A Simple Method for Measuring Tensile Force with Piezoelectric Patch

We propose a simple method for monitoring the axial tensile and compressive force in a structure by using a piezoelectric patch with the piezoelectric impedance based measurement. A simple approximate equation for estimating the tensile force in two different conditions, which can be calculated easily if the naturM frequencies in two different states are measuredt is explained in detail. On another front, the natural frequency can be very easily measured by a piezoelectric element by bonding it on the measuring subject structure, because its electric impedance of piezoelement is related to the structural mechanical impedance. Furthermore, an experiment for measuring a tensile force in a simple supported beam is carried out for validating the proposed method. The results show a good accuracy in estimating the tensile force variation by the natural frequency change measured from the piezoelement.     

An extended transfer matrix-finite element method for free vibration of plates

A combination of extended transfer matrix and finite element methods is proposed for obtaining vibration frequencies of structures. This method yields the value of the frequency once a trial value is assumed. By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller computer can be used. Besides, no plotting of the values of the determinants corresponding to each assumed frequency is necessary. A worked example is given for the case of vibration of a cantilever plate. The results show fast convergence from the assumed value to the true natural frequency.     

Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field

Free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field are of concern. On the basis of the surface elasticity theory, a model is developed to investigate the problem. The analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained. The influences of the surface effect, initial tensile force within the nanowire, strength of the longitudinal magnetic field, and electric current on the natural frequencies as well as dynamic displacements are examined. The obtained results reveal that the transverse stiffness of the nanostructure is enhanced by the surface effect and the initial tensile force, while electric current or longitudinal magnetic field reduces the nanowire's stiffness. The condition which leads to the dynamic instability of the nanostructure is obtained. Further, the roles of the influential parameters on its stability are inclusively discussed.     

ASYMPTOTIC APPROACH FOR NON-LINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURES

An asymptotic approach for determining periodic solutions of non-linear vibration problems of continuous structures (such as rods, beams, plates, etc.) is proposed. Starting with the well-known perturbation technique, the independent displacement and frequency is expanded in a power series of a natural small parameter. It leads to infinite systems of interconnected non-linear algebraic equations governing the relationships between modes, amplitudes and frequencies. A non-trivial asymptotic technique, based on the introduction of an artificial small parameter is used to solve the equations. An advantage of the procedure is the possibility to take into account a number of vibration modes. As examples, free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non-linear restoring force are considered. Resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived.     

Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.     

LD泵浦环形单频Nd∶YVO4激光器的频率调谐特性研究

利用激光谐振腔内标准具的选模调谐特性和激光晶体自身的标准具作用 ,通过调节插入标准具和激光晶体的倾斜度及微调谐振腔长度 ,在 L D泵浦 Nd∶ YVO4 单频激光器上实现了精确调谐 ,最大可调谐范围约 1 0 0 GHz     

Identification of the type and parameters of fastening from the natural frequencies of a fastened rod

A rod can be fastened in a number of ways. If the rod ends are inaccessible to visual observation, the question arises of whether it is possible to determine the type and parameters of their fastening from sound vibrations induced by an impact on the rod. In this connection, a possible statement of the problem is as follows: to identify the type and parameters of fastening on both ends of a homogeneous rod from its natural frequencies. In other words, it is necessary to determine the type of fastening of each of the ends of a homogeneous rod (clamping, free support, elastic support, elastic fixing, floating fixing, or free end) and its parameters (the stiffness coefficients of springs for elastic fixing). The duality and stability of the solution to this problem is demonstrated. A method of solving this problem with the use of 9 natural frequencies is proposed. The results of numerical experiments on reconstructing various types of fastening from 9 natural frequencies are presented.     

An exact solution for the natural frequencies and mode shapes of an immersed elastically restrained wedge beam carrying an eccentric tip mass with mass moment of inertia

In general, the exact solutions for natural frequencies and mode shapes of non-uniform beams are obtainable only for a few types such as wedge beams. However, the exact solution for the natural frequencies and mode shapes of an immersed wedge beam is not obtained yet. This is because, due to the “added mass” of water, the mass density of the immersed part of the beam is different from its emerged part. The objective of this paper is to present some information for this problem. First, the displacement functions for the immersed part and emerged part of the wedge beam are derived. Next, the force (and moment) equilibrium conditions and the deflection compatibility conditions for the two parts are imposed to establish a set of simultaneous equations with eight integration constants as the unknowns. Equating to zero the coefficient determinant one obtains the frequency equation, and solving the last equation one obtains the natural frequencies of the immersed wedge beam. From the last natural frequencies and the above-mentioned simultaneous equations, one may determine all the eight integration constants and, in turn, the corresponding mode shapes. All the analytical solutions are compared with the numerical ones obtained from the finite element method and good agreement is achieved. The formulation of this paper is available for the fully or partially immersed doubly tapered beams with square, rectangular or circular cross-sections. The taper ratio for width and that for depth may also be equal or unequal.     

LD泵浦环形单频Nd:YVO4激光器的频率调谐特性研究

利用激光谐振腔内标准具的选模调谐特性和激光晶体自身的标准具作用,通过调节插入标准具和激光晶体的倾斜度及微调谐振腔长度,在LD泵浦Nd:YVO₄单频激光器上实现了精确调谐,最大可调谐范围约100GHz.     

Thermal distribution calculation in diode pumped Nd:YAG laser rod by boundary element method

Boundary element method is used to calculate the temperature distribution by solving the heat transfer equation in a laser rod. Propagation of the pumping beam in the rod, that is assumed to be pumped longitudinally, results in a temperature gradient. Such a gradient produces radial variation of the refractive index and the rod behaves similar to a positive lens. Depending on the size of the pumping beam waist and absorption coefficient of the rod, a hot spot may form inside the rod.     

Free wave propagation in two-dimensional periodic plates

The propagation of flexural waves in a two-dimensional periodic plate which rests on an orthogonal array of equi-spaced simple line supports has been investigated. A type of plane wave motion has been considered. An energy method has been developed to predict the frequency of wave propagation in terms of the propagation constants. A Galerkin type of analysis has been used, incorporating assumed complex modes of wave motion for the identical rectangular elements of the periodic plate. Expressions for the frequency have been obtained firstly by using simple polynomial modes for the plate displacements, and then (alternatively) by using characteristics beam function modes. The use of these different modes has first been demonstrated by applying them to the analysis of wave propagation in periodic beams. A single polynomial mode which satisfies the geometric and wave-boundary conditions of the periodic plate element leads to an elegant expression relating the frequency and the wave propagation constants in the first propagation band. The frequencies so obtained compare well with those found from a multi-mode, characteristic beam function analysis. The latter involves much more algebra, is solved as an eigenvalue problem, and yields the frequencies in as many propagation bands as are desired. The bounding frequencies and corresponding wave motions in the first and higher propagation bands have been identified, and it has been shown that the propagation bands can overlap. Consideration has been given to one-dimensional “strip” structures which are equivalent to the two-dimensional plate when a plane wave in a general direction is propagating. Furthermore, it is shown that the natural frequencies of finite rectangular periodic plates can be obtained very simply from the results of the wave propagation analysis.     

空间弹性细杆在扭矩作用下的屈曲

用有限元方法研究了三维弹性细杆在扭矩作用下的屈曲.利用自然坐标形式的细长空间曲杆的能量方程和2节点12个自由度的自然坐标形式的三维曲梁单元,采用特征值分析方法,研究分析了同时受有轴力和扭矩作用时的空间弹性细杆的屈曲问题.数值结果与存在的理论解极为吻合.具有一定曲率和挠率的空间细长曲杆,其临界扭矩值与扭矩的指向有着极其明显的关系.     

Antisymmetric modes of vibration of a circular plate elastically restrained against rotation and subjected to a hydrostatic state of in-plane stress

Very simple approximate frequency equations are determined which allow prediction of natural frequencies in the case of a vibrating circular plate which executes antisymmetric modes. It is assumed that the plate has no edge deflection but is elastically restrained against rotation along the edge.     

Determination of object resonances by vibro-acoustography and their associated modes

Vibro-acoustography technique known by its noncontact excitation was used to detect resonance frequencies of objects in water. Two intersecting ultrasound beams generated by a 40 mm-diameter annular array transducer, focused at 35 mm and driven at f1=2.2 MHz and f2=2.22 MHz respectively, were targeted inside the object under test to produce a radiation force beating at the difference frequency f2-f1. This low frequency radiation force was used to excite the resonance vibration modes of the object by sweeping the frequency f2 between 2.22 and 2.275 MHz. The amplitude of the acoustic emission produced by the vibrations of the object was detected by a low frequency hydrophone (BW=60 kHz). By this approach, it was possible to detect resonance frequencies through amplitude variations of the measured acoustic emission. Experiments were conducted in a water tank for objects of different shapes and sizes. With a chalk sphere (15 mm-diameter) two resonance frequencies were detected at 45.75 and 68.75 kHz, and with a cylinder (10.38 mm-diameter and 32.20 mm-length) four principal resonance frequencies were identified in the 60 kHz-bandwidth of the hydrophone. It was shown with finite element calculations performed with Ansys, in which both solid and fluid parts were modelled, that the measured resonance frequencies corresponded to compressional or dilatation vibration modes of the object. It was verified that shear waves generated by torsional vibration modes were not propagated in water, as it is well known. The use of this technique to characterize heterogeneities in different media seems to be relatively more advantageous to other ultrasonic methods.     

Evaluation of the acoustic performance of a modular construction system: Case study

The aim of this technical note is to characterize the value of acoustic treatments applied to sustainable buildings. The technique is not common in Brazilian construction, but the market needs construction techniques like the ones that will be showed here. At the end of the article, a comparison between masonry with concrete blocks and the industrialized system (built in steel framing) is presented. The simplified method of measuring acoustics was chosen, to be as close as possible to the regular engineering method. The tested buildings have been classified accordingly. This project made use of the Brazilian law and some European laws.     

VIBRATION AND BUCKLING OF INITIALLY STRESSED CURVED BEAMS

Equations of motion for curved beams in a general state of non-uniform initial stresses are derived using the principle of virtual work. The equations are adjusted to a generic expression by using appropriate transformations. The free vibration behaviours of the curved beams subjected to a combination of uniform initial tensile of compressive stresses and uniform initial bending stress are examined. The Galerkin method is employed in obtaining accurate values of free frequencies and initial buckling stresses. The curved beam is assumed to be vibrating in its plane. Natural frequencies and initial buckling stresses for hinged supported curved beams are presented for validation. Effects of arc segment angles, elastic foundation, and initial stresses on the natural frequencies are investigated. Effects of arc segment angles, elastic foundation, and initial bending stresses on the initial buckling stresses are explored in this paper.     

Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate

The nonlinear natural frequency of a rectangular box, which consists of one flexible plate and five rigid plates, is studied in this paper. The flexible plate is assumed to vibrate like a simple piston. The behavior of the structural-acoustic coupling between the flexible plate and the air cavity is analyzed by using the proposed finite element modal method. The system finite element equation is reduced and expressed in terms of the modal coordinates with small degrees of freedom by using the proposed reduction method. The system nonlinear stiffness matrix representing the large amplitude vibration can be transformed to be a constant modal matrix. The natural frequencies are determined by using the harmonic balance method to solve the eigenvalue equations of the structural-acoustic system. The effect of the cavity depth on the natural frequencies and convergence studies are discussed in detail.     

Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements

This paper employs the numerical assembly method (NAM) to determine the “exact” frequency–response amplitudes of a multiple-span beam carrying a number of various concentrated elements and subjected to a harmonic force, and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force. First, the coefficient matrices for the intermediate concentrated elements, pinned support, applied force, left-end support and right-end support of a beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix. The graph of dynamic response amplitudes versus various exciting frequencies gives the frequency–response curve for any point of a multiple-span beam carrying a number of various concentrated elements. For the case of zero harmonic force, the above-mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained.     

颗粒物质中圆棒受到的静摩擦力

通过实验研究了圆棒在颗粒物质中受到的摩擦力与颗粒填充高度及棒径的关系.观测到摩擦力随颗粒高度和棒径而增大.用连续介质模型推导了摩擦力公式，与实验观测基本一致.结果表明，摩擦力和棒径成正比；当颗粒高度很小时，摩擦力与颗粒高度平方成正比；而当颗粒堆积很高时，摩擦力与高度成正比，即静摩擦力与接触面积成正比. 关键词： 颗粒物质 摩擦力