THE METHOD OF THE RECIPROCAL THEOREM OF FORCED VIBRATION FOR THE ELASTIC THIN RECTANGULAR PLATES(Ⅰ)—RECTANGULAR PLATES WITH FOUR CLAMPED EDGES AND WITH THREE CLAMPED EDGES

In this paper the method of the reciprocal theorem (MRT) is extended to solve the steady state responses of rectangular plater under harmonic disturbing forces. A series of the closed solutions of rectangular plates with various boundary conditions are given and the tables and figures which have practical value are provided.MRT is a simple, convenient and general method for solving the steady stale responses of rectangular plates under various harmonic disturbing forces.The paper contains three parts: (I) rectangular plates with four damped edges and with three clamped edges; (II) rectangular plates with two adjacent clamped edges; (III) cantilever plates.We arc going to publish them one after another.

THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE

With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates.

A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate

A procedure of the method of reverberation ray matrix(MRRM)is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners.A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading.Specifically,the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans,while the constraint condition of two remaining edges may be in any combination of free,simply-supported,and clamped boundary conditions.Furthermore,based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions,some recursive equations(REs)for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases,which promotes the computation efficiency.Several numerical examples are given,and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

Analyses of dynamic characteristics of a fluid-filled thin rectangular porous plate with various boundary conditions

Based on the classical theory of thin plate and Biot theory, a precise model of the transverse vibrations of a thin rectangular porous plate is proposed. The first order differential equations of the porous plate are derived in the frequency domain. By considering the coupling effect between the solid phase and the fluid phase and without any hypothesis for the fluid displacement, the model presented here is rigorous and close to the real materials. Owing to the use of extended homogeneous capacity precision integration method and precise element method, the model can be applied in higher frequency range than pure numerical methods. This model also easily adapts to various boundary conditions. Numerical results are given for two different porous plates under different excitations and boundary conditions.

Integral Transform Methods for Inverse Problem of Heat Conduction with Known Boundary of a Thin Rectangular Object and its Stresses

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D： -a〈xSa; -b〈_y〈b; 0〈z〈h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.