Simplified approach to the vibration analysis of elastic plates due to sonic boom

A theoretical study of the response of a flat plate to a sonic boom excitation is presented. For such a study, the problem of transient vibrations of elastic plates having clamped or simply supported boundary conditions under a pulse load in the shape of a capital N corresponding to a typical far-field sonic boom disturbance is discussed in a new fashion by using the concept of iso-amplitude contour lines on the surface of the plate. Series solutions consisting of products of eigenfunctions times functions of time are employed to analyse the motions. As an illustration of the technique, an elliptical plate subjected to a typical N wave arriving at normal incidence is chosen as a model because this involves a curvilinear boundary of a relatively simple shape, yet has no simple exact solution. Closed form solutions are obtained for both clamped as well as simply supported edges. The results have technical importance for the prediction of response of window panes and wall-panels to sonic boom. All details are explained by graphs.     

Extension of the spectral volume method to high-order boundary representation

In this paper, the spectral volume method is extended to the two-dimensional Euler equations with curved boundaries. It is well-known that high-order methods can achieve higher accuracy on coarser meshes than low-order methods. In order to realize the advantage of the high-order spectral volume method over the low order finite volume method, it is critical that solid wall boundaries be represented with high-order polynomials compatible with the order of the interpolation for the state variables. Otherwise, numerical errors generated by the low-order boundary representation may overwhelm any potential accuracy gains offered by high-order methods. Therefore, more general types of spectral volumes (or elements) with curved edges are used near solid walls to approximate the boundaries with high fidelity. The importance of this high-order boundary representation is demonstrated with several well-know inviscid flow test cases, and through comparisons with a second-order finite volume method.     

Structural response of cylindrically curved laminated composite shells subjected to blast loading

This paper is concerned with the theoretical analysis and correlation with the numerical results of the displacement time histories of the cylindrically curved laminated composite shells exposed to normal blast shock waves. The laminated composite shell is clamped at its all edges. The dynamic equation of the cylindrical shell used in this study is valid under the assumptions made in Love's theory of thin elastic shells. The constitutive equations of laminated composite shells are given in the frame of effective modulus theory. The governing equation of the cylindrical shell is solved by the Runge-Kutta method. In addition, a finite element modeling and analysis are presented and compared with the theoretical results. The peak deflections and response frequencies obtained from theoretical and numerical analyses are in agreement. The effects of material properties and geometrical properties are examined on the dynamic behaviour.     

STRUCTURAL RESPONSE OF LAMINATED COMPOSITE SHELLS SUBJECTED TO BLAST LOADING: COMPARISON OF EXPERIMENTAL AND THEORETICAL METHODS

The results from a theoretical and experimental investigation of the dynamic response of cylindrically curved laminated composite shells subjected to normal blast loading are presented. The dynamic equations of motion for cylindrical laminated shells are derived using the assumptions of Love's theory of thin elastic shells. Kinematically admissible displacement functions are chosen to represent the motion of the clamped cylindrical shell and the governing equations are obtained in the time domain using the Galerkin method. The time-dependent equations of the cylindrically curved laminated shell are then solved by the Runge-Kutta-Verner method. Finite element modelling and analysis for the blast-loaded cylindrical shell are also presented. Experimental results for cylindrically curved laminated composite shells with clamped edges and subjected to blast loading are presented. The blast pressure and strain measurements are performed on the shell panels. The strain response frequencies of the clamped cylindrical shells subjected to blast load are obtained using the fast Fourier transformation technique. In addition, the effects of material properties on the dynamic behaviour are examined. The strain-time history curves show agreement between the experimental and analysis results in the longitudinal direction of the cylindrical panels. However, there is a discrepancy between the experimental and analysis results in the circumferential direction of the cylindrical panels. A good prediction is obtained for the response frequency of the cylindrical shell panels.     

二维图象中二阶导数滤波器边缘定位误差的理论分析

本文从理论上讨论了低通滤波后二维图象中弯曲边缘的定位误差问题.边缘位置通常由二阶导数算子的零交叉点定义.研究表明:梯度方向上的二阶导数算子(secondderivativein gradient direction SDGD)产生向心的、可预测的边缘偏移;而线性拉普拉斯算子(Laplacian Operator)产生相反方向(离心)的可预测位置偏移.由此可推断:两者之和——称之为PLUS,将产生比其组成成份(SDGD 和 Laplace)更为精确的边缘定位算子.文章讨论了常用的低通滤波器(如 Gaussian 滤波器及 Tepee 滤波器)对边缘定位精度的影响.     

Equivalent source analysis of curved edge tapered slot-line antennas

An equivalent source model for the analysis of curved edge tapered slot-line antenna is developed, which employs effective filamentary currents along the conductor edges of the slot, but forces the electric field produced by the currents to satisfy the boundary condition on the whole conductor surface. This idea is implemented by method of moments with collocation technique, and applied to analyze a tapered slot-line antenna with arbitrarily curved edge.     

Nonlinear vibration of a curved beam under uniform base harmonic excitation with quadratic and cubic nonlinearities

This paper presents nonlinear vibration analysis of a curved beam subject to uniform base harmonic excitation with both quadratic and cubic nonlinearities. The Galerkin method is employed to discretize the governing equations. A high-dimensional model that can take nonlinear model coupling into account is derived, and the incremental harmonic balance (IHB) method is employed to obtain the steady-state response of the curved beam. The cases investigated include softening stiffness, hardening stiffness and modal energy transfer. The stability of the periodic solutions for given parameters is determined by the multi-variable Floquet theory using Hsu's method. Particular attention is paid to the anti-symmetric response with and without excitation, as the excitation frequency is close to the first and third natural frequencies of the system. The results obtained with the IHB method compare very well with those obtained via numerical integration.     

Flutter analysis of periodically supported curved panels

This paper presents the one-dimensional axial wave propagation in an infinitely long periodically supported cylindrically curved panel subjected to supersonic airflow. The aerodynamic forces are based on piston theory. For this study the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element. A high precision triangular finite element with certain wave boundary conditions (Floquet's principle) is introduced in flutter problems of the proposed structure for the first time. The airflow is assumed in the direction of the straight edges of the panel. It is assumed that the deflection function accounts for a phase lag term only and does not consider any attenuation terms. Aerodynamic damping has been neglected for brevity. For a given geometry a three-dimensional plot related to the phase constant, flutter frequency and pressure parameter has been obtained corresponding to the optimum periodic angle. The “flutter line”(line of instability) has been identified. The limiting values of flutter frequencies and pressure parameters of the “flutter line” are compared with the critical flutter condition of a single curved panel, using two methods—an exact approach and a finite element method. The critical flutter results for multi-supported (1-span, 2-span and 3-span) curved panels are obtained using the band discretization principle.     

FREE VIBRATION ANALYSIS OF ARBITRARILY SHAPED PLATES WITH A MIXED BOUNDARY CONDITION USING NON-DIMENSIONAL DYNAMIC INFLUENCE FUNCTIONS

A new approach using the non-dimensional dynamic influence functions has been developed for free vibration analysis of arbitrarily shaped plates with a mixed boundary condition involving both simply supported edges and clamped ones. Since the proposed method is based on the collocation method using one-dimensional and wave-type functions, no integration procedure is needed on boundary edges of the plate of interest and numerical calculation schemes are relatively concise. In order to settle the incompleteness of the system matrix, which is due to the discarding of a complex natural boundary condition at simply supported edges, an additional simple equation is devised by means of using a geometric approximation on curved edges. Finally, verification examples show that a complete system matrix formed in this way successfully gives accurate eigenvalues compared with FEM (ANSYS) and other methods.     

A semi-analytic solution for free vibration of annular sector plates

The paper describes a semi-analytical method in which the basic function in the circumferential direction satisfying the boundary conditions of the radial edges is substituted into the free vibration equation of the curved plate. By a suitable transformation, an ordinary differential equation is obtained. The resulting equation is solved by a finite difference technique. Tabulated results have been presented for annular sector plates possessing different boundary conditions. Excellent accuracy has been obtained wherever comparisons have been possible.     

Experiments on large-amplitude vibrations of a circular cylindrical panel

The vibration response of a thin circular cylindrical panel to harmonic excitation in the neighborhood of the first three natural frequencies has been measured for different force levels. The experimental boundary conditions approximate (i) on the curved edges: zero radial, axial and circumferential displacements; all rotations were allowed; (ii) on the straight edges: zero radial and axial displacements; all rotations and circumferential displacements were allowed. The different levels of excitation permitted reconstruction of the relatively strong, softening type non-linearity of the panel.     

基于目标三角面元模型生成FDTD共形网格的方法

 提出了一种基于目标三角面元数据的FDTD共形网格生成方法，该方法通过投影求交计算得到目标表面各三角面元与网格线的交点，将每条网格线与三角面元的交点按坐标进行排序，根据交点的坐标及其编号的奇偶性确定FDTD共形网格的位置，并生成相应的共形FDTD计算所需的元段长度。结合处理理想导体曲面的CFDTD方法修正共形网格上的磁场递推式。数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性。     

Passive vibration control of a satellite boom structure by geometric optimization using genetic algorithm

In this paper, the superior mid-frequency vibration isolation of a geometrically optimized lightweight structure is demonstrated. The initial structure under test here was a 4.5 m long satellite boom consisting of 10 identical bays with equilateral triangular cross-sections. An unusual geometric variant of this, with inherent isolation characteristics, has been designed by the use of genetic algorithm (GA) methods. In order to obtain the best design, the joints in the boom were allowed to move around by 20% of the length of each bay (i.e., ±9 cm in all three translational directions). This work is based on results from a Fortran code (which was derived from receptance analysis) that are fully validated against detailed finite element (FE) models of the structure. The experimental forced response of the regular boom structure has been measured and compared with predicted curves. Finally, having obtained the geometrically optimized boom structure, its experimental response is compared with the theoretical results predicted by the receptance method. It is shown that the average of 30 dB isolation in the vibration energy transfer between the ends of the network of beams, over a 100 Hz bandwidth predicted in the design process, is achieved experimentally in an essentially undamped structure.     

Free vibration analysis of doubly curved shallow shells using the Superposition-Galerkin method

This paper demonstrates the applicability of the Superposition Method for free vibration analysis of doubly curved thin shallow shells of rectangular planform with any possible combination of simply supported and clamped edges. The same building block yields the natural frequencies for 55 combinations of edge conditions. The natural frequency parameters of the shells were obtained using the Superposition-Galerkin Method (SGM) for seven sets of boundary conditions, several different curvature ratios and two aspect ratios. The SGM uses approximate steady state solutions as building blocks but the method proves to be accurate and efficient. It has also been shown that even with approximate building blocks, the monotonic nature of convergence of the natural frequencies with respect to the number of driving coefficients holds, as long as the number of admissible functions in the steady state solution is kept constant. The results for natural frequencies of the seven boundary conditions may be considered as benchmarks.     

A note on the damping of large amplitude beam vibrations

This paper presents a new series-type method for solving the eigenvalue problems of irregularly shaped plates clamped at all edges. An irregularly shaped plate is formed on a simply supported rectangular plate by rigidly fixing several segments. With the reaction forces and moments acting on all edges of an actual plate of irregular shape regarded as unknown harmonic loads, the stationary response of the plate to these loads is expressed by the use of the Green function. The force and moment distributions along the edges are expanded into Fourier series with unknown coefficients, and the homogeneous equations for the coefficients are derived by restraint conditions on the edges. The natural frequencies and the mode shapes of the actual plate are determined by calculating the eigenvalues and eigenvectors of the equations. The method is applied to a cross-shaped, an I-shaped and an L-shaped plate clamped at all edges, the natural frequencies and the mode shapes of the plates are calculated numerically and the effect of the shape is discussed.     

Application of RTDF to particles with curved surfaces

The applicability of the ray tracing with diffraction on facets model is extended to particles with curved surfaces. This allows tests against T-matrix calculations for larger size parameters and modelling of light scattering by more realistic particle shapes, such as ice crystals with rounded edges.     

Simulation of Lamb wave reflections at plate edges using the semi-analytical finite element method

In typical Lamb wave simulation practices, effects of plate edge reflections are often not considered in order to simplify the wave signal interpretations. Methods that are based on infinite plates such as the semi-analytical finite element method is effective in simulating Lamb waves as it excludes the effect of plate edges. However, the inclusion of plate edges in a finite plate could render this method inapplicable, especially for transient response simulations. Here, by applying the ratio of Lamb mode reflections at plate edges, and representing the reflection at plate edges using infinite plate solutions, the semi-analytical finite element method can be applied for transient response simulation, even when the plate is no longer infinite.     

Suppression of flow-acoustic coupling in sidebranch ducts by interface modification

The flow-acoustic coupling of shear layer instabilities with the acoustic resonances at the interface of a closed sidebranch and main duct can produce high-amplitude pure-tone noise, known as “whistle”. This study investigates experimentally the effect of various interface geometry modifications on whistles. The objective of the modifications is to suppress the noise by redirecting the shear layer at the main duct-sidebranch interface. Interchangeable suppressor blocks of varying shapes and sizes mounted upstream and downstream of the sidebranch opening are used to change the geometry. The block shapes include those with square edges, ramps, bevelled edges, and curved (radiused) edges. The experiments are conducted in a flow facility at conditions that include certain ranges of Strouhal numbers known to coincide with significant noise generation. The effectiveness of various suppressors in reducing the noise is assessed by analyzing the measured sound pressure levels.     

Determination of the interface strength between two polymer materials by a new curved interface tensile test: Preliminary experimental results

Recently, the authors have proposed a new experimental method for the determination of adhesion strength between two different materials. A curved interface and special arrangement of materials is used for the tensile test of bimaterial specimens to avoid singular stress fields around corners and edges. The main advantage of the test consists in the fact that the strength is determined under conditions of a uniform tensile stress field normal to the interface in the region where debonding starts. The present paper presents experimental results for two bimaterial systems - PMMA/TPE and PC/TPE (two stiff standard polymers with a thermoplastic elastomer). The expected failure behaviour was observed during the experiments, thus enabling the estimation of adhesion strength by using calculated stress concentration factors. The influence of the radius of curvature is discussed in detail.     

一种无参考型模糊图像质量评价方法

图像的边缘信息是人眼观察和识别物体的重要特征,根据模糊图像相对于清晰图像其边缘特征发生较大变化的特点,提出了一种基于边缘锐度的无参考模糊图像质量评价方法。首先,通过文中所示方法寻找图像中的所有阶跃边缘;其次,根据一些原则选择合适的部分边缘;最终,计算这些合适边缘的锐利程度作为图像的模糊度评价依据。实验结果表明,该方法相比于全参考模型SSIM能够更好地评价高斯模糊、离焦模糊等模糊类型图像,与主观评价结构相关性强,更符合人眼视觉系统特性,并且易于实现。