scholarly journals Vibration analysis of submerged rectangular microplates with distributed mass loading

2009 ◽  
Vol 465 (2104) ◽  
pp. 1323-1336 ◽  
Author(s):  
Zhangming Wu ◽  
Xianghong Ma ◽  
Peter N Brett ◽  
Jinwu Xu
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Isotropic Plate ◽  
Numerical Results ◽  
Previous Literature ◽  
Mode Shapes ◽  
Mass Loading ◽  
Coupling System ◽  
Different Types ◽  
Loaded Structure

This paper investigates the vibration characteristics of the coupling system of a microscale fluid-loaded rectangular isotropic plate attached to a uniformly distributed mass. Previous literature has, respectively, studied the changes in the plate vibration induced by an acoustic field or by the attached mass loading. This paper investigates the issue of involving these two types of loading simultaneously. Based on Lamb's assumption of the fluid-loaded structure and the Rayleigh–Ritz energy method, this paper presents an analytical solution for the natural frequencies and mode shapes of the coupling system. Numerical results for microplates with different types of boundary conditions have also been obtained and compared with experimental and numerical results from previous literature. The theoretical model and novel analytical solution are of particular interest in the design of microplate-based biosensing devices.

scholarly journals Effect of Location of Delamination on Free Vibration of Cross-Ply Conical Shells

2012 ◽  
Vol 19 (4) ◽  
pp. 679-692 ◽  
Author(s):  
Sudip Dey ◽  
Amit Karmakar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Structural Instability ◽  
Numerical Results ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Conical Shells

Location of delamination is a triggering parameter for structural instability of laminated composites. In this paper, a finite element method is employed to determine the effects of location of delamination on free vibration characteristics of graphite-epoxy cross-ply composite pre-twisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange's equation of motion neglecting Coriolis effect for moderate rotational speeds. The formulation is exercised by using an eight noded isoparametric plate bending element based on Mindlin's theory. Multi-point constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Finite element codes are developed to obtain the numerical results concerning the effects of location of delamination, twist angle and rotational speed on the natural frequencies of cross-ply composite shallow conical shells. The mode shapes are also depicted for a typical laminate configuration. Numerical results obtained from parametric studies of both symmetric and anti-symmetric cross-ply laminates are the first known non-dimensional natural frequencies for the type of analyses carried out here.

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

2016 ◽  
Vol 16 (06) ◽  
pp. 1550013 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei
Keyword(s):  
Analytical Solution ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Material Anisotropy ◽  
Rotating Speed ◽  
Multipliers Method ◽  
Free Mode ◽  
The Difference ◽  
Laminated Composite Beams

In this paper, the free vibration of rotating laminated composite beams (LCBs) with general lay-ups and single through-the-width delamination is analytically investigated. The Hamilton’s principle is used to derive the coupled governing differential equations and boundary conditions for the rotating delaminated beam, considering the effects of shear deformation, rotary inertia, material couplings (bending–tension, bending–twist and tension–twist couplings), and Poisson’s effect. Both the free mode and constrained mode assumptions are adopted. Analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the Lagrange multipliers method. The accuracy is assured by the convergence of the natural frequencies, as well as by comparison with published results. The effects of various factors such as delamination parameter, fiber angle, hub radius, material anisotropy, end mass and rotating speed are studied in detail. The difference between the results based on the free mode and constrained mode assumptions is also investigated.

Free Vibration of In-Planar Rotating Ring: An Analytical Solution

2000 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Analytical Solution ◽  
High Speed ◽  
Systematic Approach ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Stress Theory ◽  
Wave Numbers ◽  
Annular Disks ◽  
Circumferential Wave

Abstract An analytical method is presented to consider the vibration characteristics of high speed rotating rings. More specifically, a systematic approach based on an established solution for linear in-plane vibration of spinning annular disks is used to compute natural frequencies and mode shapes of rotating rings. The medium is considered to be homogenous, and elastic isotropic. The developed analytical solution is achieved by implementing the two-dimensional plane stress theory. The modal displacements and stresses at both inner and outer boundaries are determined, and the required boundary conditions are satisfied to obtain the frequency equation. The dimensionless natural frequencies for different modes, rotating speeds, and thickness ratios are computed. In addition, variations of dimensionless critical speeds for several circumferential wave numbers versus radius ratio of the ring are presented. The provided results are for the two different cases of clamped-free and free-free rings.

Free Vibration Analysis of Angle-ply Laminated Shallow Cylindrical Shell with Clamped Edges

2000 ◽  
Vol 123 (2) ◽  
pp. 188-197 ◽  
Author(s):  
Kenji Hosokawa ◽  
Minehiro Murayama ◽  
Toshiyuki Sakata
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Numerical Approach ◽  
Free Vibrations ◽  
Numerical Results ◽  
Mode Shapes ◽  
Shallow Cylindrical Shell ◽  
Plastic Composite ◽  
Vibration Tests

In a previous paper, the authors proposed a numerical approach for analyzing the free vibrations of a laminated FRP (fiber reinforced plastic) composite plate. In the present paper, this approach is modified for application to a symmetrically laminated shallow cylindrical shell having a rectangular planform. First, the natural frequencies of the shell are calculated for discussion of the convergence and accuracy of the solution. Next, the effects of the curvature ratio and stacking sequence on the natural frequencies and mode shapes of the shell are studied. Furthermore, to justify the numerical results, vibration tests of the clamped symmetrically laminated shallow cylindrical shell having a square planform are carried out. These experimental results are found to agree well with the numerical results computed using the measured material properties of the lamina.

scholarly journals Analytical Solution for the Free Vibration Analysis of Delaminated Timoshenko Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ramazan-Ali Jafari-Talookolaei ◽  
Maryam Abedi
Keyword(s):  
Analytical Solution ◽  
Free Vibration ◽  
Variational Problem ◽  
Lagrange Multipliers ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Method Of Lagrange Multipliers

This work presents a method to find the exact solutions for the free vibration analysis of a delaminated beam based on the Timoshenko type with different boundary conditions. The solutions are obtained by the method of Lagrange multipliers in which the free vibration problem is posed as a constrained variational problem. The Legendre orthogonal polynomials are used as the beam eigenfunctions. Natural frequencies and mode shapes of various Timoshenko beams are presented to demonstrate the efficiency of the methodology.

Frequencies and Mode Shapes for Axisymmetric Vibration of Shells

1967 ◽  
Vol 34 (1) ◽  
pp. 73-80 ◽  
Author(s):  
E. W. Ross ◽  
W. T. Matthews
Keyword(s):  
Theoretical Result ◽  
General Class ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Mode Shapes ◽  
Axisymmetric Vibration ◽  
Elastic Shells ◽  
Natural Frequencies And Modes

This paper treats the axisymmetric vibration of thin elastic shells. Estimates of natural frequencies and modes are obtained for a general class of domes by applying the approximations obtained in a previous paper by one of the authors. Numerical results are obtained for ellipsoidal shells, and one new theoretical result is found.

A modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform one-dimensional waveguides

2011 ◽  
Vol 225 (12) ◽  
pp. 2864-2880 ◽  
Author(s):  
M Khoshbayani-Arani ◽  
N Rasekh-Saleh ◽  
M Nikkhah-Bahrami
Keyword(s):  
Analytical Solution ◽  
Cross Section ◽  
Natural Frequencies ◽  
Exact Analytical Solution ◽  
Mode Shapes ◽  
Transmission Matrix ◽  
Approximate Methods ◽  
One Dimensional ◽  
Wave Propagation Method ◽  
Number Of Segments

In this article, using the wave propagation method, the natural frequencies and mode shapes of an arbitrary non-uniform one-dimensional waveguide are calculated. The non-uniform rods and beams are partitioned into several continuous segments with constant cross-sections, for which there exists an exact analytical solution. At the end of each segment, waves in positive and negative directions are obtained in terms of waves at initial segment and subsequently, the calculations of the mode shapes become simple. By satisfying the boundary conditions, the characteristic equation is obtained and natural frequencies are calculated for both the arbitrary non-uniform rod and beam. Also, by adding waves in positive and negative directions at the end point of each segment, the mode shapes are obtained. To verify the modified wave method presented here, the frequencies and mode shapes of the rod and the beam with a polynomial cross-section having an exact analytical solution are compared and have been proven to be of high accuracy. Besides, comparisons of finite element method are also included. Therefore, this method can also be used to calculate the natural frequencies and mode shapes of rods and beams with any arbitrary variable cross-section for which no analytical solution is available. For the ‘Modified Wave Approach’ developed here, dimensions of transmission matrix remain constant if the number of segments is increased, while in general wave propagation method, dimensions of transmission matrix increase upon increasing the number of segments. Besides this novelty, this method has the advantage that it gives all the natural frequencies and mode shapes, unlike other approximate methods such as weighted residual, Rayleigh–Ritz, and finite difference methods which have their own shortcomings such as limited number of natural frequencies. Also, since each segment has an exact analytical solution, in contrast to other approximate methods, much higher accuracy is obtained even with only a few number of partitions.

Experiments and Calculations on the Vibrations of Rotating Radial Impellers

1988 ◽  
Vol 110 (2) ◽  
pp. 137-142 ◽  
Author(s):  
Horst Irretier
Keyword(s):  
Rotational Speed ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Rotating Waves ◽  
Excitation Frequencies ◽  
Run Up

Experimental and numerical results on the vibrations of a rotating radial impeller are presented. They show natural frequencies as a function of rotational speed, the mode shapes, the resonance excitation frequencies of the forward and backward rotating waves, and a response diagram during a run-up of the impeller.

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