This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates. 相似文献
This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential
difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential
equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement
functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step
integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at
the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for
electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined.
These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into
those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of
material inhomogeneity on the elastic and electric fields is discussed.
Supported by the National Natural Science Foundation of China (Grant Nos. 10472102 and 10432030) and the Specialized Research
Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335107) 相似文献
The -th local cohomology module of a finitely generated graded module over a standard positively graded commutative Noetherian ring , with respect to the irrelevant ideal , is itself graded; all its graded components are finitely generated modules over , the component of of degree . It is known that the -th component of this local cohomology module is zero for all > 0$">. This paper is concerned with the asymptotic behaviour of as .
The smallest for which such study is interesting is the finiteness dimension of relative to , defined as the least integer for which is not finitely generated. Brodmann and Hellus have shown that is constant for all (that is, in their terminology, is asymptotically stable for ). The first main aim of this paper is to identify the ultimate constant value (under the mild assumption that is a homomorphic image of a regular ring): our answer is precisely the set of contractions to of certain relevant primes of whose existence is confirmed by Grothendieck's Finiteness Theorem for local cohomology.
Brodmann and Hellus raised various questions about such asymptotic behaviour when f$">. They noted that Singh's study of a particular example (in which ) shows that need not be asymptotically stable for . The second main aim of this paper is to determine, for Singh's example, quite precisely for every integer , and, thereby, answer one of the questions raised by Brodmann and Hellus.
Let R be a subring ring of Q. We reserve the symbol p for the least prime which is not a unit in R; if R ?Q, then p=∞. Denote by DGLnnp, n≥1, the category of (n-1)-connected np-dimensional differential graded free Lie algebras over R. In [1] D. Anick has shown that there is a reasonable concept of homotopy in the category DGLnnp. In this work we intend to answer the following two questions: Given an object (L(V), ?) in DGLn3n+2 and denote by S(L(V), ?) the class of objects homotopy equivalent to (L(V), ?). How we can characterize a free dgl to belong to S(L(V), ?)? Fix an object (L(V), ?) in DGLn3n+2. How many homotopy equivalence classes of objects (L(W), δ) in DGLn3n+2 such that H*(W, d′)?H*(V, d) are there? Note that DGLn3n+2 is a subcategory of DGLnnp when p>3. Our tool to address this problem is the exact sequence of Whitehead associated with a free dgl. 相似文献
One of the standard axioms for semiorders states that no three-point chain is incomparable to a fourth point. We refer to asymmetric relations satisfying this axiom as almost connected orders or ac-orders. It turns out that any relation lying between two weak orders, one of which covers the other for inclusion, is an ac-order (albeit of a special kind). Every ac-order is bracketed in a natural way by two weak orders, one the maximum in the set of weak orders included in the ac-order, and the other minimal, but not necessarily the minimum, in the set of weak orders that include the ac-order. The family of ac-orders on a finite set with at least five elements is not well graded (in the sense of Doignon and Falmagne, 1997). However, such a family is both upgradable and downgradable, as every nonempty ac-order contains a pair whose deletion defines an ac-order on the same set, and for every ac-order which is not a chain, there is a pair whose addition gives an ac-order. 相似文献