An analytic solution of the static problem of inclined risers conveying fluid

Meccanica - We use the method of matched asymptotic expansion to develop an analytic solution to the static problem of clamped–clamped inclined risers conveying fluid. The inclined riser is...     

Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

Considerations of nonlocal elasticity and surface effects in micro-and nanoscale beams are both important for the accurate prediction of natural frequency. In this study, the governing equation of a nonlocal Timoshenko beam with surface effects is established by taking into account three types of boundary conditions: hinged–hinged, clamped–clamped and clamped–hinged ends. For a hinged–hinged beam, an exact and explicit natural frequency equation is obtained. However, for clamped–clamped and clamped–hinged beams, the solutions of corresponding frequency equations must be determined numerically due to their transcendental nature. Hence, the Fredholm integral equation approach coupled with a curve fitting method is employed to derive the approximate fundamental frequency equations, which can predict the frequency values with high accuracy. In short,explicit frequency equations of the Timoshenko beam for three types of boundary conditions are proposed to exhibit directly the dependence of the natural frequency on the nonlocal elasticity, surface elasticity, residual surface stress, shear deformation and rotatory inertia, avoiding the complicated numerical computation.     

Multimode vibration suppression with passive two-terminal distributed network incorporating piezoceramic transducers

The design of an inductance/capacitance two-terminal distributed passive electric network for simultaneously controlling several flexural modes of vibration is discussed. The efficiency of the network to annul multimode vibrations of simply supported, clamped–clamped and cantilever beams is demonstrated.     

Generalization of Seide’s problem by the regulated stochastic linearization technique

In this paper, the nonlinear random vibration of a uniform beam clamped at both of its ends is investigated by the regulated stochastic linearization technique. A closed system of nonlinear algebraic equations for linearization coefficients is obtained using the frequency–response function matrix. Root mean-square response of maximum deflection of the beam that is obtained from the present technique is subsequently compared with that furnished by the conventional linearization. The numerical results show that the regulated stochastic linearization technique constitutes an excellent alternative to the classical linearization scheme for analyzing responses of the clamped–clamped beam.     

Bending of uniformly loaded rectangular plates with two adjacent edges clamped, one edge simply supported and the other edge free

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Determination of the complex shear modulus of structural adhesives using a doubly clamped sandwich beam

A method is described for calculating the complex shear modulus of structural adhesives from dynamic test data on a doubly clamped sandwich beam in which the adhesive is contained as a thin layer. The accuracy of the technique is validated by finite-element analysis. Values of modulus obtained using the doubly clamped beam technique are found to be in excellent agreement with values obtained from dynamic tests on bulk specimens of an epoxy adhesive.     

TENSION OF A CLAMPED RECTANGULAR PLATE CONTAINING A CENTRAL CRACK

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factars of the central cruck are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the "table of stress intensity factars".     

The buckled states of annular sandwich plates

In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner- type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.     

Active and passive magnetic constrained damping treatment

This paper has presented a new class of active and passive magnetic constrained layer damping (APMCLD) treatment for controlling vibration of three-layer clamped–clamped beams. Firstly, optimal placement strategies of discrete patches are investigated. The predictions of model are validated experimentally using three-layer clamped–clamped beams treated with fully or segmented passive magnetic constrained layer damping (MCLD) treatments. The results indicate that full MCLD treatment induces less improvement of damping characteristics. Also, the obtained results illustrate that, the improvement of damping performance using two-patched MCLD treatment becomes more apparent at the first mode compared to the corresponding performance using a single-patched MCLD treatment when the total length of damping layer is from 0.3L to 0.65L under considered magnetic force. Further, damping performances of APMCLD using several control strategies including simple PD controllers are investigated. The analytical results show that it induces less improvement of damping characteristics for higher modes using simple positive proportional feedback controllers whereas higher modes can been suppressed effectively using negative derivative feedback controllers. For broad band control of structural vibration, it is more effective using APMCLD treatments with combined proportional and derivative controllers. Moreover, the MCLD treatment still plays an important role in damping out structural vibrations even though active control systems fail.     

Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions

The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique. The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.     

Tension of a clamped rectangular plate containing a central crack

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factors of the central crack are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the “table of stress intensity factors”. This work was supported by the Science Fund of the Academy of Sciences of China.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅱ)—RECTANGULAR PLATES WITH TWO ADJACENT CLAMPED EDGES

In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two adjacent clamped edges under harmonicdistributed and concentrated loads.     

均布载荷作用下带边缘大波纹膜片的非线性弯曲

采用轴对称旋转壳体的简化Reissner方程，研究了在均布载荷作用下具有硬中心的带边缘大波纹膜片的非线性弯曲问题．应用积分方程方法，获得了具有夹紧固定和滑动固定两种外边界的膜片的特征关系，即荷载-中心挠度曲线．作为算例，给出了夹紧固定膜片中的应力分布．     

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.     

Concentrated-impact loading of circular plates

Solution to the impulsive motion of a clamped circular plate due to concentrated axisymmetric impact has been obtained. Experiments were conducted on a clamped circular-plate model under half-sine-pulse loads with several pulse durations. Experimental results are compared with the numerical results.     

Determination of the microscale stress–strain curve and strain gradient effect from the micro-bend of ultra-thin beams

A simple method is established to determine the microscale uniaxial stress–strain curve from the load and deflection data for a doubly clamped beam. The method is based on the fact that, for beam deflection much larger than the beam thickness, the axial stretching dominates the deformation in the doubly clamped beam and the doubly clamped beam behaves like a simple plastic hinge. The microscale uniaxial stress–strain curve, together with the cantilever beam experiments, is used to determine the strain gradient effect in Au thin beams. The effect of finite rotation is also discussed.     

Three-Dimensional Analysis of the Stress–Strain State of Inhomogeneous Hollow Cylinders Using Various Approaches

International Applied Mechanics - The stress–strain state of an inhomogeneous hollow cylinder with clamped edges is studied using the three-dimensional elasticity theory. The problem is...     

Post-failure response of impulsively loaded clamped beams

This paper analyses the response of a clamped rigid, perfectly plastic beam subjected to an impulsive velocity loading throughout the span. A critical velocity is determined using a damage mechanics model, beyond which a beam fails at the supports. Attention is focused on the dynamics of the beam after failure. A transient phase of deformation develops after failure and leads to a change of the beam geometry after failure. Other parameters such as the residual kinetic energy and rigid body velocity are also determined. A comparison is made between the clamped case here studied and the simply supported one described elsewhere by the authors.