A New Analytical Approach For Free Vibration Of Membrane From Wave Standpoint (original) (raw)
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FREE VIBRATIONS OF NON-HOMOGENEOUS CIRCULAR AND ANNULAR MEMBRANES
Journal of Sound and Vibration, 2001
A non-homogeneous membrane is a membrane that has variable thickness or material density. Several recent publications deal with the axisymmetric and antisymmetric modes of transverse vibration for a composite doubly connected and solid membrane with constant or variable density. In this paper, exact solutions for both the axisymmetric and antisymmetric modes of circular and annular membranes with any piecewise polynomial variation of the density are given using a power series solution. The dynamic problem is solved exactly using a recurrence relationship up to any accuracy desired, by deriving the dynamic sti!ness matrix for circular and annular membrane elements. Many results for linear, parabolic, and cubic variation of complete and annular membranes are solved using the dynamic sti!ness method and presented in the Tables.
International Journal for Numerical Methods in Engineering, 1988
In this paper a boundary element approach is presented to establish the eigenfrequencies and the mode shapes of the free vibrations of flexible membranes with arbitrary shape. The membranes may be of homogeneous, non-homogeneous or composite material, while their boundaries may be fixed or elastically supported. The implementation of the method is mainly based on the development of both a boundary element technique to compute numerically the Green function for the Laplace equation and a numerical procedure to solve domain integral equations using two-dimensional Gauss integration on regions of arbitrary shape. The efficiency of the method presented is demonstrated by applying it to study the free vibrations of membranes consisting of homogeneous, non-homogeneous and composite material, fixed or elastically supported on the boundary, and having various shapes, such as circular, rectangular, triangular, or elliptical, or being L-shaped or of arbitrary shape.
Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
Journal of Sound and Vibration, 2007
The study deals with the generalized solution of the title problem. The free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled. Previous studies by other researchers include straight parallel to the borders and oblique interfaces, and bent ones. The solution is found by means of a direct variational method with a series composed with a complete set of functions. Two alternative sets are explored: trigonometric and power series. Such series are uniformly convergent to the exact solution. The approach is straightforward and very efficient from the computational viewpoint. A determinant-factorization method is employed to automatically eliminate eventual spurious frequencies. The well-known analogy between plates and membranes does not hold in this problem and a demonstration is included. Diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented. Also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included. Comparison between the two alternatives and with other authors' results show excellent agreement. In all cases the computational cost is very low.
FREE VIBRATION ANALYSIS OF FLAT THIN MEMBRANE
This paper presents the vibration analysis for predicating the behavior of flat thin inflatable membrane structure. This is having rectangular shaped with a thickness in millimeter fabricated using the various smart materials. Within structural member, it is subjected to pre-stress rather than bending or moments. The deployable structure has the low weight (minimal mass to achieve high acceleration); large area & durable (easily withstand the temperature changes, micrometeoroid hazards in outer space). The objective of this paper is to optimize the smart material for the space satellite technology so that the light weight inflatable structure attracts in satellite application. The observations show the good agreement between finite element and analytical results.
ON THE NON-LINEAR VIBRATIONS OF A CIRCULAR MEMBRANE
Free axisymmettic vibrations of a stretched circular membrane are studied using a membrane theory consisting of a pair of non-linear partial differential equations coupled between the transverse and radial displacements of the membrane. A systematic perturbation method, in which the amplitude of the transverse displacement is taken as the perturbation parameter, is used to obtain periodic solutions of the non-linear equations. The initial membrane strain enters the problem as a parameter which is allowed to vary over a range of values. A case of self-resonance is encountered when the initial membrane strain approaches some critical values. This self-resonance case is also treated through an appropriate modification of the perturbation method.
Free Vibration Analysis of Pre-stressed Membrane Using Element Free Galerkin Method
Learning and Analytics in Intelligent Systems
Vibration analysis of pre-stressed membrane is studied using element free Galerkin method (EFGM). The discrete system of equations is derived from the governing equations of thin plates with inplane loads, by incorporating the moving least square interpolations into the variational weak form. Essential boundary conditions are applied using scaled transformation method. A bi-axially pre-stressed homogeneous membrane is analyzed using EFGM and results obtained are compared with that obtained from a commercial finite element package and also with the analytical solutions. A convergence study of the frequency obtained using EFGM is compared with that obtained using different element types in finite element method (FEM), for different modes. It is observed that, both FEM and EFGM show satisfactory results in lower modes of vibration, and in higher modes EFGM gives better results compared to FEM.
In-Plane Vibration Analysis of Inflatable Membrane Structure
2015
Purpose– The purpose of this paper is to investigate the geometrically nonlinear effect caused by the different pre-stressed in flat thin membrane structure including static and dynamic condition. The governing equation of motion is generated for free transverse vibration of the two dimensional membrane. The finite element approach is presented in which the membrane has to be pre-stressed to act as a structural element. Design/methodology/approach– This paper presents a simple two dimensional frame formulation to deal with structures undergoing large motions due to dynamic actions including very thin inflatable structures using the method of separation. Findings– The natural frequencies have been investigated for the circular and rectangular shaped flat thin membrane. The result shows that pre-stressed dominates the natural frequency and the oscillations become more and more localized around the region of excitation as the excitation frequency increases for a given pre-stressed valu...