Rongqiao Xu

Three-dimensional static analysis of multi-layered piezoelectric hollow spheres via the state space method

A general non-axisymmetric exact analysis of the statics of a laminated piezoelectric hollow sphere is presented in the paper by using a state space method. To select a proper set of state variables, three displacement functions and two stress functions are introduced. It is found that the basic equations of a spherically isotropic piezoelectric medium are eventually turned to two separated state equations with constant coefficients, the solutions of which are then obtained by virtue of matrix theory. The continuity conditions at each interface are then used to derive two relationships between respective boundary variables at the inner and outer spherical surfaces. No matter how many layers the sphere contains, the orders of the final solving equations remain unaltered.

THREE-DIMENSIONAL FREE VIBRATION ANALYSIS OF A FLUID-FILLED PIEZOCERAMIC HOLLOW SPHERE

Abstract This article presents an exact three-dimensional analysis of the free vibration of a piezoceramic hollow sphere filled with a compressible fluid medium. Three displacement functions are introduced to rewrite three components of the mechanical displacement in spherical coordinates. For the problem of general nonaxisymmetric free vibration, it is shown that the controlling equations are finally simplified to an uncoupled second-order ordinary differential equation and a coupled system of three such equations. Solutions to these differential equations are obtained. The coupled vibration problem of piezoceramic hollow sphere is then considered. It is found that there are two independent classes of vibrations. The first class is independent of the contained fluid and is not affected by the electric field, while the second is related to both the fluid parameter and the electric field. Exact frequency equations are derived and numerical results are finally presented.

Free vibration of transversely isotropic piezoelectric circular cylindrical panels

This paper presents an exact three-dimensional free vibration analysis of a transversely isotropic piezoelectric circular cylindrical panel. The general solution for coupled equations for piezoelectric media that was recently proposed by Ding et al. (Int. J. Solids Struct. 33 (1996) 2283) is employed. By using the variable separation method, three-dimensional exact solutions are obtained under several boundary conditions. Numerical results are finally presented and compared with available data in literature. The results show the non-dimensional frequencies of the piezoelectric panel are bigger than that of the non-piezoelectric one.

On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells

Abstract This paper exactly studies the coupled free vibration of a transversely isotropic cylindrical shell embedded in an elastic medium. Response of the elastic medium is represented by Winkler/Pasternak models while the behavior of the cylindrical shell is analyzed based on the three dimensional elasticity. Three displacement functions are chosen to represent three displacement components to decouple the three-dimensional equations of motion of a transversely isotropic body. After expanding these functions with orthogonal series, the coupled free vibration problem of an embedded transversely isotropic shell with ends simply-supported can be readily dealt with. In particular, Bessel function solution which includes complex arguments is directly used for the case of complex eigenvalues. Numerical examples are presented and compared to the results of existent papers.

Bending Solutions of the Timoshenko Partial-Interaction Composite Beams Using Euler-Bernoulli Solutions

For partial-interaction composite beams, two beam theories (i.e., the Euler-Bernoulli and Timoshenko beam theories) are usually used to investigate their deflections, slips, and stress resultants. However, the relationships between the solutions of partial-interaction composite beams based on the two beam theories have not been discussed while the corresponding relationships for homogeneous beams have been investigated in detail for several years. By analyzing the constitutive relationships and equations of equilibrium, the authors derived the relationships of the solutions between single-span Euler-Bernoulli and Timoshenko partial-interaction composite beams. The integral constants are also presented for various boundary conditions. Through the presented relationships, the solutions of the Timoshenko partial-interaction composite beams could be readily obtained from the solutions of the corresponding Euler-Bernoulli counterparts. As a result, the more complicated flexural-slip-shear deformation analysis based on Timoshenko beam theory may be avoided for engineering designers.

CZM-Based Debonding Simulation of Cracked Beams Strengthened by FRP Sheets

This paper uses the transfer matrix method (TMM) to analyze the interfacial behavior of a fiber-reinforced polymer (FRP)–plated beam with flexural cracks. The adhesive layer between the beam and the FRP sheet is simulated by the cohesive zone model (CZM) of a general interfacial bond-slip law. The flexural cracks are modeled by rotational springs whose rigidity is dependent on the relative depth of the cracks. The transfer matrix of the FRP-plated beam is then derived, and the joint coupling matrix (JCM) method is introduced to solve the stress resultants, displacements, interfacial shear stress, and axial force of the FRP sheet. Finally, some numerical examples are given, and the results are compared with the available analytical solutions to validate the present method.

New Beam Element for Incremental Launching of Bridges

A new beam element has been developed for the static and dynamic analysis of incrementally launched bridges. The element can describe the deformation subjected to a transverse constraint at an arbitrary point on the beam, thus enabling direct simulation of the superstructure with a continuously position-varying support during the incremental launching of bridges. This element significantly simplifies the finite-element modeling of launched bridges and greatly reduces the computational cost. Some numerical examples are given to show the superiority of the proposed element.

Variational Principles of Partial-Interaction Composite Beams

This work presents the principle of virtual work and reciprocal theorem of partial-interaction composite beams. The principle of minimum potential energy is also obtained and proved along with the variational formulae for the frequency of free vibration and the critical load of buckling of partial-interaction composite beams. Approximate solutions for bending, vibration, and buckling are finally given to demonstrate their applications. It is shown that the deflections, resonant frequencies, and critical loads of buckling of composite beams under different boundary conditions can be readily obtained with enough accuracy by using these variational principles.

Exact solution for axisymmetric deformation of laminated transversely isotropic annular plates

SummaryBased on the three-dimensional theory of elasticity, this paper presents the state space equation for axisymmetric deformation of a laminated transversely isotropic annular plate. The finite Hankel transform is then introduced and applied to the state space equation. Four exact solutions corresponding to four specified boundary conditions are obtained and expressions for displacements and stresses are presented. Numerical results are finally compared with those obtained by the classical plate theory, the Reissner plate theory and the finite element method.

Electro-mechanical analysis of piezoelectric patch bonding to beams

Due to the outstanding electromechanical coupling property, piezoelectric materials played an important role in smart structures, structural health monitoring, strain measurement, and energy harvesting. In these applications, the piezoelectric materials were usually fabricated in form of patches and bonded on the surfaces of host structures. As a result, the interaction between the surface-bonded piezoelectric patch with the host structures should be well understood to design or manufacture. However, very limited research was available in the literatures. This works derived the coupled governing equation of the strains of the piezoelectric patch and surface of the host structures including the electromechanical coupling effect of piezoelectric materials. The dynamic one was also presented and the effect of the circuit resistance was also considered. Some numerical examples were given to demonstrate the present method and the results were compared with those by finite element method.