A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

Abstract

To study the free in-plane vibration for the orthotropic circular, annular and sector plates with general boundary conditions, a modified Fourier-Ritz approach is developed. In this approach, several auxiliary closed-form functions are added to the standard Fourier cosine series to obtain a robust function. The introduction of these auxiliary functions can eliminate all the potential discontinuities of the original displacement function and its derivatives in whole domain and then effectively improve the convergence of the results. All the displacements are expressed with the modified Fourier series expansion and the arbitrary boundary conditions and the appropriate continuity conditions along the radial edges are realized by introducing the artificial boundary spring technique and artificial coupling spring technique. In addition, the Ritz procedure based on the energy functions of the plates is adopted to obtain the accurate solution since the constructed displacement field is adequately smooth in the whole solution domain. By numerical examples involving the plates of various shapes and with different boundary conditions, the reliability, accuracy and versatility of the current method get fully demonstrated. On this basis, some new results for the free in-plane vibration problem of orthotropic circular, annular and sector plates with

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

“…Five types of spring are used to describe the boundary conditions of laminated foundation plate, which are linear springs ( , V , and ) and rotational springs ( , ), respectively. The arbitrary boundary conditions can be realized by setting the stiffness values of the five different springs [46][47][48][49][50]. For instance, the free boundary condition can be easily gained when the spring stiffness values on the four edges are zero.…”

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

“…In the practical application, the Pasternak model (also referred to as the two-parameter model) [24][25][26] is widely used to describe the mechanical behavior of the foundation, in which the wellknown Winkler model [27] is a special case. In addition, the boundary condition may not always be classical case in reality, and a variety of possible boundary conditions including classical boundary conditions, elastic boundary restraints, and the combinations of two or more conditions may be encountered [6][7][8][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Based on the open published paper, we can know that merely Zhou et al [48,49] extended the Chebyshev-Ritz method to study the free vibration characteristics of rectangular thick plates and thick circular plates resting on elastic foundations, respectively.…”

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

“…The method has been subsequently exploited to determine the vibration behaviors of structures [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Recently, a new method of Fourier-Ritz approach was proposed by Jin et al [49], based on the improved Fourier series method to analyze the free vibration of laminated functionally graded shallow shells with general boundary conditions.…”