Free vibration analysis of membranes using the h–p version of the finite element method

Houmat, A.

doi:10.1016/j.jsv.2004.02.042

Cited by 17 publications

(5 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Different method, particularly h-p version of finite element method, studied Houmat in his paper. He showed results of 10 lowest frequencies of the isosceles triangular membrane, L-shaped membrane [2]. Xian Liu at el published nonlinear vibration analysis of a membrane based on large deflection theory.…”

Section: Introductionmentioning

confidence: 99%

Natural vibration of a membrane hypar in a steel frame

Stulerova

Kapolka²,

Kmeť³

2022

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

This paper deals with a subject of a natural vibration. Modal analysis was performed on a simple membrane structure. Examined model is prepared in FEM software Dlubal. The membrane structure has geometry of a hyperbolic paraboloid or so called hypar. This membrane is basically a technical textile with no bending stiffness so therefore to carry different types of external loads it needs to be pre-stressed. This stress is provided by the edge ropes located in the sleeves around the circumference of the membrane. Stated construction is anchored by 2 anchor rods and 2 actuators to the steel frame which is supported with hinged sliding supports. Natural analysis with an add-on module RF DYNAM Pro was performed. The results of the natural frequencies and mode shapes are obtained which represents first phase of a complex dynamic analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

Natural vibration of a membrane hypar in a steel frame

Stulerova

Kapolka²,

Kmeť³

2022

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…Kang and Lee [5] proposed an analytical expansion basis with sinusoidal functions to obtain the natural frequencies and mode shapes of rectangular membranes. Houmat [6] applied the h-p version of the finite element method to obtain the numerical results for natural frequencies for triangular and Lshaped membranes; shifted Legendre orthogonal polynomials were used during calculation procedure. Wu et al [7] combined the differential quadrature (DQ) method with radial basis functions (RBFs) to analyze the free vibration of arbitrarily shaped membranes.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of Orthotropic Rectangular Membrane Structures Including Modal Coupling

Dong

Zheng

Todd

2018

Journal of Applied Mechanics

View full text Add to dashboard Cite

The membrane structure has been applied throughout different fields such as civil engineering, biology, and aeronautics, among others. In many applications, large deflections negate linearizing assumptions, and linear modes begin to interact due to the nonlinearity. This paper considers the coupling effect between vibration modes and develops the theoretical analysis of the free vibration problem for orthotropic rectangular membrane structures. Von Kármán theory is applied to model the nonlinear dynamics of these membrane structures with sufficiently large deformation. The transverse displacement fields are expanded with both symmetric and asymmetric modes, and the stress function form is built with these coupled modes. Then, a reduced model with a set of coupled equations may be obtained by the Galerkin technique, which is then solved numerically by the fourth-order Runge–Kutta method. The model is validated by means of an experimental study. The proposed model can be used to quantitatively predict the softening behavior of amplitude–frequency, confirm the asymmetric characters of mode space distribution, and reveal the influence of various geometric and material parameters on the nonlinear dynamics.

show abstract

“…In order to solve this problem, local refinement techniques are developed. Many studies, including h‐version FEM, p‐version FEM,(–) hp‐version FEM,(–) and k‐version FEM, have been made. These methods enrich the large‐scale FEs by subdividing them, using a higher order of interpolation functions or combining the above 2 methods.…”

Section: Introductionmentioning

confidence: 99%

A study on the S‐version FEM for a dynamic damage model

Chen

Yue

et al. 2018

Numerical Meth Engineering

View full text Add to dashboard Cite

A mesh superposition technique is developed based on the superimposed version FEM (s-version FEM) for dynamic analysis of damage to structures. In the proposed technique, the concerned area is discretized as a rough global mesh and is overlaid into a fine local mesh of the proposed s-version FEM. To describe the small-scale stress wave, the governing equations for the internal part and boundary of the local region are proposed. The damage evolving constitutive model is substituted into these governing equations to describe the distributions of damage on a small scale. L-shape domain problem, modal, time history, and damage examples are given for the validations. The results show that the proposed s-version FEM can refine a global mesh and accurately describe the damage, stress, and deformation of a concerned area of structure on the small scale. The proposed s-version FEM can be applied to not only a dynamic problem but also a damage analysis of structures. KEYWORDS damage evolving constitutive model, dynamic problem, s-version FEM INTRODUCTIONThe finite element method (FEM) is a popular tool to analyze the dynamic problem of structure. To minimize discretization errors, the simplest way is to refine the finite element (FE) mesh uniformly. However, the computational cost for dynamic analysis of large structures is enormous, although the computational environment has been significantly improved. In order to solve this problem, local refinement techniques are developed. Many studies, including h-version FEM, 1 p-version FEM, 2-6 hp-version FEM, 7-9 and k-version FEM, 10 have been made. These methods enrich the large-scale FEs by subdividing them, using a higher order of interpolation functions or combining the above 2 methods.

show abstract

Free vibration analysis of membranes using the h–p version of the finite element method

Cited by 17 publications

References 7 publications

Natural vibration of a membrane hypar in a steel frame

Natural vibration of a membrane hypar in a steel frame

Nonlinear Vibration of Orthotropic Rectangular Membrane Structures Including Modal Coupling

A study on the S‐version FEM for a dynamic damage model

Contact Info

Product

Resources

About