scholarly journals An accurate frequency-domain model of water interaction with cylinders of arbitrary shape during earthquakes

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Mi Zhao ◽  
Xiaojing Wang ◽  
Piguang Wang ◽  
Chao Zhang ◽  
Xiuli Du
Keyword(s):  
Frequency Domain ◽  
Seismic Response ◽  
Stiffness Matrix ◽  
Continued Fraction ◽  
Numerical Solutions ◽  
Dynamic Stiffness ◽  
Arbitrary Cross Section ◽  
Domain Model ◽  
Weighted Residual Method ◽  
Dynamic Stiffness Matrix

AbstractAn accurate frequency domain model is proposed to analyze the seismic response of uniform vertical cylinders with arbitrary cross section surrounded by water. According to the boundary conditions and using the variables separation method, the vertical modes of the hydrodynamic pressure are firstly obtained. Secondly, the three-dimensional wave equation can be simplified to a two-dimensional Helmholtz equation. Introducing the scaled boundary coordinate, a scaled boundary finite element (SBFE) equation which is a linear non-homogeneous second-order ordinary equation is derived by weighted residual method. The dynamic-stiffness matrix equation for the problem is furtherly derived. The continued fraction is acted as the solution of the dynamic-stiffness matrix for cylinder dynamic interaction of cylinder with infinite water. The coefficient matrices of the continued fraction are derived recursively from the SBFE equation of dynamic-stiffness. The accuracy of the present method is verified by comparing the hydrodynamic force on circular, elliptical and rectangle cylinders with the analytical or numerical solutions. Finally, the proposed model is used to analyze the natural frequency and seismic response of cylinders.

A wavelet-based model of one-dimensional periodic structure for wave-propagation analysis

2009 ◽  
Vol 466 (2113) ◽  
pp. 263-281 ◽  
Author(s):  
Parikshit Sonekar ◽  
Mira Mitra
Keyword(s):  
Wave Propagation ◽  
Frequency Domain ◽  
Periodic Structure ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Fe Model ◽  
Loading Conditions ◽  
Dynamic Stiffness Matrix ◽  
One Dimensional ◽  
Propagation Analysis

In this paper, a wavelet-based method is developed for wave-propagation analysis of a generic multi-coupled one-dimensional periodic structure (PS). The formulation is based on the periodicity condition and uses the dynamic stiffness matrix of the periodic cell obtained from finite-element (FE) or other numerical methods. Here, unlike its conventional definition, the dynamic stiffness matrix is obtained in the wavelet domain through a Daubechies wavelet transform. The proposed numerical scheme enables both time- and frequency-domain analysis of PSs under arbitrary loading conditions. This is in contrast to the existing Fourier-transform-based analysis that is restricted to frequency-domain study. Here, the dispersion characteristics of PSs, especially the band-gap features, are studied. In addition, the method is implemented to simulate time-domain wave response under impulse loading conditions. The two examples considered are periodically simply supported beam and periodic frame structures. In all cases, the responses obtained using the present periodic formulation are compared with the response simulated using the FE model without the periodicity assumption, and they show an exact match. This validates the accuracy of the periodic assumption to obtain the time- and frequency-domain wave responses up to a high-frequency range. Apart from this, the proposed method drastically reduces the computational cost and can be implemented for homogenization of PSs.

Frequency domain-based analysis of floor vibrations using the dynamic stiffness matrix method

2018 ◽  
Vol 25 (4) ◽  
pp. 763-776 ◽  
Author(s):  
Tong Guo ◽  
Zhiliang Cao ◽  
Zhiqiang Zhang ◽  
Aiqun Li
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Stiffness Matrix ◽  
Road Traffic ◽  
Dynamic Stiffness ◽  
Design Stage ◽  
Element Analysis ◽  
Frequency Spectra ◽  
Dynamic Stiffness Matrix ◽  
Floor Vibrations

Buildings may experience excessive floor vibrations due to inner excitations such as walking people and running machines, or ground motion caused by the road traffic. Therefore, it is often necessary to evaluate the vibration level at the design stage. In this paper, a frequency domain-based model for predicting vertical vibrations of a building floor is provided, where the floor is simplified as a rectangular plate stiffened by beams in two orthogonal directions, while vertical motion and rotation of the slab–column joints are viewed as the unknown degrees of freedom. The dynamic stiffness matrix of the whole structure is obtained from those of the floor and column elements. To validate the proposed solution, a five-story building was analyzed, and frequency spectra were compared with those from the finite element method. Besides, a prototype building was analyzed and validated based on field measured data. It is found that the proposed solution could predict vibration responses with satisfactory accuracy, and is more computationally efficient than finite element analysis.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

Steady-State Unbalance Response of Continuous Rotors on Anisotropic Supports

1993 ◽  
Author(s):  
Graziano Curti ◽  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Steady State ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Analytical Investigation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Beam Elements ◽  
Unbalance Response ◽  
Constant Coefficients ◽  
Linearized Model

Abstract An analytical investigation of the steady-state unbalance response of axisymmetric rotor systems with anisotropic, flexible and damped bearings is presented. According to the exact approach of the dynamic stiffness method, the rotor is modelled by means of continuous beam elements. In this work, the expression of the 8 × 8 dynamic stiffness matrix of a rotating Timoshenko beam is derived and it is shown that it is related, by means of a simple law, to the previously published 4 × 4 dynamic stiffness matrix, which holds for the isotropic bearings case. The effects of concentrated disks and bearings are included into the formulation; in particular, each bearing is described by eight constant coefficients, according to the well-known linearized model of the bearing forces. The unbalance response of a typical rotor system taken from the literature is analyzed. A comparison is presented with the finite element results reported by other authors.

Vibration Modeling of Machine Tool Spindles: A Calibrated Dynamic Stiffness Matrix Method

2013 ◽  
Vol 651 ◽  
pp. 710-716 ◽  
Author(s):  
Omar Gaber ◽  
Seyed M. Hashemi
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Dynamic Stiffness Matrix ◽  
Spring Element ◽  
Linear Spring ◽  
Beam Bending ◽  
The Stability ◽  
Spinning Speed ◽  
Vibration Modeling

The effects of spindles vibrational behavior on the stability lobes and the Chatter behavior of machine tools have been established. The service life has been observed to reducethe system natural frequencies. An analytical model of a multi-segment spinning spindle, based on the Dynamic Stiffness Matrix (DSM) formulation, exact within the limits of the Euler-Bernoulli beam bending theory, is developed. The system exhibits coupled Bending-Bending (B-B) vibration and its natural frequencies are found to decrease with increasing spinning speed. The bearings were included in the model usingboth rigid, simply supported, frictionless pins and flexible linear spring elements. The linear spring element stiffness is then calibrated so that the fundamental frequency of the system matches the nominal value.

scholarly journals Seismic Analysis of the Transportation Portal by the Combined Asymptotic Method

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
Alexander Tyapin
Keyword(s):  
Asymptotic Method ◽  
Stiffness Matrix ◽  
Transfer Functions ◽  
Seismic Analysis ◽  
Dynamic Stiffness ◽  
Free Field ◽  
Structural Dynamic ◽  
Dynamic Stiffness Matrix ◽  
Double Support ◽  
Soil Dynamic

The author extends the previously proposed combined asymptotic method (CAM) of seismic SSI analysis for the multi-support systems and applies it to the transportation portal as a double-support system (together with the reactor building). The key issue is the development of the structural dynamic stiffness matrix condensed to the supports by the modal approach. Then the condensed structural matrix is combined with the soil dynamic stiffness matrix also condensed to the rigid basements. As a result, a very simple linear system is solved in the frequency domain. This gives the transfer functions from the free-field motion to the motion of the basements. The only important limitations are the linearity of the soil’s and structure’s properties and the rigidity of the basements. The results for the sample system are checked against the full SASSI solution. The results can be used to justify the further simplification of the system.

Updating of Dynamic Finite Element Models Based on Experimental Receptances and the Reduced Analytical Dynamic Stiffness Matrix

1995 ◽  
Author(s):  
Stefan Lammens ◽  
Marc Brughmans ◽  
Jan Leuridan ◽  
Ward Heylen ◽  
Paul Sas
Keyword(s):  
Stiffness Matrix ◽  
Model Updating ◽  
Dynamic Stiffness ◽  
Computational Cost ◽  
Computational Effort ◽  
Reduction Scheme ◽  
Dynamic Stiffness Matrix ◽  
Simple Strategy ◽  
A Minor ◽  
Analytical Dynamic

Abstract This paper presents a model updating method based on experimental receptances. The presented method minimises the so called ‘indirect receptance difference’. First, the reduced analytical dynamic stiffness matrix is expressed as an approximate, linearised function of the updating parameters. In a numerically stable, iterative procedure, this reduced analytical dynamic stiffness matrix is changed in such a way that the analytical receptances match the experimental receptances at the updating frequencies. The updating frequencies are a set of selected frequency points in the frequency range of interest. Some considerations about an optimal selection of the updating frequencies are given. Finally, a mixed static-dynamic reduction scheme is discussed. Dynamic reduction of the analytical dynamic stiffness matrix at each updating frequency is physically exact, but it involves a great computational effort. The presented mixed static-dynamic reduction scheme is a simple strategy to reduce the computational cost with a minor loss of accuracy.

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