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Stiffened panels are encountered in many engineering systems since the stiffeners comprise the mechanism which provides support and rigidity to the panel's skin. Either a mechanical excitation or an acoustic load can be applied on a stiffened panel creating vibration that is transmitted in all panel components. Mechanical excitation tends to be localized in nature, originating from operating machinery mounted on the panel, while the acoustic excitation tends to be distributed over the entire panel, since it typically originates from an external acoustic source which creates an acoustic field impinging on the entire panel. In the Energy Finite Element Analysis (EFEA) various degrees of fidelity are possible when modeling the response of a stiffened panel. In this paper, the theoretical background and the corresponding implications associated with each alternative modeling approach are presented first.

In order to be effective and maximize the weight and cost savings when designing for noise and vibration attributes, the structural-acoustics design effort must be concurrent with the efforts of other engineering disciplines (i.e. durability, crashworthiness, etc.). In this manner, it will be possible to account for the effects of structural changes across disciplines and improve the NVH performance while the structure is being configured rather than attempting to improve NVH characteristics after the structural design has been completed.

The hybrid FEA method combines the conventional FEA method with the energy FEA (EFEA) for computing the structural vibration in vehicle structures when the excitation is applied on the load bearing stiff structural members. Conventional FEA models are employed for modeling the behavior of the stiff members in the vehicle. In order to account for the effect of the flexible members in the FEA analysis, appropriate damping and spring/mass elements are introduced at the connections between stiff and flexible members. Computing properly the values of these damping and spring/mass elements is important for the overall accuracy of the computations. Utilizing in these computations the analytical solutions for the driving point impedance of infinite or semi-infinite members introduces significant approximations.

The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration and the interior noise level of complex structural-acoustic systems by solving governing differential equations with energy densities as primary variables. Results from EFEA simulations have been compared successfully with test results for Naval, automotive, and aircraft structures. The Energy Boundary Element Analysis (EBEA) has been developed for exterior acoustic computations using the acoustic energy density as primary variable in the formulation. EBEA results have been compared successfully to the test results in the past for predicting the exterior acoustic field around a vehicle structure due to external noise sources. In this paper, the EBEA and EFEA methods are combined for predicting the interior noise levels in a vehicle due to exterior acoustic sources.

The Energy Boundary Element Analysis (EBEA) has been utilized in the past for computing the exterior acoustic field at high frequencies (above ∼400Hz) around vehicle structures and numerical results have been compared successfully to test data [1, 2 and 3]. The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration of complex structures at high frequencies and validations have been presented in previous publications [4, 5]. In this paper the EBEA is utilized for computing the acoustic field around a vehicle structure due to external acoustic noise sources. The computed exterior acoustic field comprises the excitation for the EFEA analysis. Appropriate loading functions have been developed for representing the exterior acoustic loading in the EFEA simulations, and a formulation has been developed for considering the acoustic treatment applied on the interior side of structural panels.

An energy finite element analysis (EFEA) formulation is developed for predicting high frequency vibration response of cylindrical shells with periodically axial and circumferential stiffeners. In this method, the structure is modeled using EFEA method. The power transfer coefficients, employed in the joint matrices of the EFEA formulation at the location of the periodic stiffeners are computed based on Periodic Structure (PS) theory. Results from the new simulation method are compared to experimental data for the vibration response of a periodically circumferentially and axially stiffened cylinder (NASA aluminum testbed cylinder). The observed good correlation indicates that the new EFEA formulation captures properly the periodic characteristics for both the axial stringers and ring stiffeners.

The Energy Finite Element Analysis(EFEA) is a recent development for high frequency vibro-acoustic analysis, and constitutes an evolution in the area of high frequency computations. The EFEA is a wave based approach, while the SEA is a modal based approach. In this paper the similarities in the theoretical development of the two methods are outlined. The main scope of this paper is to establish the validity of the EFEA by analyzing several complex structural-acoustic systems. The EFEA solutions are compared successfully to SEA results and to solutions obtained from extremely dense conventional FEA models.