Parameter identification of new bidirectional tuned liquid column and sloshing dampers

A tuned liquid column and sloshing damper (TLCSD) is introduced in this study. It shows dynamic behavior of both tuned liquid column damper (TLCD) and tuned liquid damper (TLD) in the direction of two axes perpendicular with each other. As a preliminary study for applying the TLCSD to bidirectional control of building structures, one of objectives of this study is to derive analytical dynamics to investigate coupled effects due to TLCD and TLD. Another objective is to investigate the effect of coupled control force due to TLCD and TLD on the dynamic characteristic of the TLCSD based on analytical dynamics. Shaking table test is undertaken to experimentally grasp dynamic characteristics of TLCSD under white noise excitation with various amplitude levels. Its dynamic characteristics are expressed by the transfer function from the shaking table acceleration to the control force generated from a TLCSD. The analytical dynamics of TLCSD is derived from the equivalent linearized TMD model. The coupled dynamics of TLCSD is expressed in terms of those of both TLCD and TLD. Finally, the key parameters of both TLCD and TLD are identified based on the coupled dynamics proposed in this study, which include the mass ratio of horizontal liquid column to total liquid for a TLCD, and the participation factor of the fundamental liquid sloshing for a TLD and damping ratio for both cases.     

Thermally induced vibrations of viscoelastic shallow shells

A method for the study of thermally induced vibrations of viscoelastic shallow shells of arbitrary shaped plane-form is proposed. It is shown that the time behaviour can be found by assuming a normal mode expansion in tems of the eigenfunctions of the associated elastic shallow shell problem and the deflection is obtained with the aid of the correspondence principle. The response of a shallow shell with rectangular as well as elliptical base to the sudden application of a temperature distribution on the surface of the shell is discussed. For rapidly applied heat inputs, an approximate analysis for its rapid estimation is also presented. All details are illustrated by graphs.     

A large time step 1D upwind explicit scheme (CFL > 1): Application to shallow water equations

It is possible to relax the Courant–Friedrichs–Lewy condition over the time step when using explicit schemes. This method, proposed by Leveque, provides accurate and correct solutions of non-sonic shocks. Rarefactions need some adjustments which are explored in the present work with scalar equation and systems of equations. The non-conservative terms that appear in systems of conservation laws introduce an extra difficulty in practical application. The way to deal with source terms is incorporated into the proposed procedure. The boundary treatment is analysed and a reflection wave technique is considered. In presence of strong discontinuities or important source terms, a strategy is proposed to control the stability of the method allowing the largest time step possible. The performance of the above scheme is evaluated to solve the homogeneous shallow water equations and the shallow water equations with source terms.     

Long wave run-up on random beaches

The estimation of the maximum wave run-up height is a problem of practical importance. Most of the analytical and numerical studies are limited to a constant slope plain shore and to the classical nonlinear shallow water equations. However, in nature the shore is characterized by some roughness. In order to take into account the effects of the bottom rugosity, various ad hoc friction terms are usually used. In this Letter, we study the effect of the roughness of the bottom on the maximum run-up height. A stochastic model is proposed to describe the bottom irregularity, and its effect is quantified by using Monte Carlo simulations. For the discretization of the nonlinear shallow water equations, we employ modern finite volume schemes. Moreover, the results of the random bottom model are compared with the more conventional approaches.     

Covolume-upwind finite volume approximations for linear elliptic partial differential equations

In this paper, we study covolume-upwind finite volume methods on rectangular meshes for solving linear elliptic partial differential equations with mixed boundary conditions. To avoid non-physical numerical oscillations for convection-dominated problems, nonstandard control volumes (covolumes) are generated based on local Peclet’s numbers and the upwind principle for finite volume approximations. Two types of discretization schemes with mass lumping are developed with use of bilinear or biquadratic basis functions as the trial space respectively. Some stability analyses of the schemes are presented for the model problem with constant coefficients. Various examples are also carried out to numerically demonstrate stability and optimal convergence of the proposed methods.     

Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry

In this paper we present the exact solution of the Riemann problem for the non-linear shallow water equations with a step-like bottom. The solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step. The resulting solution is unique and satisfies the principle of dissipation of energy across the shock wave. We provide examples of possible wave patterns. Numerical solution of a first-order dissipative scheme as well as an implementation of our Riemann solver in the second-order upwind method are compared with the proposed exact Riemann problem solution. A practical implementation of the proposed exact Riemann solver in the framework of a second-order upwind TVD method is also illustrated.     

A modal method for finite amplitude, nonlinear sloshing

A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefficients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difficult to obtain otherwise. For example, it is found that for the initial interface profile considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.     

Acoustic wave scattering from a composed shell reinforced by a single rib: characteristics of peripheral waves

The steady-state axisymmetrical problem of a plane acoustic wave scattering from a composed shell is considered. The shell has a cylindrical part and two hemispherical endcaps. The rib is a ring of rectangular cross-section that divides the shell into two equal parts. The motion of the shell and the rib is described by the equations of elasticity theory, and the liquid is described by the Helmholtz equation. The solution is obtained numerically by a coupled finite element/boundary element model. Two peripheral waves are generated in the shell: the membrane S0 wave and the bending type water-borne A wave. The form function, acoustic spectrogram and dispersion curves of the phase velocities are presented, and the effect of the rib on the peripheral waves is discussed.     

Non-linear vibrations of a flat plate with initial stresses

Non-linear free vibrations of a simply supported rectangular elastic plate are examined, by using stress equations of free flexural motions of plates with moderately large amplitudes derived by Herrmann. A modal expansion is used for the normal displacement that satisfies the boundary conditions exactly, but the in-plane displacements are satisfied approximately by an averaging technique. Galerkin technique is used to reduce the problem to a system of coupled non-linear ordinary differential equations for the modal amplitudes. These nonlinear differential equations are solved for arbitrary initial conditions by using the multiple-time-scaling technique. Explicit values of the coefficients that appear in the forementioned Galerkin system of equations are given, in terms of non-dimensional parameters characterizing the plate geometry and material properties, for a four-mode case, for which results for specific initial conditions are presented. A comparison of the results with those obtained in previous studies of the problem is presented. In addition, effects of prescribed edge loadings are examined for the four-mode case.     

Variations on the slotted-tube resonator: rectangular and elliptical coils.

Two designs (one rectangular, one elliptical) are proposed as efficient alternatives to noncylindrical birdcage RF coils. These designs are based on the slotted-tube resonator and their performance relies on the natural current distribution in the conductors due to the eddy current effects at high frequencies. A Finite element method program, solving the full set of Maxwell's equations, has been employed to accurately characterize and optimize the field homogeneity of the proposed noncylindrical coils. The optimum configuration of each design is presented, taking into account the effect of the RF shield. The proposed designs are compared to several configurations presented in the literature. Two coils (one rectangular, one elliptical) have been constructed and tested in a 0.6 T imaging system. A rectangular coil has been built to operate at 300 MHz. MR images substantiate the usefulness of these coils.     

Wave numbers of partially filled rectangular waveguide

An approximate method is proposed for determination of the wave numbers of a partially filled rec angular waveguide. The method employs the eigenvalues and parameters of Mathieu equations. The natural H-and E-waves of a partially filled rectangular waveguide are expressed in terms of Mathieu functions. Numerical results of waven number studies are presented and interpreted graphically.     

Free vibration analysis of ribbed plates by a combined analytical–numerical method

An easy to code and computationally efficient analytical–numerical method for quick prediction of the modal characteristics of rectangular ribbed plates is presented. The approach is suitable for low-frequency free vibration analysis of thin rectangular plates reinforced by a small number of light stiffeners. The assumed-modes method is used to formulate the equations of motion of the plate and the rib separately. The motion of the built-up structure is then obtained by enforcing appropriate continuity conditions between the two. The resulting sparse generalized eigenvalue problem can be profitably solved by reliable methods to calculate only a small set of selected eigenmodes. An alternative formulation is also proposed for the single-ribbed case which leads to a compact analytical form of the frequency equation whose solution can be easily determined either graphically or numerically. The present method demonstrates good agreement with published results and standard finite element analysis.     

Equations of equilibrium for a strongly heterogeneous shallow shell

A linear set of equations is proposed for a strongly thickness-heterogeneous (in particular, multilayer) shallow shell. The model unifies the equations of the Mushtary?Donnell?Vlasov technical-theory and the Timoshenko?Reissner equations, which take into account transverse shear. The thickness-heterogeneous shell is replaced with an equivalent homogeneous transversally isotropic shell, the elasticity modula of which are chosen just as the previously determined elasticity modula for heterogeneous plates. In the test example for a multilayered cylindrical shell, the approximate solution according to the proposed model is compared with the exact solution of the three-dimensional problem. The model gives good results in accuracy for a reasonably wide level of inhomogeneity.     

A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid

A novel accurate numerical model for shallow water equations on sphere have been developed by implementing the high order multi-moment constrained finite volume (MCV) method on the icosahedral geodesic grid. High order reconstructions are conducted cell-wisely by making use of the point values as the unknowns distributed within each triangular cell element. The time evolution equations to update the unknowns are derived from a set of constrained conditions for two types of moments, i.e. the point values on the cell boundary edges and the cell-integrated average. The numerical conservation is rigorously guaranteed. In the present model, all unknowns or computational variables are point values and no numerical quadrature is involved, which particularly benefits the computational accuracy and efficiency in handling the spherical geometry, such as coordinate transformation and curved surface.Numerical formulations of third and fourth order accuracy are presented in detail. The proposed numerical model has been validated by widely used benchmark tests and competitive results are obtained. The present numerical framework provides a promising and practical base for further development of atmospheric and oceanic general circulation models.     

Field reconstruction in an anisotropic elastic medium

For steady-state vibrations of an anisotropic elastic body of finite dimensions, a method of the determination of the vibration energy flows in the body is proposed. The method is based on the measurements of the surface values of the stress and displacement vectors at a part of the boundary. The proposed algorithm of the wave field reconstruction is reduced to solving nonclassical boundary integral equations of the first kind with smooth kernels. The formulation of these equations does not require the determination of fundamental solutions, but represents a conditionally well-posed problem. The numerical realization of the proposed method is based on the Tikhonov regularization method and the idea of the boundary element method. Numerical experiments consisting in the reconstruction of the displacements and stresses at the boundary of a rectangular and a circular domains of austenitic steel are performed in the framework of a planar problem of the orthothropic elasticity theory.     

Initial value problem solution of nonlinear shallow water-wave equations

The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.     

Analysis and computation of the vibration spectrum of the shallow circular cylindrical shell with rectangular domain

An asymptotic method of Bolotin, for the computation of eigenvalues of self-adjoint problems on rectangular domains, is extended to the shallow shell equations for the vibrating circular cylindrical shell. These same eigenfrequencies are then computed using the Legendre-tau spectral method. The asymptotic and numerical results are seen to be in good agreement and, as expected, approach those of the flat plate as the curvature tends to zero.     

Stabilization of an axially moving web via regulation of axial velocity

In this paper, a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented. The principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly. The optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations (ODEs). For control design purposes, these ODEs are rewritten into state-space equations. The vibration energy of the axially moving beam is represented by the quadratic form of the state variables. In the optimal control problem, the cost function modified from the vibration energy function is subjected to the constraints on the state variables, and the axial transport velocity is considered as a control input. Numerical simulations are performed to confirm the effectiveness of the proposed control algorithm.     

Transient sloshing in half-full horizontal elliptical tanks under lateral excitation

A semi-analytical mathematical model is developed to study the transient liquid sloshing characteristics in half-full horizontal cylindrical containers of elliptical cross section subjected to arbitrary lateral external acceleration. The problem solution is achieved by employing the linear potential theory in conjunction with conformal mapping, resulting in linear systems of ordinary differential equations which are truncated and then solved numerically by implementing Laplace transform technique followed by Durbin's numerical inversion scheme. A ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of tank aspect ratio, excitation input time, and baffle configuration on the resultant sloshing characteristics are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained.