Nickolas Vlahopoulos

A computational acoustic field reconstruction process based on an indirect boundary element formulation

The objective of the work presented in this paper is to develop a computational capability based on the indirect boundary element method (IBEM) for evaluating appropriate velocity boundary conditions on an assembly of piston type sources in order to recreate a prescribed acoustic field. Information for the acoustic pressure of the original acoustic field at certain field points constitutes the input to the developed process. The velocities on the piston type sources are computed from transfer functions evaluated between the field points where the acoustic pressure of the original field is prescribed and the velocity boundary condition on each element of the generic source. The IBEM is employed for computing the transfer functions in order to accommodate the presence of openings in the model and radiation from both sides of the piston type sources. Simulating the generic source as a thin surface that radiates from both sides eliminates the presence of irregular frequencies in the analysis. A singular value decomposition (SVD) solver is integrated with the IBEM computations in order to evaluate the velocity boundary conditions from the transfer functions. The number of field points where the acoustic pressure is defined can be considerably smaller than the number of elements where the velocity is computed. The solution that demonstrates the smallest magnitude is selected from all possible solutions. An algorithm is also developed for identifying the optimum field points where the acoustic pressure of the original field must be prescribed. The optimum field points are selected from a set of prescribed candidate points. The number of optimum points is considered smaller than the number of elements where the velocity is computed. The properties of the transformation matrix and the quality of the reconstruction depend on the location of the field points. Thus, the selection of the optimum points is based on achieving the highest possible orthogonality among the vectors that comprise the range of the transformation matrix. Several validation and application cases are presented.

Design sensitivity analysis for sequential structural–acoustic problems

Abstract A design sensitivity analysis of a sequential structural–acoustic problem is presented in which structural and acoustic behaviors are de-coupled. A frequency-response analysis is used to obtain the dynamic behavior of an automotive structure, while the boundary element method is used to solve the pressure response of an interior, acoustic domain. For the purposes of design sensitivity analysis, a direct differentiation method and an adjoint variable method are presented. In the adjoint variable method, an adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process for the structural part. The proposed sensitivity results are compared to finite difference sensitivity results with excellent agreement.

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 alternative energy finite element formulation based on incoherent orthogonal waves and its validation for marine structures

An alternate formulation is presented for deriving the governing differential equations of the energy finite element analysis (EFEA). The formulations for interior acoustic spaces and for thin plates are presented. The new formulations are based on considering the acoustic or the flexural response as a summation of incoherent orthogonal waves. The validity of the EFEA is demonstrated by comparing vibration results from very dense conventional finite element models to EFEA results. Actual marine structures are analyzed. Comparison between statistical energy analysis and EFEA is also performed for a vessel that is comprised by both acoustic spaces and structural components. Good agreement is demonstrated between the two methods and the validity of the EFEA is established.

Basic development of hybrid finite element method for midfrequency structural vibrations

The theoretical development of a hybrid finite element method is presented. It combines conventional finite element analysis (FEA) with energy FEA (EFEA) to achieve a numerical solution to midfrequency vibrations. In the midfrequency range a system comprises some members that contain several wavelengths and some members with just a few wavelengths within their lengths. 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. The formulation for one flexural degree of freedom in colinear beams is presented in this fundamental development. The excitation is considered to be applied on a long member, and the response of the entire system is computed. Uncertainty effects are imposed only on the long members of the system. Validation cases for several configurations are presented. They compare closed-form analytical solutions to numerical results produced by the hybrid finite element method. Good correlation is observed for all analyses. The resonant behavior of the short members is captured correctly in the response of the system.

Calculation of Journal Bearing Dynamic Characteristics Including Journal Misalignment and Bearing Structural Deformation

A detailed journal bearing analysis for accurate evaluation of film dynamic characteristics is presented. The new formulation is based on a local perturbation of the oil film at each computational node that captures the important effects of journal misalignment and bearing structural deformation in rotor dynamics and engine NVH applications. The new algorithm is an extension to the classical approach of evaluating film dynamic characteristics based on journal eccentricity perturbation. The governing equations for the oil film pressure, stiffness, and damping are solved using a finite difference approach and their output is validated with numerical results from the literature.

Integration of finite element and boundary element methods for calculating the radiated sound from a randomly excited structure

Abstract In this work, boundary element methods and finite element methods are combined with stochastic analysis to calculate noise radiated from a structure subjected to random excitation. A simply supported plate excited by a turbulent boundary layer flow is used to illustrate the developed technology. The auto and cross power spectral terms of the boundary layer are considered for prescribing the excitation. The development is validated through comparison of the numerical results with analytical results and test data available in literature.

Numerical implementation and applications of a coupling algorithm for structural-acoustic models with unequal discretization and partially interfacing surfaces

Abstract The numerical implementation of a coupled finite element–boundary element algorithm for computing simultaneously the structural vibration and the associated acoustic field and a complete set of validation and application data is presented. The new developments in the coupling algorithm presented in this paper are associated with a capability for unequal mesh density between the structural and the acoustic model, division of both models into interfacing and non-interfacing zones, efficient computation of the coupling matrices, and incorporation of acoustic multiple connection constraints in the coupling computations. Applications are identified in the area of launch vehicle dynamics where a reverberant acoustic environment provides the excitation for computing either noise transmitted through flexible structures, or noise-induced vibration due to acoustic loads. Results and correlation to test data are presented for a fairing and an expansion nozzle of a rocket. Numerical results are also compared to an analytical solution for noise transmitted through a flexible cavity backed plate.

An Elastohydrodynamic Coupling of a Rotating Crankshaft and a Flexible Engine Block

A comprehensive formulation is presented for the dynamics of a rotating flexible crankshaft coupled with the dynamics of an engine block through a finite difference elastohydrodynamic main bearing lubrication algorithm. The coupling is based on detailed equilibrium conditions at the bearings. The component mode synthesis is employed for modeling the crankshaft and block dynamic behavior. A specialized algorithm for coupling the rigid and flexible body dynamics of the crankshaft within the framework of the component mode synthesis has been developed. A finite difference lubrication algorithm is used for computing the oil film elastohydrodynamic characteristics. A computationally accurate and efficient mapping algorithm has been developed for transferring information between a high-density computational grid for the elastohydrodynamic bearing solver and a low-density structural grid utilized in computing the crankshaft and block structural dynamic response. The new computational capability is used to compute the vibratory response of an automotive V6 engine due to combustion and inertia loading.

A basic hybrid finite element formulation for mid-frequency analysis of beams connected at an arbitrary angle

Abstract When beams are connected at an arbitrary angle and subjected to an external excitation, both longitudinal and bending waves are generated in the system. Since longitudinal wavelengths are considerably longer than bending wavelengths in the mid-frequency region, the number of bending wavelengths in the beams is considerably larger than the number of longitudinal wavelengths. In this paper, plannar beams connected at arbitrary angles are considered. The energy finite element analysis (EFEA) is employed for modelling the bending behavior of the beams and the conventional finite element analysis (FEA) is utilized for modelling the longitudinal vibration in the beams. Thus, a basic hybrid FEA formulation is presented for mid-frequency analysis of systems that contain two types of energy. The bending vibration is associated with the long members in the system and the longitudinal vibration is associated with the short members. The long members are considered to have high modal overlap and to contain several wavelengths within their dimension, and uncertainty effects are present. The short members contain a small number of wavelengths, and exhibit a low modal overlap. Due to the low modal overlap the resonant frequencies are spaced far apart in the frequency domain, therefore the short members exhibit resonant or non-resonant behavior depending on the frequency of the excitation. In this work, the bending and the longitudinal vibration within the same beam member are treated as a long and as a short member, respectively. A hybrid joint formulation is developed between long and short members. Power reflection and transmission coefficients are derived for each joint. The distribution of the energy throughout the system demonstrates a strong dependency on the power transfer coefficients. Several systems are analyzed by the hybrid FEA and by analytical solutions, and good correlation between them is observed.