Analysis of Vibration of a Tank Caused by an Explosion

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
M. Utsumi ◽  
H. Tazuke
Keyword(s):  
Fluid Motion ◽  
Three Dimensional ◽  
Longitudinal Axis ◽  
Reduced Order Model ◽  
Fe Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Large Tank ◽  
The Galerkin Method

The vibration of a large tank caused by an explosion that occurs at a place apart from the tank is analyzed. Because the tank is double-walled and the liquid is contained in the inner shell, the vibration of the outer shell subjected to the explosion-induced pressure wave that travels outside the tank is analyzed without considering the liquid. A cylindrical tank with a spherical roof is considered as a realistic three-dimensional (3D) model, and a computationally efficient semi-analytical method that is applicable to the 3D geometry of the tank–fluid interface is investigated. First, cylindrical coordinates are introduced such that the longitudinal axis intersects the center of the tank base and is normal to the explosion source plane, thereby defining the inner and outer radii of the analysis domain of the fluid motion. Next, the solutions are expressed in terms of coordinate-dependent eigenvalues and a reduced order model is developed by applying the Galerkin method to the governing equations that take into account the compressibility and nonlinearity of the fluid motion. The method is verified by comparing with earlier results obtained by a numerical method. We also analyze the vibration of the tank shell by developing its finite element (FE) model and transforming the model into modal equations to develop a reduced order model for the fluid–tank system.

A Reduced Order Model of Unsteady Flows in Turbomachinery

1994 ◽  
Author(s):  
Kenneth C. Hall ◽  
Răzvan Florea ◽  
Paul J. Lanzkron
Keyword(s):  
Fluid Motion ◽  
Unsteady Flows ◽  
Reduced Order Model ◽  
Lanczos Algorithm ◽  
Order Model ◽  
Reduced Order ◽  
Unsteady Aerodynamic ◽  
Natural Modes ◽  
Wide Range ◽  
Modes Of Vibration

A novel technique for computing unsteady flows about turbomachinery cascades is presented. Starting with a frequency domain CFD description of unsteady aerodynamic flows, we form a large, sparse, generalized, non-Hermitian eigenvalue problem which describes the natural modes and frequencies of fluid motion about the cascade. We compute the dominant left and right eigenmodes and corresponding eigenfrequencies using a Lanczos algorithm. Then, using just a few of the resulting eigenmodes, we construct a reduced order model of the unsteady flow field. With this model, one can rapidly and accurately predict the unsteady aerodynamic loads acting on the cascade over a wide range of reduced frequencies and arbitrary modes of vibration. Moreover, the eigenmode information provides insights into the physics of unsteady flows. Finally we note that the form of the reduced order model is well suited for use in active control of aeroelastic and aeroacoustic phenomena.

Decentralized Control of a Tower Crane

1999 ◽  
Author(s):  
Kiyoshi Takagi ◽  
Hidekazu Nishimura
Keyword(s):  
Decentralized Control ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Flexible Structure ◽  
Order Model ◽  
Modeling And Control ◽  
Reduced Order ◽  
Tower Crane ◽  
Three Dimensional Models ◽  
And Control

Abstract This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes the sway of the load rope and the vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. This paper makes its three-dimensional models for simulation and reduced-order-model in order to design the decentralized control system. Then, we design the decentralized H∞ compensator and verify the efficiency by simulations and experiments.

Design of a Kangaroo Inspired Hopping Robot for Unrestricted Locomotion and Controller Development

2019 ◽  
Author(s):  
Austin Curtis ◽  
James Mynderse ◽  
Hamid Vejdani
Keyword(s):  
Frequency Response ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Design Parameters ◽  
Order Model ◽  
Reduced Order ◽  
Gait Performance ◽  
System Parameters ◽  
Hopping Robot ◽  
The Relationship

Abstract Inspired by the agility and maneuverability of running kangaroos, a prototype robot was developed using a reduced order model to constrain the system. Both passive and active models were used to understand the relationship between system parameters and gait performance. A frequency response experiment was performed on the prototype to quantify the relationship between design parameters and system responses. Additionally, preliminary tail controllers were tested. Based on the results of the initial platform, a new robot was designed and built as a platform for the study of three dimensional hopping.

A Nonlinear Reduced-Order Model of the Corpus Callosum Under Planar Coronal Excitation

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Alireza Mojahed ◽  
Javid Abderezaei ◽  
Mehmet Kurt ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Corpus Callosum ◽  
Human Brain ◽  
Strain Localization ◽  
High Frequency ◽  
Reduced Order Model ◽  
Fe Model ◽  
Order Model ◽  
Reduced Order ◽  
Biomechanical Behavior ◽  
The Brain

Abstract Traumatic brain injury (TBI) is often associated with microstructural tissue damage in the brain, which results from its complex biomechanical behavior. Recent studies have shown that the deep white matter (WM) region of the human brain is susceptible to being damaged due to strain localization in that region. Motivated by these studies, in this paper, we propose a geometrically nonlinear dynamical reduced order model (ROM) to model and study the dynamics of the deep WM region of the human brain under coronal excitation. In this model, the brain hemispheres were modeled as lumped masses connected via viscoelastic links, resembling the geometry of the corpus callosum (CC). Employing system identification techniques, we determined the unknown parameters of the ROM, and ensured the accuracy of the ROM by comparing its response against the response of an advanced finite element (FE) model. Next, utilizing modal analysis techniques, we determined the energy distribution among the governing modes of vibration of the ROM and concluded that the demonstrated nonlinear behavior of the FE model might be predominantly due to the special geometry of the brain deep WM region. Furthermore, we observed that, for sufficiently high input energies, high frequency harmonics at approximately 45 Hz, were generated in the response of the CC, which, in turn, are associated with high-frequency oscillations of the CC. Such harmonics might potentially lead to strain localization in the CC. This work is a step toward understanding the brain dynamics during traumatic injury.

A Method for Reducing the Order of Nonlinear Dynamic Systems

1984 ◽  
Vol 51 (2) ◽  
pp. 391-398 ◽  
Author(s):  
S. F. Masri ◽  
R. K. Miller ◽  
H. Sassi ◽  
T. K. Caughey
Keyword(s):  
Dynamic Systems ◽  
Three Dimensional ◽  
Element Model ◽  
Random Excitation ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Dimensional Finite Element ◽  
Restoring Forces ◽  
Three Dimensional Finite Element

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

scholarly journals An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

2014 ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Galerkin Method ◽  
Electrostatic Force ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Complicated Form ◽  
The Galerkin Method ◽  
Expanded Form

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

scholarly journals A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

2019 ◽  
Vol 9 (22) ◽  
pp. 4762
Author(s):  
Wang ◽  
Bi ◽  
Zheng
Keyword(s):  
Vibration Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Normal Modes ◽  
Order Reduction ◽  
Symmetry Analysis ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Reduced Order

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

scholarly journals Sampling-free parametric model reduction of systems with structured parameter variation

2018 ◽  
Author(s):  
Christopher Beattie ◽  
Serkan Gugercin ◽  
Zoran Tomljanović
Keyword(s):  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Mass Matrix ◽  
Reduction Process ◽  
Parametric Model ◽  
Reduced Order Model ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order

We consider a parametric linear time invariant dynamical systems represented in state-space form as $$E \dot x(t) = A(p) x(t) + Bu(t), \\ y(t) = Cx(t),$$ where $E, A(p) \in \mathbb{R}^{n\times n}$, $B\in \mathbb{R}^{n\times m} $ and $C\in \mathbb{R}^{l\times n}$. Here $x(t)\in \mathbb{R}^{n} $ denotes the state variable, while $u(t)\in \mathbb{R}^{m}$ and $y(t)\in \mathbb{R}^{l}$ represent, respectively, the inputs and outputs of the system. We assume that $A(p)$ depends on $k\ll n$ parameters $p=(p_1, p_2, \ldots, p_k)$ such that we may write $$A(p)=A_0+U\,\diag (p_1, p_2, \ldots, p_k)V^T,$$ where $U, V \in \mathbb{R}^{n\times k}$ are given fixed matrices.We propose an approach for approximating the full-order transfer function $H(s;p)=C(s E -A(p))^{-1}B$ with a reduced-order model that retains the structure of parametric dependence and (typically) offers uniformly high fidelity across the full parameter range. Remarkably, the proposed reduction process removes the need for parameter sampling and thus does not depend on identifying particular parameter values of interest. Our approach is based on the classic Sherman-Morrison-Woodbury formula and allows us to construct a parameterized reduced order model from transfer functions of four subsystems that do not depend on parameters, allowing one to apply well-established model reduction techniques for non-parametric systems. The overall process is well suited for computationally efficient parameter optimization and the study of important system properties. One of the main applications of our approach is for damping optimization: we consider a vibrational system described by $$ \begin{equation}\label{MDK} \begin{array}{rl} M\ddot q(t)+(C_{int} + C_{ext})\dot q(t)+Kq(t)&=E w(t),\\ z(t)&=Hq(t), \end{array} \end{equation} $$ where the mass matrix, $M$, and stiffness matrix, $K$, are real, symmetric positive-definite matrices of order $n$. Here, $q(t)$ is a vector of displacements and rotations, while $ w(t) $ and $z(t) $ represent, respectively, the inputs (typically viewed as potentially disruptive) and outputs of the system. Damping in the structure is modeled as viscous damping determined by $C_{int} + C_{ext}$ where $C_{int}$ and $C_{ext}$ represent contributions from internal and external damping, respectively. Information regarding damper geometry and positioning as well as the corresponding damping viscosities are encoded in $C_{ext}= U\diag{(p_1, p_2, \ldots, p_k)} U^T$ where $U \in \mathbb{R}^{n\times k}$ determines the placement and geometry of the external dampers. The main problem is to determine the best damping matrix that is able to minimize influence of the disturbances, $w$, on the output of the system $z$. We use a minimization criteria based on the $\mathcal{H}_2$ system norm. In realistic settings, damping optimization is a very demanding problem. We find that the parametric model reduction approach described here offers a new tool with significant advantages for the efficient optimization of damping in such problems.

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