Free vibration of two elastically coupled rectangular plates with uniform elastic boundary restraints

Curved and Layered Structures

et al. 2016

A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

Section: Kinematic Relations and Stress Resultantsmentioning

confidence: 99%

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Wang

Shi

Curved and Layered Structures

et al. 2016

“…In order to achieve the above requirements, the authors draw on the experience of two elastically coupled rectangular plates [56] to present a coupling spring technique. As one innovation point of present study, three groups of linear and two groups of coupling springs are applied to imitate the kinematic compatibility and physical compatibility conditions of functionally graded panels at the common meridian of = 0 and 2 when a complete shell of revolution is considered.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Mathematical Problems in Engineering

et al. 2017

The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

“…It is worthwhile to note that the interest of researches in this procedure is increasing due to its great simplicity and versatility. Therefore, this simple and direct procedure can be applied to a large number of structures, that is, beams [60][61][62][63], plates [5,[64][65][66][67][68][69][70][71][72][73][74][75][76], shells [77][78][79][80][81][82][83], coupled structures [84][85][86][87][88], and so on. In addition, compared with other methods, the present method can obtain accurate results and circumvent the difficulties of programming complex algorithms for the computer as well as the excessive use of storage and computer time.…”

Section: Introductionmentioning

confidence: 99%

Benchmark Solution for Free Vibration of Moderately Thick Functionally Graded Sandwich Sector Plates on Two-Parameter Elastic Foundation with General Boundary Conditions

Wang

et al. 2017

Shock and Vibration

The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the powerlaw distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.