|Table of Contents|

Citation:
　Guo-yong Jin,Hao Chen,Jin-tao Du,et al.The Influence of Edge Restraining Stiffness on the Transverse Vibrations of Rectangular Plate Structures[J].Journal of Marine Science and Application,2010,(4):393-402.
Click and Copy

The Influence of Edge Restraining Stiffness on the Transverse Vibrations of Rectangular Plate Structures

Info

Title:
The Influence of Edge Restraining Stiffness on the Transverse Vibrations of Rectangular Plate Structures
Author(s):
Guo-yong Jin;  Hao Chen;  Jin-tao Du;  Tie-jun Yang and Wan-you Li
Affilations:
Author(s):
Guo-yong Jin;  Hao Chen;  Jin-tao Du;  Tie-jun Yang and Wan-you Li
College of Power and Energy Engineering, Harbin Engineering University，Harbin 150001, China
Keywords:
vibration;  plate;  double Fourier series;  elastic restraints
分类号:
-
DOI:
-
Abstract:
This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.

References:

Bapat AV, Venkatramani N, Suryanarayan S (1988). Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates. Journal of Sound and Vibration, 120, 127-140.
 Beslin O, Nicolas J (1997). A hierarchical functions sets for very high-order plate bending modes with any boundary conditions. Journal of Sound and Vibration, 202, 633-655.
 Bhat RB (1985). Natural frequencies of rectangular plates using characteristic orthogonal polynomials in the Rayleigh-Ritz method. Journal of Applied Mechanics, 102, 493-499.
 Carmichael TE (1959). The vibration of a rectangular plate with edges elastically restrained against rotation. Quarterly Journal of Mechanics and Applied Mathematics, 12, 29-42.
Cupial P (1997). Calculation of the natural frequencies of composite plates by the Rayleigh-Ritz method with orthogonal polynomials. Journal of Sound and Vibration, 201, 385-387.
Dickinson SM. (1982), Li, EKH. On the use of simply supported plate functions in the Rayleigh – Ritz method applied to the vibration of rectangular plates. Journal of Sound and Vibration , 80, 292-297.
Dickinson SM (1986). On the use of orthogonal polynomials in the Rayleigh – Ritz method for the flexural vibration and buckling of isotropic and orthotropic rectangular plates. Journal of Applied Mechanics, 108, 51-62.
Du JT (2009). Study on modeling methods for structural vibration, enclosed sound field and their coupling system subject to general boundary conditions. Ph.D. thesis, Harbin Engineering University, China. (in Chinese)
Filipich CP (1978). Free vibrations of rectangular plates elastically restrained against rotation and translation simultaneously at the four edges. Journal of Sound and Vibration, 56, 299-302.
Filipich CP, Rosales MB (2000). Arbitrary precision frequencies of a free rectangular thin plate. Journal of Sound and Vibration, 230, 521-539.
Gorman DJ (1980). A comprehensive study of the free vibration of rectangular plates resting on symmetrically distributed uniform elastic edge supports. Journal of Applied Mechanics, 56, 893-899.
Hurlebaus S, Gaul L , Wang JT (2001). An exact series solution for calculating the natural frequencies of orthotropic plates with completely free boundary. Journal of Sound and Vibration, 244, 747-759.
Laura,PAA ,Luisoni LE, Flipich C(1977). A note on the determination of the fundamental frequency of vibration of thin rectangular plates with edges possessing different rotational flexibility coefficients. Journal of Sound and Vibration, 55, 327-333.
Laura PAA (1978). Transverse vibration of a rectangular plate elastically restrained against rotation along three edges and free on the fourth edge. Journal of Sound and Vibration, 59, 355-368.
Laura PAA (1981). Transverse vibrations of rectangular plates with edges elastically restrained against translation and rotation. Journal of Sound and Vibration, 75, 101-108.
Laura PAA (1978). On the effect of different edge flexibility coefficients on transverse vibrations of thin rectangular plates. Journal of Sound and Vibration, 57, 333-340.
Leissa AW (1973). The free vibrations of rectangular plates. Journal of Sound and Vibration, 31, 257-293.
Leissa AW (1993). Vibration of Plates. Acoustical Society of America.
Li WL (2000). Free vibrations of beams with general boundary conditions. Journal of Sound and Vibration, 237, 709-725.
Li WL (2002). Comparison of Fourier sine and cosine series expansions for beams with arbitrary boundary conditions. Journal of Sound and Vibration, 255, 185-194.
Li WL (2004). Vibration analysis of rectangular plates with general elastic boundary supports. Journal of Sound and Vibration, 273, 619-635.
Li WL, Zhang XF, Du JT, Liu ZG (2009). An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports. Journal of Sound and Vibration, 321, 254-269.
Mukhopadhyay M (1979). Free vibration of rectangular plates with edges having different degrees of rotational restraint. Journal of Sound and Vibration, 67, 459-468.
Ramkumar RL, Chen PC, Sanders WJ (1987). Free vibration solution for clamped orthotropic plates using Lagrangian multiplier technique. American Institute of Aeronautics and Astronautics, 25, 146-151.
Warburton GB (1984). Vibrations of rectangular plates with elastically restrained edges. Journal of Sound and Vibration, 95, 537-552.
Warburton GB (1979). Response using the Rayleigh-Ritz method. Journal of Earthquake Engineering and Structural Dynamics, 7, 327-334.
Warburton GB, Edney SL (1984). Vibrations of rectangular plates with elastically restrained edges. Journal of Sound and Vibration, 95, 537-552.
Zhou D (1996). Natural frequencies of rectangular plates using a set of static beam functions in the Rayleigh-Ritz method. Journal of Sound and Vibration, 189, 81-88.
Zhou D (2001). Vibrations of mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method. International Journal of Solids and Structures, 38, 5565-5580.

Memo

Memo:
-
Last Update: 2011-04-29