scholarly journals Boundary condition modelling and identification for cantilever-like structures using natural frequencies

2019 ◽  
Vol 32 (6) ◽  
pp. 1451-1464 ◽  
Author(s):  
Wei LIU ◽  
Zhichun YANG ◽  
Le WANG ◽  
Ning GUO
Keyword(s):  
Boundary Condition ◽  
Natural Frequencies

scholarly journals Isospectrals of non-uniform Rayleigh beams with respect to their uniform counterparts

2018 ◽  
Vol 5 (2) ◽  
pp. 171717 ◽  
Author(s):  
Srivatsa Bhat K ◽  
Ranjan Ganguli
Keyword(s):  
Boundary Condition ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Beam Equation ◽  
The Finite Element Method ◽  
Rayleigh Beam ◽  
Uniform Beam ◽  
Governing Differential Equation ◽  
The Given

In this paper, we look for non-uniform Rayleigh beams isospectral to a given uniform Rayleigh beam. Isospectral systems are those that have the same spectral properties, i.e. the same free vibration natural frequencies for a given boundary condition. A transformation is proposed that converts the fourth-order governing differential equation of non-uniform Rayleigh beam into a uniform Rayleigh beam. If the coefficients of the transformed equation match with those of the uniform beam equation, then the non-uniform beam is isospectral to the given uniform beam. The boundary-condition configuration should be preserved under this transformation. We present the constraints under which the boundary configurations will remain unchanged. Frequency equivalence of the non-uniform beams and the uniform beam is confirmed by the finite-element method. For the considered cases, examples of beams having a rectangular cross section are presented to show the application of our analysis.

A Probabilistic Analysis for Static and Dynamic Frequency of Blade With Uncertain Boundary Conditions

2005 ◽  
Author(s):  
Z. Q. Wang ◽  
L. Q. An ◽  
Z. Z. Peng
Keyword(s):  
Boundary Condition ◽  
Probabilistic Analysis ◽  
Natural Frequencies ◽  
Perturbation Technique ◽  
Ritz Method ◽  
Joint Stiffness ◽  
Matrix Perturbation ◽  
Sensitivity Matrix ◽  
The Matrix ◽  
Uncertain Boundary

A probabilistic analysis method is developed for frequencies analysis of turbine blade with uncertain boundary condition at the root of blade. The Ritz method is used to derive the eigenvalues equation of the rotating blade with uncertain root boundary condition. The matrix perturbation technique is employed for the probabilistic analysis to obtain the deterministic part of natural frequencies and vibration modes, the sensitivity matrix, the covariance matrix and the coefficient of variance (COV) for the natural frequencies. The effects of variations in the expectation and the variance of joint stiffness on the expectation and the variance of the natural frequencies are investigated.

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

Mechanics Mechanism Analysis of Concrete Pavement Resonant Rubblization

2015 ◽  
Vol 667 ◽  
pp. 365-369
Author(s):  
Peng Chen ◽  
Xin Qiu ◽  
Qing Zhu ◽  
Chan Chan Ouyang
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Elastic Foundation ◽  
Thin Plate ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Concrete Pavement ◽  
Mechanism Analysis ◽  
Vibration Theory ◽  
Fundamental Natural Frequency

Based on the assumption of thin plate of elastic foundation and vibration theory, a method for calculating the fundamental natural frequency of cement slab is presented and the certain relationship between the fundamental natural frequency of cement slab and cement slab boundary condition is discussed. As well, according to the analysis results of fundamental natural frequencies of the typical cement pavements of China, the selected proposals of the excitation frequency of the resonant rubblization machine are presented .The research results provide a theory support to popularize resonant rubblization technology in overlaying and rebuilding engineering of the existed cement pavements in China.

Estimation of Tension Force in Short Hangers Using Added Mass Method

2013 ◽  
Vol 658 ◽  
pp. 124-133
Author(s):  
Yong Gang Shen ◽  
Xu Xie ◽  
Liang Feng Sun ◽  
Sai Hua Huang
Keyword(s):  
Genetic Algorithm ◽  
Boundary Condition ◽  
Natural Frequencies ◽  
Flexural Rigidity ◽  
Field Testing ◽  
Added Mass ◽  
Testing Technology ◽  
Adaptive Crossover ◽  
Two Parameters ◽  
Crossover And Mutation

For short hangers, the influence of flexural rigidities and boundary conditions on tension measuring cannot be neglected. But there has no effective method to precisely calculate hanger tension considering the two parameters. This paper proposes the Added Mass Method (AMM) to simultaneously identify the tension, flexural rigidity and boundary condition of short hangers. In this method, the effect of mass distribution of structure on natural frequencies has been studied to add extra calculation conditions for establishing the eigenvalue equation set. The method of Genetic Algorithm (GA) with adaptive crossover and mutation rate is used to solve the equation set quickly. The results provides that the AMM is a high-accurate field testing technology in tension measurement for short hanger of arch bridge.

scholarly journals Natural Frequencies of a Cracked Beam Coupled with a Compressible Sloshing Fluid

2004 ◽  
Vol 11 (3-4) ◽  
pp. 505-519 ◽  
Author(s):  
Michele Di Sciuva ◽  
Cecilia Surace
Keyword(s):  
Boundary Condition ◽  
Viscous Fluid ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Coupled System ◽  
Cracked Beam ◽  
Structure Interaction ◽  
Linear Fracture ◽  
Cantilevered Beam ◽  
Interaction Problem

This article describes studies into the flexural vibration of a cracked cantilevered beam in contact with a non-viscous fluid. The crack has been represented by a mass-less rotational spring, the flexibility of which has been calculated using linear fracture mechanics. The coupled system is subject to undisturbed boundary condition at infinity in the fluid domain. A range of different boundary conditions have been analysed such as both incompressible and compressible fluid, with and without sloshing. Various crack sizes and positions have been considered in order to assess the effect of damage in the fluid-structure interaction problem.

scholarly journals Vibration Analysis of Cracked Structures as a Roving Body Passes a Crack Using the Rayleigh-Ritz Method

2018 ◽  
Vol 1 (2) ◽  
pp. 30-34
Author(s):  
Sinniah Ilanko ◽  
Yusuke Mochida ◽  
Julian De Los Rois
Keyword(s):  
Boundary Condition ◽  
Frequency Shift ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Test Body ◽  
The Body ◽  
Rotary Inertia ◽  
Cracked Structures ◽  
Frequency Changes

The natural frequencies of a cracked plate with a roving mass were computed using the Rayleigh-Ritz Method for various sets of boundary condition. The obtained frequencies exhibit a sudden shift as a roving body crosses a crack. If the crack is only partial and continuity of translation is maintained, then the frequency shift occurs only when the body possesses a rotary inertia. If the crack is a complete one (through thickness) which permits differential translation to occur on either side of the crack, a particle having mass only (translatory inertia) is sufficient to cause a sudden shift. There is no need for a rotary inertia. This is potentially useful in detecting cracks in structures, as it is possible to track the changes in the natural frequencies of a structure as a test body such as a vehicle on a bridge moves and identify points where sudden frequency changes occur.

Dynamic Characteristics of Resonant Beams With Passive Thermal Stress Regulators

2018 ◽  
Author(s):  
Tyler Kellar ◽  
Pezhman Hassanpour
Keyword(s):  
Boundary Condition ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Mode Shapes ◽  
Elastic Boundary ◽  
Special Cases ◽  
Angular Displacements

This paper addresses the dynamic characteristics of a beam with a particular elastic boundary condition. In this elastic boundary condition, the lateral and angular displacements of the beam are coupled through the elastic constraints. The dynamic characteristic, namely natural frequencies and mode shapes of vibrations are frequently encountered in the design and modeling of resonant micro-structures. The governing equations of motion of the beam is derived using Euler-Bernoulli beam theory considering the elastic coupling between the transverse and rotational displacements of the beam’s end. The characteristic equation for the natural frequencies and mode shapes of vibration is derived by applying the method of separation of variables to the governing partial differential equation of motion. The natural frequencies and mode shapes of the system are derived for various combinations of compliance values of the elastic support and are compared with those of several special cases, namely clamped-free, clamped-guided, clamped-pinned and clamped-clamped beams.

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