Energy Finite Element Analysis Formulation Research Articles

Energy finite element formulation for unbound acoustic domains

The Energy Finite Element Analysis (EFEA) method has been developed for conducting structural-acoustics simulations for complex vehicles at mid-to-high frequencies where conventional finite element methods are no longer computationally efficient. In applications where exterior heavy fluid loading effects must be included in the model, these effects are currently accounted in the EFEA formulation through an added mass and a radiation damping approach. This is suitable when there is an interest in computing the vibration of the structure and the total radiated power emitted in the exterior fluid. A new formulation for modeling the exterior fluid explicitly with energy finite elements is presented. There are three main components in the new development: deriving the differential equation; solving it numerically using a finite element approach; and introducing infinite finite elements in order to represent the non-reflective conditions at the outer domain of a finite element model. In this presentation, the technical aspects associated with the main elements of the new EFEA formulation for exterior non-reverberant acoustic domains will be discussed. Comparisons with analytical closed form solutions for validating the new developments and their numerical implementation will be presented.

Power Transfer Coefficients between Two 3D Semi-Infinite Solids in EFEA Formulation

The energy finite element analysis (EFEA) is more effective for analyzing high frequency vibration problem compared to the traditional finite element method (FEM). When applying the EFEA to complicated structures, it is necessary to obtain power transfer coefficients at structural joints. This paper proposes the theoretical formulations of computing power transfer coefficients between two 3D semi-infinite solids, and demonstrates the validation of the developed theoretical formulations through two examples with different incident waves: dilatational wave and distortional wave.

Energy Finite Element Analysis Developments for Vibration Analysis of Composite Aircraft Structures

The Energy Finite Element Analysis (EFEA) has been utilized successfully for modeling complex structural-acoustic systems with isotropic structural material properties. In this paper, a formulation for modeling structures made out of composite materials is presented. An approach based on spectral finite element analysis is utilized first for developing the equivalent material properties for the composite material. These equivalent properties are employed in the EFEA governing differential equations for representing the composite materials and deriving the element level matrices. The power transmission characteristics at connections between members made out of non-isotropic composite material are considered for deriving suitable power transmission coefficients at junctions of interconnected members. These coefficients are utilized for computing the joint matrix that is needed to assemble the global system of EFEA equations. The global system of EFEA equations is solved numerically and the vibration levels within the entire system can be computed. The new EFEA formulation for modeling composite laminate structures is validated through comparison to test data collected from a representative composite aircraft fuselage that is made out of a composite outer shell and composite frames and stiffeners. NASA Langley constructed the composite cylinder and conducted the test measurements utilized in this work.

Energy finite-element analysis of the NASA aluminum test-bed cylinder

A formulation was developed in the energy finite-element analysis (EFEA) for modeling the vibration of cylindrical structures with periodic axial and circumferential stiffeners. Appropriate power transfer coefficients are computed from the values of the propagation constants. The joint matrices of the EFEA formulation are computed based on the power transfer coefficients derived from periodic structure theory. EFEA analyses are performed for the NASA aluminum test-bed cylinder and simulations are compared to experiments. Excitation is applied on the test-bed cylinder by four shakers and the vibration is measured at 40 bays formed by axial and circumferential stiffeners. The EFEA results are compared successfully to test data between the 1/3 octave bands of 315 and 6300 Hz. [Work sponsored by NASA Langley Structural Acoustics Branch.]

A vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation

An energy finite element analysis (EFEA) formulation for high frequency vibration analysis of stiffened plates under heavy fluid loading is presented. The added mass effect and the radiation dampin...

A vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation

An energy finite element analysis (EFEA) formulation for high frequency vibration analysis of stiffened plates under heavy fluid loading is presented. The added mass effect and the radiation damping effect due to the fluid loading are incorporated in the derivation of the EFEA governing differential equations. In addition, the fluid loading effect and the presence of a stiffener are accounted when computing the power transfer coefficients through plate/stiffener junctions. The effect of the fluid on power transfer coefficients of a plate/stiffener junction is analyzed and discussed. The new formulation is validated by comparing EFEA results to solutions by very dense finite element models for several plate/stiffener assemblies, which include two coplanar plates connected by a stiffener, two plates connected at a 45° angle by a stiffener, and a section of a typical naval structure. All plates are considered in contact with dense fluid from one side. The energy ratios between the receiving sections of the plates and the excited sections of the plates are computed and good correlations are observed between the EFEA and the very dense FEA results.

An energy finite element formulation for high-frequency vibration analysis of externally fluid-loaded cylindrical shells with periodic circumferential stiffeners subjected to axi-symmetric excitation

A hybrid method is developed for predicting the high-frequency vibration response of fluid-loaded cylindrical shells with periodic circumferential stiffeners. In this method, the cylindrical shell is modeled using the Energy Finite Element Analysis (EFEA) method which includes added mass and radiation effects due to the surrounding exterior fluid medium. The joint matrices of the EFEA formulation at the location of the periodic stiffeners are computed based on Periodic Structure (PS) theory. Thus, the periodicity effects such as pass/stop characteristics are captured in the EFEA solution. The hybrid EFEA-PS method is used to analyze the vibration of a fluid-loaded axisymmetric cylindrical shell with periodic circumferential stiffeners. The flexural energy stored in each periodic section is computed. The results are compared with the solution produced by a very dense axisymmetric Finite Element (FE) model with infinite finite elements for the fluid domain. The good correlation indicates that the new hybrid method captures properly both the heavy fluid effects of the exterior fluid medium and the periodicity characteristics due to periodic stiffeners.

High-frequency vibration analysis of thin elastic plates under heavy fluid loading by an energy finite element formulation

An energy finite element analysis (EFEA) formulation for computing the high frequency behavior of plate structures in contact with a dense fluid is presented. The heavy fluid loading effect is incorporated in the derivation of the EFEA governing differential equations and in the computation of the power transfer coefficients between plate members. The new formulation is validated through comparison of EFEA results to classical techniques such as statistical energy analysis (SEA) method and the modal decomposition method for bodies of revolution. Good correlations are observed and the advantages of the EFEA formulation are identified.

An approach for modeling spot-welded joints in an energy finite element formulation

An emerging simulation technology is the energy finite element analysis (EFEA) [P. Cho, ‘‘Energy Flow Analysis of Coupled Structures,’’ Ph.D. dissertation, Purdue University, 1993; O. M. Bouthier and R. J. Bernhard, ‘‘Models of space averaged energetics of plates,’’ AIAA J. 30(3) (March 1992)]. In order for this method to be applicable to automotive structures it is important that it be suitable for modeling spot-welded joints. This work presents a development effort in computing the energy transmitted through spot-welded joints, and utilizing the information in an EFEA formulation. It is based on principles utilized for deriving coupling loss factors for statistical energy analysis (SEA) from conventional finite element models [C. Simmons, ‘‘Structure-borne sound transmission through plate junctions and estimates of SEA coupling loss factors using the finite element method,’’ J. Sound Vib. 144(2), 215–227 (1991)]. There are two components to the new development: (i) Deriving numerically information about the energy ratio between spot-welded members. (ii) Incorporating information for the energy transferred between members in the EFEA analysis. Technical information and comparison of numerical results to test data will be presented. [Work supported by Automated Analysis Corp. and Ford Motor Co.]