Effect of Vertical Elastic Baffle on Liquid Sloshing in Rectangular Rigid Container

2021 ◽  
pp. 2150167
Author(s):  
Xun Meng ◽  
Ding Zhou ◽  
Jiadong Wang
Keyword(s):  
Wave Equations ◽  
Velocity Potential ◽  
Separation Of Variables ◽  
Structural Instability ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
System Response ◽  
Coupled Mode ◽  
Response Equation ◽  
Liquid Oscillation

Sloshing may induce adverse loads to cause structural instability and damage. A vertical elastic baffle mounted at the inside bottom of a rectangular container is used as an anti-slosh device to attenuate the liquid oscillation. A semi-analytical model is presented to analyze the hydroelastic problem. The liquid is partitioned into four simple sub-domains with three hypothetical interfaces. The velocity potential of each sub-domain is analytically deduced by the separation of variables. The baffle deflection is expanded into the Fourier series by its dry modals. The eigenvalue equation is formulated by plugging the velocity potentials into the sloshing conditions, interface continuity conditions, as well as the dominant equation and compatibility conditions of the baffle. Then, the velocity potential is expressed by a complete basis of the coupled mode shapes for the system considered under lateral excitation. The system response equation is constituted by inserting the velocity potential into wave equations and baffle equation. The proposed method is verified by comparing the present results with the available data. In addition, numerical analyses are performed to examine the effects of baffle parameters on the natural frequencies, mode shapes and dynamic responses of the container. The sloshing frequency may be altered to a higher value due to the installation of the elastic baffle.

scholarly journals Vibration characteristics of triple-gear-rotor system in compressed air energy storage under variable torque load

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042098705
Author(s):  
Xinran Wang ◽  
Yangli Zhu ◽  
Wen Li ◽  
Dongxu Hu ◽  
Xuehui Zhang ◽  
...  
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Element Model ◽  
Rotor System ◽  
Dynamic Responses ◽  
System Response ◽  
Rotating Speed ◽  
Torque Load ◽  
Set Up ◽  
Two Stages

This paper focuses on the effects of the off-design operation of CAES on the dynamic characteristics of the triple-gear-rotor system. A finite element model of the system is set up with unbalanced excitations, torque load excitations, and backlash which lead to variations of tooth contact status. An experiment is carried out to verify the accuracy of the mathematical model. The results show that when the system is subjected to large-scale torque load lifting at a high rotating speed, it has two stages of relatively strong periodicity when the torque load is light, and of chaotic when the torque load is heavy, with the transition between the two states being relatively quick and violent. The analysis of the three-dimensional acceleration spectrum and the meshing force shows that the variation in the meshing state and the fluctuation of the meshing force is the basic reasons for the variation in the system response with the torque load. In addition, the three rotors in the triple-gear-rotor system studied show a strong similarity in the meshing states and meshing force fluctuations, which result in the similarity in the dynamic responses of the three rotors.

Dynamic Model and Simulation of Flag Vibrations Modeled as a Membrane

2014 ◽  
Author(s):  
Gary Frey ◽  
Ben Carmichael ◽  
Joshua Kavanaugh ◽  
S. Nima Mahmoodi
Keyword(s):  
Constant Velocity ◽  
Cross Flow ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Mode Shapes ◽  
System Response ◽  
Wind Flow ◽  
Pressure Function ◽  
Model And Simulation ◽  
Reasonable Model

A flag is modeled as a membrane to investigate the two-dimensional characteristics of the vibration response to an uniform wind flow. Both the affecting tension and pressure functions for the wind flow with constant velocity are introduced and utilized in the modeling. In this case, the tension is caused by the weight of the flag. The pressure function is a function describing the pressure variations caused on the flag when in uniform flow. The pressure function is found by assuming that the air flow is relatively slow and that the flag is wide enough to minimize cross flow at the boundaries. An analysis of the downstream motion of the flag is necessary as well. Hamilton’s principle is employed to derive the partial differential equation of motion. The flag is oriented in the vertical direction to neglect the effect of the flag’s weight on the system’s response. Galerkin’s method is used to solve for the first four mode shapes of the system, and the system response is numerically solved. Simulations reveal a very reasonable model when the flag is modeled as a membrane.

scholarly journals Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Nizar Faisal Alkayem ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Structural Damage ◽  
Model Updating ◽  
Complex Problem ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Strain Energy ◽  
3D Structures ◽  
Multiobjective Particle Swarm Optimization ◽  
Damage Tracking

Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

A Coupled-Mode Technique for the Run-Up of Non-Breaking Dispersive Waves on Plane Beaches

2006 ◽  
Author(s):  
K. A. Belibassakis ◽  
G. A. Athanassoulis
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Breaking Waves ◽  
Numerical Results ◽  
Coupled Mode Theory ◽  
Mode Theory ◽  
Coupled Mode ◽  
Run Up

A coupled-mode model is developed and applied to the transformation and run-up of dispersive water waves on plane beaches. The present work is based on the consistent coupled-mode theory for the propagation of water waves in variable bathymetry regions, developed by Athanassoulis & Belibassakis (1999) and extended to 3D by Belibassakis et al (2001), which is suitably modified to apply to a uniform plane beach. The key feature of the coupled-mode theory is a complete modal-type expansion of the wave potential, containing both propagating and evanescent modes, being able to consistently satisfy the Neumann boundary condition on the sloping bottom. Thus, the present approach extends previous works based on the modified mild-slope equation in conjunction with analytical solution of the linearised shallow water equations, see, e.g., Massel & Pelinovsky (2001). Numerical results concerning non-breaking waves on plane beaches are presented and compared with exact analytical solutions; see, e.g., Wehausen & Laitone (1960, Sec. 18). Also, numerical results are presented concerning the run-up of non-breaking solitary waves on plane beaches and compared with the ones obtained by the solution of the shallow-water wave equations, Synolakis (1987), Li & Raichlen (2002), and experimental data, Synolakis (1987).

scholarly journals Local fractional heat and wave equations with Laguerre type derivatives

2020 ◽  
Vol 24 (4) ◽  
pp. 2575-2580 ◽  
Author(s):  
Chun-Fu Wei
Keyword(s):  
Differential Equation ◽  
Bounded Domain ◽  
Wave Equations ◽  
Separation Of Variables ◽  
Fractional Pde

In this paper, we investigate a local fractional PDE with Laguerre type derivative. The considered equation represents a general extension of the classical heat and wave equations. The method of separation of variables is used to solve the differential equation defined in a bounded domain.

DAMAGE DETECTION OF RC SLABS USING NONLINEAR VIBRATION FEATURES

2009 ◽  
Vol 09 (04) ◽  
pp. 687-709 ◽  
Author(s):  
XINQUN ZHU ◽  
HONG HAO
Keyword(s):  
Reinforced Concrete ◽  
Nonlinear Vibration ◽  
Structural Damage ◽  
Concrete Structures ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Reinforced Concrete Structures ◽  
Vibration Frequencies ◽  
Skeleton Curve ◽  
Time Frequency

Studied herein are the signatures of nonlinear vibration characteristics of damaged reinforced concrete structures using the wavelet transform (WT). A two-span RC slab built in 2003 was tested to failure in the laboratory. Vibration measurements were carried out at various stages of structural damage. The vibration frequencies, mode shapes, and damping ratios at each loading stage were extracted and analyzed. It is found that the vibration frequencies are not sensitive to small damages, but are good indicators when damage is severe. The dynamic responses are also analyzed in the time–frequency domain by WT and the skeleton curve is constructed to describe the nonlinear characteristics in the reinforced concrete structures. The results show that the skeleton curves are good indicators of damage in the reinforced concrete structures because they are more sensitive to small damages than vibration frequencies.

Resonance Analysis of Cantilever Plates Subjected to Moving Forces by a Semi-Analytical Method

2020 ◽  
Vol 20 (04) ◽  
pp. 2050049
Author(s):  
Qi Li ◽  
Xing Li ◽  
Qi Wu
Keyword(s):  
Analytical Method ◽  
Ritz Method ◽  
High Order Mode ◽  
Dominant Frequency ◽  
High Order ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Superposition Method ◽  
Cantilever Plate ◽  
Exciting Frequency

Cantilever plate structures are widely used in civil and aerospace engineering. Here, a semi-analytical method is proposed to calculate the dynamic responses of cantilever plates subjected to moving forces. The Rayleigh–Ritz method is used to obtain the semi-analytical modal frequencies and shapes of a thin, isotropic, and rectangular cantilever plate using the assumed mode shapes that fulfill the boundary conditions of the plate. The modal superposition method is used to decouple the motion equations of the cantilever plate to obtain a series of modal equations. Then, the generalized forces are transformed into a Fourier series in terms of discrete harmonic forces. The dynamic responses of the cantilever plate are obtained by superimposing the analytical responses of a number of single-degree-of-freedom modal systems under discrete harmonic forces. The proposed semi-analytical method is verified through comparison with the numerical method. Then, the vibration of the cantilever plate under the action of moving forces is investigated based on the semi-analytical results. It is found that the contribution of the high-order modes to the dynamic responses of the plate cannot be ignored. In addition, the wavelengths of the mode shapes not only affect the magnitude of the modal forces but also the dominant frequency of the modal forces. Resonant responses of the plate are produced by the moving forces when the load interval equals the wavelength of the mode shape of a high-order mode and the exciting frequency of the moving forces equals the natural frequency of this mode.

Analysis of water wave interaction with a submerged quarter-circular breakwater using multipole method

2020 ◽  
Vol 234 (4) ◽  
pp. 846-860
Author(s):  
Ai-jun Li ◽  
Yong Liu ◽  
Zuo-rui Lyu
Keyword(s):  
Water Wave ◽  
Series Solution ◽  
Velocity Potential ◽  
Separation Of Variables ◽  
Wave Interaction ◽  
Wave Forces ◽  
Submerged Breakwater ◽  
Circular Arc ◽  
Internal Fluid ◽  
Multipole Expansion Method

This article studies water wave interaction with a submerged quarter-circular breakwater based on potential theory and multipole expansion method. The obliquely and normally incident waves are independently considered. The series solution of velocity potential in the external fluid domain is expressed through the multipole expansions, while the series solution of velocity potential in the quarter-circular internal fluid domain is obtained through the separation of variables. Then, the unknown coefficients in the series solutions are determined by matching the boundary conditions between external and internal fluid domains. The calculation methods for the reflection and transmission coefficients of the submerged quarter-circular breakwater as well as the horizontal and vertical wave forces on the breakwater are presented. The wave forces acting on the submerged breakwater with a seaside quarter-circular-arc and that with a leeside quarter-circular-arc are compared. The hydrodynamic quantities of the submerged quarter-circular breakwater are also compared with those of the submerged semi-circular breakwater. In addition, the effects of breakwater radius, incident frequency, and incident angle on the hydrodynamic quantities of the quarter-circular breakwater are clarified. Valuable results for practical engineering application are drawn.

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.

scholarly journals Surge motion on a floating cylinder in water of finite depth

2003 ◽  
Vol 2003 (57) ◽  
pp. 3643-3656 ◽  
Author(s):  
Dambaru D. Bhatta
Keyword(s):  
Velocity Potential ◽  
Separation Of Variables ◽  
Finite Depth ◽  
Added Mass ◽  
Computational Results ◽  
Complex Matrix ◽  
Interior Region ◽  
Exterior Region ◽  
Damping Coefficients ◽  
Calm Water

We derived added mass and damping coefficients of a vertical floating circular cylinder due to surge motion in calm water of finite depth. This is done by deriving the velocity potential for the cylinder by considering two regions, namely, interior region and exterior region. The velocity potentials for these two regions are obtained by the method of separation of variables. The continuity of the solutions has been maintained at the imaginary interface of these regions by matching the functions and gradients of each solution. The complex matrix equation is numerically solved to determine the unknown coefficients. Some computational results are presented for different depth-to-radius and draft-to-radius ratios.

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