An Analytical Investigation for Vibration Characteristics of a Beam-Type Liquid Micro-Pump

2020 ◽  
Vol 12 (02) ◽  
pp. 2050016
Author(s):  
Hamed Hatami ◽  
Ahmad Bagheri ◽  
Reza Ansari
Keyword(s):  
Fluid Flow ◽  
Natural Frequencies ◽  
Separation Of Variables ◽  
Elastic Beam ◽  
Coupled System ◽  
Analytical Investigation ◽  
Mode Shapes ◽  
Micro Pump ◽  
Cartesian Coordinate ◽  
Forced Vibration Analysis

This paper studies the characteristics of a micro-beam interacting with an incompressible fluid in a fluid chamber with an opening in its bottom face for fluid flow. The Euler–Bernoulli equation for transverse deformation of an elastic beam is coupled with the fundamental hydrodynamic equation, which is solved by Galerkin and separation of variables method. The 2D fluid flow assumption in Cartesian coordinate has been used. Natural frequencies and mode shapes of wet beam are calculated and compared with the dry beam. The effects of geometrical parameter changes are also computed as a benchmark for the design of the micro-pump. It is observed that fluid coupling causes a decrease for beam’s natural frequencies, especially in higher modes. Furthermore, since the results of the dry and wet beam show a small discrepancy in lower modes, the mode related to the dry beam was employed as the trial function in the forced vibration analysis of the coupled system.

Forced Vibration of Mistuned Bladed Discs in Last Stage LP Steam Turbine

2016 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin ◽  
Leszek Kubitz ◽  
Ryszard Szczepanik
Keyword(s):  
Steam Turbine ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Lower Stress ◽  
Free And Forced Vibrations ◽  
Specific Order ◽  
Last Stage ◽  
Forced Vibration Analysis ◽  
Blade Geometry

During the exploitation of a commercial LP steam turbine, self-excitation occurred in the last stage of slender blades, inducing high vibration amplitudes. These problems were solved by changing the geometry of certain blades (feathering) and arranging them in a specific order (alternating mistuning). This paper presents free and forced vibrations of various mistuned steam turbine bladed discs. The natural frequencies and mode shapes of the steam turbine bladed discs were calculated using FEM models. Two different approaches to mistuning were applied: either the blade geometry or the Young’s Modulus were changed. Next, the results were compared. This showed that blade geometry mistuning gave the best results for long blades in the case of higher mistuning. The forced vibration analysis showed that the maximal blade stress location differed, depending on the kind of mistuning. The application feathering and alternating mistuning showed lower stress levels than the tip-timing measured standard mistuning pattern.

Vibrations of Suspended Cables

1983 ◽  
Vol 50 (3) ◽  
pp. 687-689
Author(s):  
J. G. Gale ◽  
C. E. Smith
Keyword(s):  
Natural Frequencies ◽  
Analytical Investigation ◽  
Plane Motion ◽  
Mode Shapes ◽  
Arc Length ◽  
Power Series Solutions ◽  
Out Of Plane ◽  
Independent Variable ◽  
Suspended Cables ◽  
Frequency Ratios

An analytical investigation of the small, normal-mode motions of a homogeneous, inextensible, perfectly flexible cable suspended in a gravitational field was made. With cable arc length as the independent variable, the differential equations that govern the mode shapes have irrational coefficients. A transformation of the independent position variable yields equations that have polynominal coefficients, which then lend themselves to power series solutions. Natural frequencies of oscillation and corresponding mode shapes are determined from these solutions. Figures showing the natural frequency ratios for a variety of cable support geometries are presented for both in-plane and out-of-plane motion.

An Approximate Method for the Determination of the Response Frequency of Pipe Whip

1980 ◽  
Vol 102 (2) ◽  
pp. 174-181
Author(s):  
S. A. Haktanir ◽  
G. C. Tolle
Keyword(s):  
Fluid Flow ◽  
Linear Problem ◽  
Natural Frequencies ◽  
Pipe Wall ◽  
Virtual Work ◽  
Fluid Velocity ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Work Technique

This paper is concerned with the effect of fluid flow on the static and dynamic characteristics of a simply supported pipe having a hole through the pipe wall to permit a fluid flow. In this approximate analysis based on the virtual work technique, system natural frequencies and mode shapes are determined and compared to the analytical solution of the linear problem given by G. W. Housner [3] and experimental solution of H. L. Dodds, Jr., and H. L. Runyan [2]. An approximate solution satisfying the initial and boundary conditions is presented for free vibrations and for steady-state forced vibrations for the nonlinear problem. In addition, the critical fluid velocity at which the system becomes statically unstable is verified.

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.

Free and Forced Vibration Analysis of an Idealized Compliant Tower With Superstructure, due to Current Loads, Wave Excitation, and Earthquake Impulses

2014 ◽  
Author(s):  
Ankit ◽  
N. Datta
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Wave Excitation ◽  
Uniform Beam ◽  
Compliant Tower ◽  
Forced Vibration Analysis ◽  
Beam Mode

A compliant tower (CT) is modeled as a partially dry, partially tapered, damped Timoshenko beam with the superstructure modeled as an eccentric tip mass, and a non-classical damped boundary at the base. The foundation is modeled as a combination of a linear spring and a torsional spring, along with linear and torsional dampers. The mean empty space factor due to the truss type structure of the tower is included. The effect of shear deformation and rotary inertia are included in the vibration analysis; with the non-uniform beam mode-shapes being a weighted sum of the uniform beam mode-shapes. The weights are evaluated by the Rayleigh-Ritz method, using the first ten modes and verified using Finite Element Method (FEM). The superstructure adds to the kinetic energy without affecting the stiffness of the beam, thereby reducing the natural frequencies. The weight of the superstructure acts as an axial compressive load on the beam, reducing its frequencies further. Kelvin-Voigt model of structural damping is included. A part of the structure being underwater, the virtual added inertia is included to calculate the wet natural frequencies. The CT is first subjected to steady current loads of a given velocity profile. The static deflection and overturning moment is estimated for current loads. The CT is then studied for wave excitation at various seas states. Morrison’s equation and Pierson-Moskowitz Spectrum are used to derive the forces for different sea states. The forced vibration analysis of the structure is done via Rayleigh-Ritz method and verified using FEM. The maximum horizontal deflection and shear stress of the base of the superstructure, and the normal/shear stresses at the foundation are analyzed. Finally, the CT is subjected to earthquake excitation, modeled as an arbitrary horizontal impact excitation at the base. The above forced vibration analysis is repeated.

Multistage Coupling of Eight Bladed Discs on a Solid Shaft

2010 ◽  
Author(s):  
Romuald Rza˛dkowski ◽  
Marcin Drewczynski
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Centrifugal Stiffening ◽  
Shaft Deflection ◽  
Forced Vibration Analysis

Considered here is the effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that the flexible modes of the tuned bladed discs affected by shaft motion were those with zero, one and two nodal diameters. In these modes shaft deflection was clearly visible. In forced vibration analysis a different EO excitation was applied for each stage. The importance of using models with different numbers of blades on each disc is apparent when compared with earlier results concerning discs with identical numbers of blades. Here the model of 8 discs with an equal number of blades on each disc is referred to as (Model 1), and the model of 8 discs with a different number of blades on each disc is referred to as (Model 2).

scholarly journals Identification of dynamical characteristics for distributed parameters systems from measured vibration data

1995 ◽  
Vol 17 (1) ◽  
pp. 35-44
Author(s):  
Nguyen Tien Khiem ◽  
Dao Nhu Mai ◽  
Nguyen Van Dac ◽  
Nguyen Viet Khoa
Keyword(s):  
Natural Frequencies ◽  
Damping Ratio ◽  
Elastic Beam ◽  
Mode Shapes ◽  
Vibration Data ◽  
Dynamical Characteristics ◽  
Distributed Parameters

This article is devoted to determinate the dynamical characteristics (Natural Frequencies, Mode Shapes, Damping Ratio) of elastic beam from measured responce auto-spectrum. Developed here method is based on the assumptions of smallness of the damping and sparse distribution of natural frequencies. Accuracy and practical meaning of the method are confirmed by the agreement of the theory with experiments.

Efficient Theoretical and Numerical Methods for Solving Free Vibrations and Transient Responses of a Circular Plate Coupled With Fluid Subjected to Impact Loadings

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Coupling Parameter ◽  
Coupled System ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transient Responses

Abstract This paper presents an easy-to-use theoretical method and an efficient numerical method for solving free vibrations and transient responses of a circular plate coupled with fluid subjected to impact loadings and provides insights into various coupling cases with these developed methods. The Kirchhoff plate theory, Mindlin–Reissner plate theory, and the linear velocity potential function are used. The wet mode of the coupled system is described as the superposition of dry modes of the plate, which has been considered in few studies. The natural frequencies and corresponding mode shapes are solved using the orthogonality of dry modes. The transient responses of the plate are then solved using the superposition of the wet modes and the orthogonality of dry modes. To validate the theoretical results, an efficient and flexible finite element method is proposed and verified by comparing with commercial software. The four-node mixed interpolation of the tensorial component quadrilateral plate finite element (MITC4) and the eight-node acoustic pressure element are used to model the plate and the fluid, respectively. The theoretical and numerical methods provide reliable and accurate results. Parametric studies are performed to investigate the influence of geometric sizes, plate material properties, and fluid properties on the natural frequencies of the coupled system. A coupling parameter of fluid–structure interaction is proposed. The nondimensional added virtual mass incremental (NAVMI) factor decreases as the coupling parameter increases. Besides, the influence of fluid on wet modes of the plate decreases with the order.

Pedestrian Bridge Evaluation and Modelling Subjected to Running Load Cases

2022 ◽  
Author(s):  
Alejandro Bernabeu Larena ◽  
Javier Gómez Mateo ◽  
Francisco Burgos Ruiz ◽  
Ginés Garrido Colmenero
Keyword(s):  
Natural Frequencies ◽  
Coupled System ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Dynamic Measurements ◽  
Transient Event ◽  
Single Degree Of Freedom ◽  
Pedestrian Bridges ◽  
Bridge Evaluation ◽  
Modelling Strategies

<p>This paper presents the dynamic measurements performed at two pedestrian bridges in Sweden subjected to different loading scenarios. Using accelerometers, the natural frequencies, the experimental mode shapes, and damping properties were determined for each bridge. Analysis were performed using the generalized single degree of freedom theory, the finite element method and the coupled system approach taking into account the flying phase of the running load. Additionaly, a simplified sensitivity analysis is presented in terms of accelerations due to the pedestrian transient event of a running load case. Results indicate that there is an excellent agreement between the aforementioned modelling strategies and, that it is possible to have human structure interaction under running load scenarios.</p>

Assessment of Serviceability of the Footbridge Across Opatovska Street

2016 ◽  
Vol 827 ◽  
pp. 263-266
Author(s):  
Vladimír Sana
Keyword(s):  
Theoretical Analysis ◽  
Modal Analysis ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Fe Model ◽  
Matlab Code ◽  
Forced Vibration Analysis

This paper is focused on the assessment of serviceability of the footbridge structure, which has been excited by pedestrians and vandals. The three dimensional FE model of the footbridge structure was created for the necessities of theoretical modal analysis. Computed mode shapes and natural frequencies were subsequently used for the forced vibration analysis as an input files into MATLAB code. Results obtained by the theoretical analysis were compared with the experimental results. At the end of this paper, the comfort criterion of crossing pedestrians has been evaluated.

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