The effects of distributed masses on acoustic radiation behavior of plates

The acoustic radiation behavior of a plate with a distributed mass loading is studied. A set of in vacuo normal modes or fluid-loaded undamped normal modes are used for modal analysis of the acoustic radiation from a plate in air or in water. Modal radiation efficiency, modal volume displacement, modal input energy and sound power level are computed to show the effects of size and location of the mass loading on the acoustic radiation of the plate. It is observed that the acoustic radiation behavior of a mode in both cases will have relatively larger changes if the mass loading is placed on an antinode of the mode shape or the mass loading is more concentrated. The acoustic radiation behavior of a mode and the radiated power of the plate in water have less change than those in air with the same mass loading due to the added mass of the water, especially for the first few modes.     

A reduction method for problems of vibration of orthotropic plates

It is shown that the problem of vibration of an orthotropic plate can be reduced to that of another orthotropic plate by a simple co-ordinate transformation, and reduction formulae are obtained. To justify the reduction formulae, fundamental natural frequencies of orthotropic rectangular plates with various boundary conditions and of a clamped orthotropic elliptical plate are discussed. As an example, an exact natural frequency of a simply supported generally orthotropic skew plate with special flexural rigidities is obtained from that of a simply supported isotropic rectangular plate.     

Free vibration analysis of stiffened plates using finite difference method

Free vibration characteristics of rectangular stiffened plates having a single stiffener have been examined by using the finite difference method. A variational technique has been used to minimize the total energy of the stiffened plate and the derivatives appearing in the energy functional are replaced by finite difference equations. The energy functional is minimized with respect to discretized displacement components and natural frequencies and mode shapes of the stiffened plate have been determined as the solutions of a linear algebraic eigenvalue problem. The analysis takes into consideration inplane deformation of the plate and the stiffener and the effect of inplane inertia on the natural frequencies and mode shapes. The effect of the ratio of stiffener depth to plate thickness on the natural frequencies of the stiffened plate has also been examined.     

Analysis of the flow-induced vibrations of viscoelastically supported rectangular plates

The purpose of this study was to develop a theoretical model for the flow-induced vibration of viscoelastically supported rectangular plates. In particular, the influence of the dynamic mechanical properties of the elements supporting the plate was investigated. The case of a homogeneous rectangular plate supported along all four edges by a complex viscoelastic element was treated. The Rayleigh-Ritz method was used applying beam functions as the trial functions. This approach ensured a fast convergence rate, which is advantageous for vibration analysis of high order modes. The flow-induced vibration of the plate was calculated using the Corcos model for the surface pressure loading. The results suggest that there is an optimal support stiffness that minimizes the flow-induced vibration response of the plate.     

求解水中加肋板声辐射特性的虚拟声源法*

发展一种利用虚拟声源离散声场的方法求解加肋板在水中的声振耦合问题。由波叠加原理和单元体积速度匹配的原则,根据离散的结构单元满足的动力方程和结构与介质的交界相容性条件,确定虚拟声源强度,计算结构的声辐射功率。本文以简支矩形加肋板为例,在不获得结构表面振速和声压的情况下,计算了结构在水中的声辐射功率,并与解析方法计算的结果进行了比较,表明了该方法具有较好的计算精度。     

水中矩形板的共振声辐射

研究共振声辐射理论(Resonance Radiation Theory:RRT)在水中矩形板的应用。导出了矩形板的共振声辐射公式、并数值验证了其适用性。深入分析了有流体负荷矩形板的复共振频率的物理意义及其与导纳留数、模态辐射率的关系,复共振频率的实部表示实际共振频率,虚部反映模态辐射能力。根据复共振频率容易找到辐射能力相对较强的模态,为有针对性控制声辐射提供了新的思路。鉴于复平面搜根求解模态复共振频率的困难,针对矩形板的特点提出了一种求解复共振频率及留数的快速方法。结合该方法及RRT,提出了一种快速计算辐射声功率的方法,数值验证表明该方法精度高、速度快。      

含损伤黏弹性阻尼加筋层合板声功率和指向性变异

该文旨在研究损伤位置和程度对自由阻尼加筋层合板声辐射功率和指向性的影响.基于Mindlin和Timoshenko梁理论,建立了自由阻尼层合板-梁组合结构有限元模型.数值求解四边简支边界条件自由阻尼加筋层合板振动响应,继而通过Rayleigh积分计算加筋层合板辐射声功率和指向性.将计算得到的前4阶模态固有频率、声辐射功率...     

The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates

The boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency. To investigate this effect in a systematic way, the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach. Whereas analytical expressions exist for simply supported boundary conditions, a numerical approach is required for other cases. Nine combinations of boundary conditions are considered, consisting of simply supported, clamped and free edges on different plate edges. The structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies. This assumption is checked against a finite element model and shown to give reliable results. It is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency. Other combinations of boundary condition give intermediate results according to the level of constraint introduced. The differences depend on frequency: excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 dB in the middle part of the short-circuiting region, decreasing towards the critical frequency. At low frequency the differences can be even greater, in some cases up to 20 dB. These conclusions are shown to hold for a range of plate thicknesses and dimensions.     

Geometrically nonlinear dynamic response of stiffened plates with moving boundary conditions

An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The first approximation solution of the non-resonance is obtained by means of the method of multiple scales. The primary parametric resonance and primary resonance of the stiffened plate are studied by using the same method. The accuracy of the method is validated by comparing the results with those of finite element analysis via ANSYS. Numerical examples for different stiffened plates are presented to discuss the steady response of the non-resonance and the amplitude-frequency relationship of the primary parametric resonance and primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude-frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.     

Free vibration analysis of rectangular plates with symmetrically distributed point supports along the edges

In this paper a highly accurate mathematical technique for establishing the free vibration eigenvalues and mode shapes of rectangular plates with symmetrically distributed point supports is introduced. The method is based on the principle of superposition and it constitutes, in essence, an extension of a technique described earlier for the analysis of completely free plates. Eigenvalues, covering numerous modes and aspect ratios, are tabulated for corner supported rectangular plates. It is seen that with some modifications the method is equally applicable to problems where the point supports are not symmetrically distributed.     

Large amplitude flexural vibration of eccentrically stiffened plates

The large amplitude free flexural vibrations of thin, orthotropic, eccentrically and lightly stiffened elastic rectangular plates are investigated. Clamped boundary conditions with movable in-plane edge conditions are assumed. A simple modal form of one-term transverse displacement is used and in-plane displacements are made to satisfy the in-plane equilibrium equations. By using Lagrange's equation, the modal equations for the nonlinear free vibration of stiffened plates are obtained for the cases when the stiffeners are assumed to be smeared out over the entire surface of the plate, and when the stiffeners are located at finite intervals. Numerical results are obtained for various possibilities of stiffening and for different aspect ratios of the plate. By particularizing the problem to different known cases, the results obtained here are compared with available analytical and experimental results, and the agreement is good.     

Radiation efficiency of a baffled circular plate in flexural vibration

The radiation efficiency of an edge-clamped circular plate, which is vibrating flexurally in one of its natural modes and is mounted in an infinite baffle, is theoretically determined from the total power radiated to the far field. The vibrations of the plate are investigated both by the classical plate theory and by the improved plate theory (Mindlin plate theory). Approximation formulae for the low frequency region are derived, and curves covering the entire frequency range for the first fifteen modes are obtained through numerical calculation. Except for frequencies much higher than the critical frequency, there exist some differences in the radiation efficiencies between the results obtainedby the two theories. The difference increases with the thickness of the plate and with the mode numbers, especially for modes having many nodal diameters.     

弯曲振动矩形板辐射阻抗的计算

本文推导了四边简支矩形板的辐射阻抗表达式, 利用高斯数值积分方法, 计算了其相对辐射阻抗的数值解. 由不同模态下相对辐射阻抗与频率以及不同长宽比对应的相对辐射阻抗与频率的关系可知, 在中低频段, 模态越低, 辐射阻抗越大, 也就意味着辐射声功率和同振质量越大; 对于一定面积和模态的矩形板, r (r=a/b, 长与宽之比)值越接近1, 即越接近正方形, 辐射阻和辐射抗越大. 本文的方法能对其他复杂边界条件下的、无振动解析解的矩形板的辐射阻抗数值量级大小提供一个参考, 也可由计算弯曲振动的阻抗自然地过渡到活塞振动阻抗的计算.     

Estimation of broadband acoustic power radiated from a turbulent boundary layer-driven reinforced finite plate section due to rib and boundary forces

Previous papers considered an infinite fluid-loaded plate with parallel line attachments, driven by a wave-number-white pressure excitation invariant in the direction of an attachment, and established the conditions and procedure for estimating the broadband radiated power by assuming the ribs to radiate independently. This paper applies those results to a finite rectangular ribbed plate, and extends the methodology to include the contribution of the plate's boundary support forces to the radiation and the consideration of excitation that varies in the direction parallel to the ribs. The approach is relevant to problems of sound radiation by underwater stiffened steel plates driven by turbulent boundary layer (TBL) pressures, and is also applicable to stiffened circular cylindrical shells when the response is dominated by bending. Comparisons of sample calculations with results of rigorous models validate the approximation.     

An experimental study of the effects of resilient bars on plate vibration

Resilient bars can provide a low-cost, effective improvement to sound insulation performance. They are commonly used in timber-framed floor/ceiling assemblies in North America and Europe. Resilient bars are often modelled as springs isolating the two connected plates thereby forming a mass-spring-mass system. However, as a furring system of plates, resilient bars may modify the vibration energy distribution across a connected plate by acting as stiffeners. The authors investigate this issue by measuring acceleration levels at different locations relative to the fixing positions and thereby derive vibration waveforms for the connected plate in a small-scale structural simulation of a floor-ceiling system. The results were compared with timber-joist-ribbed, and timber-brander-ribbed, structures. The vibration modes of a suspended plate were also measured for comparative purposes. The results indicated that resilient bars did not perform as stiffeners whereas joists and timber branders did effectively stiffen their connected plates. Resilient bars neither forced orthotropic plate behaviour at low frequencies, nor separated the plate into sub-plates at higher frequencies. Resilient-bar-ribbed plates may also differ from independent plates. The modal behaviour of resilient-bar-ribbed plates is more complex and their effect on modal density and radiation efficiency are worthy of further research.     

Forced vibrations of a non-uniform thickness rectangular plate with two free sides

A forced vibration of a rectangular plate with thickness varying linearly in one direction is studied. The plate is simply supported along two opposite sides, and is free along the other sides. Approximate formulae are proposed for estimating the maximum deflection and surface stresses of a rectangular plate subject to a uniformly distributed harmonic lateral load. The accuracy of the formulae is discussed. The approximate formulae show the possibility that one can obtain solutions for the forced vibration of a plate with non-uniform thickness from those for the static bending of the same plate when the plate is subjected to a uniformly distributed load.     

Smearing technique for vibration analysis of simply supported cross-stiffened and doubly curved thin rectangular shells

Plates stiffened with ribs can be modeled as equivalent homogeneous isotropic or orthotropic plates. Modeling such an equivalent smeared plate numerically, say, with the finite element method requires far less computer resources than modeling the complete stiffened plate. This may be important when a number of stiffened plates are combined in a complicated assembly composed of many plate panels. However, whereas the equivalent smeared plate technique is well established and recently improved for flat panels, there is no similar established technique for doubly curved stiffened shells. In this paper the improved smeared plate technique is combined with the equation of motion for a doubly curved thin rectangular shell, and a solution is offered for using the smearing technique for stiffened shell structures. The developed prediction technique is validated by comparing natural frequencies and mode shapes as well as forced responses from simulations based on the smeared theory with results from experiments with a doubly curved cross-stiffened shell. Moreover, natural frequencies of cross-stiffened panels determined by finite element simulations that include the exact cross-sectional geometries of panels with cross-stiffeners are compared with predictions based on the smeared theory for a range of different panel curvatures. Good agreement is found.     

Natural vibration of rectangular plates with an internal line hinge using the first order shear deformation plate theory

This paper presents exact solutions for vibration of rectangular plates with an internal line hinge. The rectangular plate is simply supported on two parallel edges and the remaining two edges may take any combination of support conditions. The line hinge is perpendicular to the two simply supported parallel edges. The Lévy type solution method and the state-space technique are employed in connection with the first order shear deformation plate theory (FSDT) to study natural vibration of rectangular plates with an internal line hinge. In particular, exact vibration frequencies are obtained for rectangular plates of different aspect ratios and edge support conditions. The influence of the internal line hinge on the vibration behavior of rectangular plates is studied.     

Plate-shaped non-contact ultrasonic transporter using flexural vibration

We developed a plate-shaped non-contact transporter based on ultrasonic vibration, exploiting a phenomenon that a plate can be statically levitated at the place where its gravity and the acoustic radiation force are balanced. In the experiment, four piezoelectric zirconate titanate elements were attached to aluminum plates, on which lattice flexural vibration was excited at 22.3 kHz. The vibrating plates were connected to a loading plate via flexible posts that can minimize the influence of the flexure induced by heavy loads. The distribution of the vibration displacement on the plate was predicted through finite-element analysis to find the appropriate positions of the posts. The maximum levitation height of this transporter was 256 μm with no load. When two vibrating plates were connected to a loading plate, the maximum transportable load was 4.0 kgf.