Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell

In this paper, the axisymmetric vibration of a fluid-filled spherical membrane shell is studied based on nonlocal elasticity theory. The membrane shell is considered elastic, homogeneous and isotropic. The shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The membrane shell is completely filled with an inviscid fluid. The motion of the fluid is governed by the wave equation. Nonlocal governing equations of motion for the fluid-filled spherical membrane shell are derived. Along the contact surface between the membrane and the fluid, the compatibility requirement is applied and Legendre polynomials, associated Legendre polynomials and spherical Bessel functions are used to obtain the natural frequencies of the fluid-filled spherical membrane shells. The frequencies for both empty and fluid-filled spherical membrane shell are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. An excellent agreement is found between the present and previous ones available in the literature. The variations of the natural frequencies with the small-scale parameter, density ratio, wave speed ratio and Poisson’s ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.     

充液压电阻尼圆柱壳的有限元建模

基于Mindlin板理论、压电理论、粘弹性理论和理想流体方程，对充液圆柱壳主动约束阻尼结构在流固耦合条件下的建模进行了研究。利用拉格朗日方法得到结构的动力学方程，利用GHM方法描述粘弹性阻尼的本构关系，结合流体方程建立主动约束阻尼结构在流固耦合条件下的动力学方程。建立从压电材料的电压到流固耦合边界下的圆柱壳结构振动的频响函数，利用实验结果对理论计算加以验证，结果表明该建模方法是可行的。     

On the steady-state transverse vibrations of a cracked spherical shell

Using an integral formulation, the problem of a spherical shell containing a through crack of length 2c and subjected to periodic transverse vibrations of frequency is solved for the in-plane and Kirchhoff bending stresses. The usual inverse square root singular behavior characteristic to crack problems is recovered. Furthermore, it is found that the transverse vibrations reduce the stresses in the vicinity of the crack tip, except when the forcing frequency reaches the natural frequency of the uncracked shell in which case they become infinite.

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Zusammenfassung Das Problem einer sphärischen Hülle, mit einem sich über die gesamte Dicke der Hülle hinziehenden Riß der Länge 2c, welche Querschwingungen mit einer Pulsierung unterworfen ist, wurde für die Fälle von koplanaren and von Kirchhoff-Biegebeanspruchungen mit Hilfe einer Integralformulierung gelöst. Hierbei ergab sich wiederum das fur Riß-probleme charakteristische Gesetz der umgekehrten Quadratwurzel.Außerdem zeigte sich, das Querschwingungen die Spannungen in der Umgebung der Rißspitze vermindern, ausgenommen der Fall, wo die Frequenz der aufgezwungenen Schwingung mit der Eigenfrequenz der unbeschädigten Hülle übereinstimmt, wo sie dann ins Unendliche ansteigen.

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Résumé On analyse le problème de l'enveloppe sphérique ayant une fissure de longeur 2c de part en part de son épaisseur, et sujette à des vibrations transversales de pulsation ; on résoud ré problème à l'aide de fonctions intégrales, pour les contraintes coplanaires et les contraintes de flexion de Kirchhoff.On retrouve le comportement singulier habituel d'ordre 1/2, caractéristique des problèmes de fissuration. En outre, on trouve que des vibrations transversales ont tendance à réduire les contraintes au voisinage de l'extrémitée des fissures, sous réserve que leur fréquence atteigne la fréquence naturelle de l'enveloppe non fissurée; dans ces conditions les contraintes deviennent en effet infinies.

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List of Symbols and Notations c half crack length - D Eh ³/[12(1 – v ²)] = flexural rigidity - E Young's modulus of elasticity - F (x, y, t), (x,y) stress functions - ^(c)(x,y) complementary stress function - G shear modulus - h thickness - K _n modified Bessel function of the third kind of order n - L _i kernels as defined in text - m ₀ constant as defined in text - M _x ^(c) , M _y ^(c) , M _xy ^(c) complementary bending forces - M _x ^(p) , M _y ^(p) , M _xy ^(p) particular bending forces - n ₀ constant as defined in text - N _x ^(c) , N _y ^(c) , N _xy ^(c) complementary membrane forces - N _x ^(p) , N _y ^(p) , N _xy ^(p) Particular membrane forces - N _n Newman function of order n - q(x, y, t), q(x, y) internal pressure - r - R radius of curvature of the shell - R - t time variables - U(s–), U(–s) the unit step function - V _y equivalent shear - W(x, y, t), (x, y, t) displacement functions - ^(c)(x,y) complementary displacement function - dimensionless rectangular coordinates - X, Y, Z rectangular cartesian coordinates     

引入减基法的压电层合板瞬态响应分析

摘要：用减基法（RBM）结合有限元法、傅里叶变换和Newmark直接积分法,研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散,得到时间域内的运动方程,通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势,并在Newmark法求解过程嵌入减基法,构造减基空间,把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶,得到减缩的Newmark增量式,从而快速求解得到原结构波数域响应,通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明,求解过程引入减基法能更快得到结构的瞬态响应,并保证了精度。     

Thermoelastic response in a symmetric spherical shell

This paper is concerned with the determination of thermoelastic stresses, strain and conductive temperature in a spherically symmetric spherical shell. The two-temperature three-phase-lag thermoelastic model (2T3P) and two-temperature Green–Naghdi model III (2TGNIII) are combined into a unified formulation. There is no temperature at the outer boundary, and thermal load is applied at the inner boundary. The basic equations have been written in the form of a vector–matrix differential equation in the Laplace transform domain which is then solved by the state-space approach. The numerical inversion of the transform is carried out using Fourier series expansion techniques. Because of the short duration of the second sound effects, small time approximations of the solutions are studied. The physical quantities have been computed numerically and presented graphically in a number of figures. A complete and comprehensive analysis of the results has been presented for the 2T3P and the 2TGNIII models. These results have also been compared with those of the one-temperature three-phase-lag thermoelastic model (1T3P) and one-temperature Green–Naghdi model III (1TGNIII).     

箱包炸弹内爆作用下单层球面网壳结构的动力响应分析

运用ANSYS/LS-DYNA建立跨度40 m凯威特K8单层球面网壳,采用流固耦合算法,考虑箱包炸弹在网壳内部爆炸的最不利类型,获取其动力响应规律.研究结果表明:在不同炸点水平位置下,网壳内部流场分布特征、冲击波传播路径以及冲击波与网壳作用过程存在差异,各特征响应随炸点水平位置的改变变化较大,网壳杆件塑性应变百分率大致...     

ALE方法模拟爆炸载荷作用下球壳反直观行为

本文利用任意拉格朗日与欧拉（ALE）方法,模拟了球壳在爆炸载荷作用下的动力反直观行为,得到了球壳中点位移时程曲线以及最终变形模式等动力响应。在研究中,考虑了材料的应变率效应,并对球壳的矢高和厚度对其反直观行为的影响进行了参数分析。结果表明,只有炸药距球壳距离在特定范围内,球壳才能发生反直观行为;当炸药当量一定时,球壳发生反直观行为的爆心距区域段随球壳矢高增加而减少,矢跨比大于一定值后,将不会发生反直观行为     

Dynamic response in magnetic force control using a laminate composite of magnetostrictive and piezoelectric materials

We investigate the dynamic response of a magnetic force control device composed of a laminate composite of magnetostrictive/piezoelectric material. The device exploits the inverse magnetostrictive effect of a magnetostrictive material so that the variation in the magnetization of the material, and hence the magnetic force in a magnetic circuit, can be controlled with a voltage to the piezoelectric material. Here, we compare the voltage-induced frequency responses of the admittance and flux (magnetic force) between the new device and a conventional electromagnet in order to identify the factors that degrade the response of the device. A finite-element calculation of the modal shape of the composite supports the observed correlation between the vibration of the composite and the flux in the gap in dynamic response.     

Reduced effects of spherical aberration on penetration depth under two-photon excitation

We compare the effects of spherical aberration on the penetration depth of single-photon and two-photon excitation for instances in which the aberration is caused by the refractive-index mismatch when a beam is focused through an interface. It is shown both theoretically and experimentally that two-photon fluorescence imaging experiences less spherical aberration and can thus propagate to a deeper depth within a thick medium.     

Effects of design inhomogeneities of the dynamic response of a spherical shell

An experimental study has been done on how the rigidity and menial parameters of design inhomogeneities affect the dynamic deformation in a spherical shell on account of an explosion at the center in a spherical charge of condensed explosive. The dynamic response in particular includes a cyclic increase in the oscillation amplitude (pumping effect), but it is substantially dependent on the size and mass of the design inhomogeneities. Assumptions made by others on the pumping mechanisms in theoretical studies are confirmed.Translated from Problemy Prochnosti, No. 1, pp. 89–96, January, 1993.     

UHMWPE球面层合板弹道侵彻性能研究

进行了超高分子量聚乙烯(UHMWPE)平面层合板、平面夹芯结构以及球面夹芯结构的弹道侵彻实验研究,发现凸球面结构的抗侵彻能力低于平面结构,根据实验现象对球面结构初始曲率的不利影响作了初步分析.应用DYTRAN软件对不同曲率的UHMWPE层合板弹道侵彻进行了数值仿真,分析了层合板曲率对弹道性能的影响规律,认为曲率对层合板变形的限制作用以及由此导致的应力集中是造成抗侵彻能力下降的主要原因.     

The static and fatigue response of metal laminate and hybrid fibre-metal laminate doublers joints under tension loading

Experimental and numerical studies have been undertaken on metal laminate (ML) doublers and hybrid fibre-metal (aluminium–Glare) laminate (FML) doublers to investigate their static and fatigue response under tension loading. Inevitably sheets in these laminates butt together and these butts can affect the joint strength. Progressive damage modelling, including the damage in the adhesive bondline, the butt, the metal and the fibre has been undertaken in both static and fatigue loading. This modelling was found to be in good agreement with the experiment data in terms both of the strength and the failure mechanisms. In ML, the butt influenced the static and fatigue response. In hybrid FML, the specimens either have the fibres parallel to the loading direction (spanwise) or perpendicular to the loading direction (chordwise). The spanwise specimen was found to have the highest strength followed by chordwise specimens without butts and finally chordwise specimens with butts. The most critical position for a butt was found to be adjacent to the doubler end. Without butts the static strength for spanwise and chordwise specimens was controlled by the failure in the Glare layer whilst the fatigue failure was precipitated by failure in the aluminium sheet.     

结构频带激励下的整体动响应优化

结合频响函数的性质,采用目标频带内各模态峰值响应的 -范数作为整体响应水平的衡量指标,将等效目标函数的灵敏度表示为固有频率和振型灵敏度的函数,进而采用基于梯度的迭代方法求解,实现结构在宽频激励下的整体动响应优化,该方法适合于多频带的响应控制。此外,在频带响应优化模型的基础上,提出了通过增加频率约束,使之能应用于密集频率结构,避免迭代过程中的密频和重频现象。最后通过桁架截面优化和形状优化的数值算例,表明了本文提出方法的合理性和有效性。     

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.     

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.     

Equivalent linearization of MDOF systems under external Poisson white noise excitation

Equivalent linearization (EQL) techniques are developed and evaluated for multidimensional systems under external Poisson white noise excitation. Especially, a simulation strategy for the calculation of the linearization coefficients is proposed. The methods are illustrated by several examples that have been treated under Gaussian white noise excitation in the literature. It is shown that EQL for MDOF systems under Poisson white noise excitation is able to deal with problems of nearly the same dimension as under Gaussian white noise excitation.     

Interlayer stress in laminate beam of piezoelectric and elastic materials

This paper studies interfacial mechanical behavior of laminate beams, consisting of two piezoelectric facial sheets and an elastic core. The study is based on coupled multi-filed finite element formulation. The emphasis is placed on mechanical and electric behavior of interfaces between piezoelectric material and elastic material, including effect of geometrical parameters, stress distribution and stress concentration near free edge of the beam subjected to coupling electric and mechanical loads. In particular, various parametric effect of laminate beam is explored and some conclusions are presented which may be useful for designing laminate beam and minimizing stress concentration at the free edges of the beam.