Keyword(s):  
Closed Form ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Mode Superposition Method ◽  
Tip Mass

Under the specified assumptions for the equation of motion, the closed-form solution for the natural frequencies and associated mode shapes of an immersed "Euler-Bernoulli" beam carrying an eccentric tip mass possessing rotary inertia has been reported in the existing literature. However, this is not true for the immersed "Timoshenko" beam, particularly for the case with effect of axial load considered. Furthermore, the information concerning the forced vibration analysis of the foregoing Timoshenko beam caused by wave excitations is also rare. Therefore, the first purpose of this paper is to present a technique to obtain the closed-form solution for the natural frequencies and associated mode shapes of an axial-loaded immersed "Timoshenko" beam carrying eccentric tip mass with rotary inertia by using the continuous-mass model. The second purpose is to determine the forced vibration responses of the latter resulting from excitations of regular waves by using the mode superposition method incorporated with the last closed-form solution for the natural frequencies and associated mode shapes of the beam. Because the determination of normal mode shapes of the axial-loaded immersed "Timoshenko" beam is one of the main tasks for achieving the second purpose and the existing literature concerned is scarce, the details about the derivation of orthogonality conditions are also presented. Good agreements between the results obtained from the presented technique and those obtained from the existing literature or conventional finite element method (FEM) confirm the reliability of the presented theories and the developed computer programs for this paper.

Parallelogrammic elements in the solution of rhombic cantilever plate problems

1966 ◽  
Vol 1 (3) ◽  
pp. 223-230 ◽  
Author(s):  
D. J. Dawe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequencies ◽  
Cantilever Plate ◽  
Plate Element ◽  
The Finite Element Method ◽  
Skew Angle ◽  
Distributed Load ◽  
Uniformly Distributed Load ◽  
Element Method

The finite element method is applied to the calculation of the deflection under a uniformly distributed load and the natural frequencies of the rhombic cantilever plate. This has required the derivation of stiffness and inertia matrices for a plate element of parallelogrammic planform. Although, in common with the work of past investigators, the accuracy of the results decreases with increase in skew angle it is shown that the method is adequate for angles up to about 45°.

Study of natural frequencies of natural rubber cored novel sandwich structure without tip mass

Structures ◽  
2020 ◽  
Vol 28 ◽  
pp. 651-658
Author(s):  
Krishanu Gupta ◽  
Biplab Bhattacharjee ◽  
Sonu Kumar Gupta ◽  
Prasun Chakraborti
Keyword(s):  
Natural Rubber ◽  
Sandwich Structure ◽  
Natural Frequencies ◽  
Tip Mass

Vibration of Double-Walled Carbon Nanotube-Based Mass Sensor via Nonlocal Timoshenko Beam Theory

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhi-Bin Shen ◽  
Bin Deng ◽  
Xian-Fang Li ◽  
Guo-Jin Tang
Keyword(s):  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Tube Length ◽  
Beam Model ◽  
Mass Sensor ◽  
Nonlocal Timoshenko Beam Theory ◽  
Double Walled Carbon Nanotubes ◽  
Tip Mass

The potential of double-walled carbon nanotubes (DWCNTs) as a micromass sensor is explored. A nonlocal Timoshenko beam carrying a micromass at the free end of the inner tube is used to analyze the vibration of DWCNT-based mass sensor. The length of the outer tube is not equal to that of the inner tube, and the interaction between two tubes is governed by van der Waals force (vdW). Using the transfer function method, the natural frequencies of a nonlocal cantilever with a tip mass are computed. The effects of the attached mass and the outer-to-inner tube length ratio on the natural frequencies are discussed. When the nonlocal parameter is neglected, the frequencies reduce to the classical results, in agreement with those using the finite element method. The obtained results show that increasing the attached micromass decreases the natural frequency but increases frequency shift. The mass sensitivity improves for short DWCNTs used in mass sensor. The nonlocal Timoshenko beam model is more adequate than the nonlocal Euler-Bernoulli beam model for short DWCNT sensors. Obtained results are helpful to the design of DWCNT-based resonator as micromass sensor.

Comment on "Natural Frequencies of a Cantilever with Slender Tip Mass"

AIAA Journal ◽  
1978 ◽  
Vol 16 (1) ◽  
pp. 94-96
Author(s):  
Alexander H. Flax
Keyword(s):  
Natural Frequencies ◽  
Tip Mass

scholarly journals Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7279
Author(s):  
Jin Wei ◽  
Tao Yu ◽  
Dongping Jin ◽  
Mei Liu ◽  
Dengqing Cao ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Dynamic ◽  
Natural Frequencies ◽  
Great Influence ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Nonlinear Odes ◽  
Global Mode ◽  
Orthogonality Relations ◽  
Tip Mass

A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

Design of a Vibration-Based Energy Harvester With Adjustable Natural Frequency

2010 ◽  
Author(s):  
Mohamed O. Mansour ◽  
Mustafa H. Arafa ◽  
Said M. Megahed
Keyword(s):  
Energy Harvesting ◽  
Natural Frequency ◽  
Piezoelectric Layer ◽  
System Performance ◽  
Energy Harvester ◽  
Natural Frequencies ◽  
Opposite Polarity ◽  
Energy Harvesters ◽  
Close Proximity ◽  
Tip Mass

The recent years have witnessed a wealth of research on energy harvesting technologies. To maximize the output power, vibration-based energy harvesters are normally designed to have natural frequencies that match those of the excitation. This has spurred interest into the design of devices that possess tunable natural frequencies to cope with sources which exhibit varying frequencies. In this work, an energy harvester is proposed in the form of a base excited cantilever treated with a piezoelectric layer. The cantilever carries a tip mass in the form of a magnet which is placed in close proximity to another magnet with opposite polarity. Different values of axial tensions, and hence different natural frequencies, are obtained by adjusting the gap between the magnets. A dynamic model to predict the system performance is presented and verified experimentally. Based on the findings of this paper, natural frequencies ranging from 3.19–12 Hz were achieved.

Closed-Form Solution of Natural Frequencies of a Cantilever Beam Under Longitudinal Rotation of the Support

2005 ◽  
Author(s):  
Mehdi Esmaeili ◽  
Mohammad Durali ◽  
Nader Jalili
Keyword(s):  
Closed Form ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Longitudinal Direction ◽  
Form Solution ◽  
Governing Equations ◽  
Well Drilling ◽  
General Base ◽  
Tip Mass

This paper presents the modeling steps towards development of frequency equations for a cantilever beam with a tip mass under general base excitations. More specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived using Extended Hamilton’s Principle with general 6-DOF base motion. The natural frequency equations are then extracted in closed-form for the case where the base undergoes longitudinal rotation. For validation purposes, the resulting natural frequencies are compared with two example case studies; one with a beam on a stationary base and the other one with a rotor having flexible shaft.

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