J.M. Dunsdon

Free vibration analysis of coplanar sandwich panels

Abstract A comprehensive vibration study of simple three-layer sandwich plates, based on the h - p version of the finite element method, is presented. The methodology incorporates a new set of trigonometric functions to provide the element p -enrichment—these functions exhibit good convergence characteristics, and enable the medium frequency regime to be explored at minimum computational expense. Elements may be joined together to model more general coplanar assemblies, and the trade-off between h -division and p -enrichment is discussed. Excellent agreement has been found with the work of other investigators, and new results are presented for (i) a completely free, symmetric section, rectangular sandwich panel whose core thickness is varied as a function of the overall plate thickness whilst the mass per unit area is maintained constant, and (ii) a cantilevered, T-planform, asymmetric section, sandwich plate. The results from this latter case are compared with those forthcoming from a proprietary finite element package; outstanding agreement is obtained, and a reduction of over 30% in the total number of degrees of freedom is demonstrated.

Free and forced vibration analysis of thin, laminated, cylindrically curved panels

A comprehensive vibration study of thin, laminated, cylindrically curved shell panels (based on the shell theory of Love with a modification by Arnold and Warburton) is conducted by using the h-p version of the finite-element method (FEM). Polynomially enriched stiffness and mass matrices are derived from classical shell theory using Symbolic Computing, and then stored in algebraic form for a single, generic element. A number of such elements may then be combined to form the global stiffness and mass matrices for a more general co-axial and/or co-circumferential assembly. Any of the classical edge conditions, or point corner supports, may be accommodated in the analysis; forcing may be applied through one or more point forces acting normal to the shell surface. Excellent agreement has been found with the work of other investigators, and some new results are presented for a multiply supported curved panel made from the aluminium-glass-fibre hybrid GLARE. The h-p method is shown, by example, to offer an efficient means of conducting typical repetitive sensitivity analyses, such as varying the fibre orientation and the stacking sequences of a given panel.

Free vibration analysis of thin coplanar rectangular plate assemblies — Part I: theory, and initial results for specially orthotropic plates

Abstract This paper communicates a new h - p finite element methodology for studying the free vibration of generally orthotropic coplanar plate assemblies. In Part I, hierarchically enriched stiffness and mass matrices of a generally orthotropic rectangular plate element are derived using symbolic computing. These may then be combined, via a special connectivity matrix, to form the global stiffness and mass matrices of a more general coplanar plate structure. A variety of different boundary conditions may be accommodated in the model by specifying whether an element edge is simply supported, clamped, free, or whether an element corner is point supported. The natural frequencies, and the associated normal modes, are then sought from the resulting matrix-eigenvalue problem. Detailed comparisons with the work of other investigators confirm the validity of the methodology for specially orthotropic plates; the validation for generally orthotropic plates, and plate assemblies, is addressed in Part II.

FREE-VIBRATION ANALYSIS OF THIN RECTANGULAR LAMINATED PLATE ASSEMBLIES USING THE H-P VERSION OF THE FINITE-ELEMENT METHOD

A vibration study of thin, laminated plate assemblies is conducted by using the h-p version of the finite element method (FEM). Polynomially-enriched stiffness and mass matrices are derived from classical plate theory using Symbolic Computing, and then stored in algebraic form for a single, generic element. A number of such elements may then be combined to form the global stiffness and mass matrices for a more general planar assembly. Any of the classical edge conditions, or point corner supports, may be accommodated in the analysis, and the natural frequencies are sought from a standard matrix-eigenvalue problem. Excellent agreement has been found with the work of other investigators. The h-p method is shown, by example, to offer considerable savings in computational effort when compared with the standard h-version of the FEM. One further development of the method is presented which illustrates how it might form the basis of a condition monitoring measuring technique based on natural frequency shifts arising from non-propagating, through-the-thickness, crack damage.

Free vibration analysis of thin coplanar rectangular plate assemblies Part II: further results for generally orthotropic plates

In Part II of this paper, the theme that was introduced in Part I is developed through a series of validation exercises for generally orthotropic rectangular plates. Excellent agreement is found with the work of other investigators, and the efficacy of the h-p methodology is established. Some new results are presented for the natural frequencies and modes of a completely free square, generally orthotropic plate, which should serve as a useful benchmark test for other investigators. The paper is concluded with detailed vibration analyses of both a partially supported rectangular, holed plate with a corner cut-out, and an exaggerated J-planform plate clamped around its perimeter. These latter two examples vividly illustrate the unusually diverse and complex manner in which such irregular planform plates vibrate, and the need for a comprehensive analysis technique to predict accurately their dynamic characteristics.