Study of a Vibration Problem for a Perforated Plate with Fourier Boundary Conditions

2001 ◽  
pp. 230-244
Keyword(s):  
Boundary Conditions ◽  
Perforated Plate ◽  
Vibration Problem

Teaching Vibration Analysis Using Symbolic Computation Software

1998 ◽  
Vol 26 (2) ◽  
pp. 75-88
Author(s):  
Hemanshu R. Pota ◽  
Thomas E. Alberts
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Vibration Analysis ◽  
Complete Solution ◽  
Linear Equations ◽  
Flexible Systems ◽  
Beam Vibration ◽  
Different Boundary Conditions ◽  
Vibration Problem ◽  
Forcing Functions

This paper presents a general approach to modelling and learning vibration analysis for simple beams using symbolic computation software. The emphasis here is on the fact that a complete solution of the beam vibrations problem, for different boundary conditions and arbitrary forcing functions, is made very simple by using symbolic computation software. The heart of the procedure is to convert the beam vibration problem into a system of simultaneous algebraic linear equations and then use symbolic computation software to solve it. The analysis here also shows how to obtain models suitable to design controllers for flexible systems.

scholarly journals Effects of Boundary Conditions on the Modal and Spectral Properties of the Shaft

2020 ◽  
Vol 22 (1) ◽  
pp. 42-47
Author(s):  
Petr Hruby ◽  
Tomas Nahlik ◽  
Dana Smetanova
Keyword(s):  
Boundary Conditions ◽  
Spectral Properties ◽  
Rotating Shaft ◽  
The Real ◽  
Vibration Problem ◽  
Modal Properties ◽  
Fixed End

Influence of boundary conditions (i.e. mounting type of shafts ends) on spectral and modal properties is studied in this paper. Cases with joints at both ends and with joint at one end and fixed end are described in detail. The vibration problem of rotating shaft is generalized to problem of vibration of the shaft in the rotating plane. The problem is illustrated on testing models. The real mounting type of shafts is presented.

An Analytical Model to Determine Fundamental Frequency of Free Vibration of Perforated Plate by Using Greatest Integer Functions to Express Non Homogeneity

2012 ◽  
Vol 622-623 ◽  
pp. 600-604 ◽  
Author(s):  
Kiran D. Mali ◽  
Pravin M. Singru
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Modal Analysis ◽  
Fundamental Frequency ◽  
Perforated Plate ◽  
Floor Function ◽  
Greatest Integer Function

This paper aims at determining the fundamental frequency of square perforated plate with square perforation pattern of square holes. Rayleigh’s method is used for the solution of this problem. Non homogeneity in Young’s modulus and density at the perforation is expressed by using greatest integer function i.e. floor function. Boundary condition considered is clamped on all edges. Perforated plate is considered as plate with uniformly distributed mass and holes are considered as non homogeneous patches. The deflected surface of the plate is approximated by a function which satisfies the boundary conditions. Finite Element Method (FEM) modal analysis is carried out to validate the results of the proposed approach.

The Role of Nonlinear Acoustic Boundary Conditions in Combustion/Acoustic Coupled Instabilities

2009 ◽  
Author(s):  
T. Schuller ◽  
N. Tran ◽  
N. Noiray ◽  
D. Durox ◽  
S. Ducruix ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Perforated Plate ◽  
Mode Switching ◽  
Describing Function ◽  
Complex Flow ◽  
Acoustic Boundary Conditions ◽  
Practical Applications ◽  
Bias Flow ◽  
Flow Interactions ◽  
Flame Response

Triggering, frequency shifting, mode switching and hysteresis are commonly encountered during self-sustained oscillations in combustors. These mechanisms cannot be anticipated from classical linear stability analysis and the nonlinear flame response to incident flow perturbations is often invoked to interpret these features. However, the flame may not be solely responsible for nonlinearities. Recent studies indicate that interactions with boundaries can be influenced by the perturbation level and that this needs to be considered. The nonlinear response of acoustic boundary conditions to flow perturbations is here exemplified in two configurations which typify practical applications. The first corresponds to a perforated plate backed by a cavity conveying a bias flow and the second corresponds to a set of flames stabilized at a burner outlet. These systems are submitted to acoustic perturbations of increasing amplitudes as can be encountered during unstable operation. It shown that these terminations can be characterized by an impedance featuring an amplitude dependent response. The classical linear impedance Z(ω) is then replaced by its nonlinear counterpart an Impedance Describing Function (IDF), which depends on the perturbation level input Z(ω, |p′| or |u′|). Using this concept, it is shown that the passive perforated plate optimized to damp instabilities of small amplitudes may eventually loose its properties when submitted to large sound pressure levels and that the flame response shifts when the amplitude of incoming flow perturbations is amplified. The influence of these nonlinear elements on the stability of a generic burner is then examined using a methodology which extends a previous analysis based on the Flame Describing Function (FDF) to systems with complex flow interactions at the boundaries.

VIBRATION OF INITIALLY STRESSED MICRO- AND NANO-BEAMS

2007 ◽  
Vol 07 (04) ◽  
pp. 555-570 ◽  
Author(s):  
C. M. WANG ◽  
Y. Y. ZHANG ◽  
S. KITIPORNCHAI
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Initial Stress ◽  
Transverse Shear ◽  
Virtual Work ◽  
Nonlocal Elasticity Theory ◽  
Rotary Inertia ◽  
Small Scale ◽  
Transverse Shear Deformation ◽  
Vibration Problem

This paper is concerned with the vibration problem of initially stressed micro/nano-beams. The vibration problem is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of initial stress, transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. These equations are solved analytically for the vibration frequencies of micro/nano-beams with different initial stress values and boundary conditions. The effect of the initial stress on the fundamental frequency and vibration mode shape of the beam is investigated. The solutions obtained provide a better representation of the vibration behavior of initially stressed micro/nano-beams which are stubby and short, since the effects of small scale, transverse shear deformation and rotary inertia are significant and cannot be neglected.

Exact Analytical Solutions for the Free Vibration of Steam Generator U-Tubes

1988 ◽  
Vol 110 (4) ◽  
pp. 422-429 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Steam Generator ◽  
Analytical Solutions ◽  
Analytical Study ◽  
Interface Boundary ◽  
Exact Analytical Solutions ◽  
Vibration Problem ◽  
Interface Boundary Conditions ◽  
Similar Solutions

Exact analytical solutions for free vibration of straight tubes have been known for many years, with solutions for curved tubes being developed more recently. In this paper it is shown how these solutions can be exploited to obtain similar solutions for the free vibration of U-tubes. All of the required interface boundary conditions are developed in detail and it is shown how advantage can be taken of U-tube symmetry where it exists. Illustrative results of two studies are presented. This represents, to the author’s knowledge, the first comprehensive analytical study of the U-tube free vibration problem.

scholarly journals Implementation of the Nodal Discontinuous Galerkin Method for the Plate Vibration Problem using Linear Elasticity Equations

2019 ◽  
Vol 105 (4) ◽  
pp. 668-681
Author(s):  
Indra Sihar ◽  
Maarten Hornikx
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Discontinuous Galerkin ◽  
Linear Elasticity ◽  
Plate Vibration ◽  
Vibration Problem ◽  
Elasticity Equations ◽  
Dg Method ◽  
Linear Elasticity Equations ◽  
Plate Vibration Problem

This work presents a numerical solution of the forced plate vibration problem using the nodal discontinuous Galerkin (DG) method. The plate is modelled as a three-dimensional domain, and its vibration is governed by the linear elasticity equations. The nodal DG method discretises the spatial domain and computes the spatial derivatives of the equations element-wise, while the time integration is conducted using the Runge-Kutta method. This method is in particular of interest as it is very favourable to carry out the computation by a parallel implementation. Several aspects regarding the numerical implementation such as the plate boundary conditions, the point force excitation, and the upwind numerical flux are presented. The numerical results are validated for rectangular concrete plates with different sets of boundary conditions and thicknesses, by a comparison with the exact mobilities that are derived from the classical plate theory (CPT) and the first order shear deformation theory (FSDT). The plate thickness is varied to understand its effect regarding the comparison with the CPT. An excellent agreement between the numerical solution and the FSDT was found. The agreement with the CPT occurs only at the first couple of resonance frequencies, and as the plate is getting thinner. Furthermore, the numerical example is extended to an L-shaped concrete plate. The mobility is then compared with the mobilities obtained by the CPT, FSDT, and linear elasticity equations.

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