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A hybrid Finite Element Analysis (hybrid FEA) formulation has been developed in the past for computing the mid-frequency vibration of systems that contain one type of energy. The hybrid FEA is based on characterizing as long members in a system all the members that contain a large number of wavelengths within their dimension. All the remaining members are considered as short. The Energy Finite Element Analysis (EFEA) is employed for modeling the behavior of the long members, while the conventional FEA method is utilized for modeling the short members. In this paper the hybrid FEA formulation is extended to plate structures that are spot-welded to a frame comprised by tubular members. The new formulation is validated by comparing the hybrid FEA solution to results produced by very dense conventional FEA models in the mid-frequency range.

A new development in the area of the hybrid Finite Element Analysis (hybrid FEA) is presented. The hybrid FEA method combines the conventional FEA method with energy FEA (EFEA) for analysis of systems that contain both flexible and stiff members, and is suitable for mid-frequency computations. A formulation for analyzing flexible plates spot-welded to stiff beams when the excitation is applied on the stiff members is developed. Conventional FEA models are employed for modeling the behavior of the stiff members in a system. Appropriate damping elements are introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones.

Assessing the dynamic performance of multilayer plates subjected to impulsive loading is of interest for identifying configurations that either absorb energy or transmit the energy in the transverse directions, thereby mitigating the through-thickness energy propagation. A reduced-order modeling approach is presented in this paper for rapidly evaluating the structural dynamic performance of various multilayer plate designs. The new approach is based on the reverberation matrix method (RMM) with the theory of generalized rays for fast analysis of the structural dynamic characteristics of multilayer plates. In the RMM model, the waves radiated from the dynamic load are reflected and refracted at each interface between layers, and the waves within each layer are transmitted with a phase lag. These two phenomena are represented by the global scattering matrix and the global phase matrix, respectively.

In applications of the Energy Finite Element Analysis (EFEA) there is an increasing need for developing comprehensive models with a large number of elements which include both structural and interior fluid elements, while certain parts of the structure are considered to be exposed to an external fluid loading. In order to accommodate efficient computations when using simulation models with a large number of elements, joints, and domains, a substructuring computational capability has been developed. The new algorithm is based on dividing the EFEA model into substructures with internal and interface degrees of freedom. The system of equations for each substructure is assembled and solved separately and the information is condensed to the interface degrees of freedom. The condensed systems of equations from each substructure are assembled in a reduced global system of equations. Once the global system of equations has been solved the solution for each substructure is pursued.

A formulation that accounts for manufacturing variability in the analysis of structural/acoustic systems is presented. The methodology incorporates the concept of fast probability integration with finite element (FEA) and boundary element analysis (BEA) for producing the probabilistic acoustic response of a structural/acoustic system. The advanced mean value method is used for integrating the system probability density function. FEA and BEA are combined for producing the acoustic response that constitutes the performance function. The probabilistic acoustic response is calculated in terms of a cumulative distribution function. The new methodology is used to illustrate the difference between the results from a probabilistic analysis that accounts for manufacturing uncertainty, and an equivalent deterministic simulation through applications. The probabilistic computations are validated by comparison to Monte Carlo simulations.

A hybrid finite element formulation for analyzing flexible plates connected to stiff frame was developed. The excitation was considered to be applied on the stiff members. Conventional FEA models were employed for modeling the behavior of the stiff members in a system. Appropriate damping elements were introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones. Once the vibration of the stiff members and the amount of power dissipated at the damping elements was identified, an EFEA analysis was performed in order to determine the amount of vibrational energy in the flexible members. The hybrid FEA is applied to a Body-In-White (BIW). The results of the hybrid FEA are compared with results from very dense conventional finite element analyses.

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.

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.

The Hybrid Finite Element Analysis (HFEA) method is based on combining conventional Finite Element Analysis (FEA) with analytical solutions and energy methods for mid-frequency computations. The method is appropriate for computing the vibration of structures which are comprised by stiff load bearing components and flexible panels attached to them; and for considering structure-borne loadings with the excitations applied on the load bearing members. In such situations, the difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the HFEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior of the panels.

The theoretical development of a hybrid finite element method is presented. It combines conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) in order to achieve a numerical solution to mid-frequency vibrations. In the mid-frequency range a system is comprised by some members that contain several wavelengths and some members that contain a small number of wavelengths. The former are considered long members and they are modeled by the EFEA. The latter are considered short and they are modeled by the FEA. The new formulation is based on deriving appropriate interface conditions at the joints between sections modeled by the EFEA and the FEA methods. Since the work presented in this paper constitutes a fundamental step in the development of a hybrid method for mid-frequency analysis, the formulation for one flexural degree of freedom in co-linear beams is presented.

Vehicle design is a complex process requiring interactions and exchange of information among multiple disciplines such as fatigue, strength, noise, safety, etc. Simulation models are employed for assessing and potentially improving a vehicle's performance in individual technical areas. Challenges arise when designing a vehicle for improving mutually competing objectives, satisfying constraints from multiple engineering disciplines, and determining a single set of values for the vehicle's characteristics. It is of interest to engage simulation models from the various engineering disciplines in an organized and coordinated manner for determining a design configuration that provides the best possible performance in all disciplines. The multi-discipline design process becomes streamlined when the simulation methods integrate well with finite element or computer aided design models.

The Indirect Boundary Element Analysis is employed for developing a computational pass-by noise simulation capability. An inverse analysis algorithm is developed in order to generate the definition of the main noise sources in the numerical model. The individual source models are combined for developing a system model for pass-by noise simulation. The developed numerical techniques are validated through comparison between numerical results and test data for component level and system level analyses. Specifically, the source definition capability is validated by comparing the actual and the computationally reconstructed acoustic field for an engine intake manifold. The overall pass-by noise simulation capability is validated by computing the maximum overall sound pressure level for a vehicle under two separate driving conditions.

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.

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.

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 is based on combining conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) for mid-frequency computations. The difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the Hybrid FEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior. The excitation is considered to be applied on the conventional FEA model and the vibration analysis is conducted. The power flow through the dynamic impedance elements is computed and applied as excitation to the EFEA model of the flexible panels. The EFEA analysis computes the vibration of the flexible panels.

In this paper an algorithm is developed for combining finite element analysis and boundary element techniques in order to compute the noise radiated from a panel subjected to boundary layer loading. The excitation is presented in terms of the auto and cross power spectral densities of the fluctuating wall pressure. The structural finite element model for the panel is divided into a number of sub-panels. A uniform fluctuating pressure is applied as excitation on each sub-panel separately. The corresponding vibration is computed, and is utilized as excitation for an acoustic boundary element analysis. The acoustic response is computed at any data recovery point of interest. The relationships between the acoustic response and the pressure excitation applied at each particular sub-panel constitute a set of transfer functions.

The Energy Finite Element Analysis (EFEA) has been developed for evaluating the vibro-acoustic behavior of complex systems. In the past EFEA results have been compared successfully to measured data for Naval, automotive, and aircraft systems. The main objective of this paper is to present information about the process of developing EFEA models for two configurations of a business jet, performing analysis for computing the vibration and the interior noise induced from exterior turbulent boundary layer excitation, and discussing the correlation between test data and simulation results. The structural EFEA model is generated from an existing finite element model used for stress analysis during the aircraft design process. Structural elements used in the finite element model for representing the complete complex aircraft structure become part of the EFEA structural model.

A hybrid finite element method (hybrid FEA) for computing mid-frequency vibrations for systems that contain one energy type is presented. In the mid-frequency range a system is comprised of both long and short members. Long members contain several wavelengths and they are modeled by the Energy Finite Element Analysis (EFEA). Short members contain a small number of wavelengths and they are modeled by the Finite Element Analysis (FEA). External excitation can be applied on long and/or on short members. Systems are analyzed by both the hybrid FEA method and an analytical solution in order to validate the hybrid FEA developments. The interaction among long and short members is defined by a set of equations between the EFEA and the FEA primary variables at the interfaces between long and short members. The numerical systems of equations for the long and the short members, and the interface equations are solved simultaneously.

In order to develop confidence in numerical models which are used for automotive crash simulations, results are compared with test data. Modeling assumptions are made when constructing a simulation model for a complex system, such as a vehicle. Through a thorough understanding of the modeling assumptions an appropriate set of variables can be selected and adjusted in order to improve correlation with test data. Such a process can lead to better modeling practices when constructing a simulation model. Comparisons between the time history of acceleration responses from test and simulations are the most challenging. Computing accelerations correctly is more difficult compared to computing displacements, velocities, or intrusion levels due to the second order differentiation with time. In this paper a methodology for enabling the update of a simulation model for improved correlation is presented.