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Frequency Response Function (FRF)

FRF is a transfer function between structural response and input excitation in steady state vibration. FRF varies with excitation frequency. FRF reveals dynamic properties of structures and it is characteristics of the structures. Based on different excitation and response type, FRF has different names in industry such as Accelerance (Inertance), Effective Mass, Mobility, Dynamic Stiffness, etc. FRF is obtained by modal superposition method in LS-DYNA. For results, they can be expressed as frequency curves of amplitude and phase angle (or real and imaginary parts). Several options are available to define the damping (e.g. constant damping, mode dependent damping and Rayleigh damping). In LS-DYNA, FRF can be obtained in single input / multiple output mode. User can also perform mode contribution analysis by choosing the participating modes in modal superposition.

FRF has important application in auto NVH analysis such as energy transfer path study.

Steady State Dynamics (SSD)

SSD calculates steady state vibration response of structures due to periodic loading. The response is dependent on excitation frequency. Loading can be given as concentrated nodal force, pressure, base acceleration and enforced motion, etc. Damping can be defined by several ways. The computational results are saved as binary plot file d3ssd. By running SSD, user can get distribution of the structural dynamic response including magnitude and phase angle under different loading frequencies.

Random Vibration and Fatigue

Random vibration analysis provides PSD and RMS of structural dynamic response, under random excitations. A variety of random excitations can be considered, including base acceleration, concentrated nodal force, pressure, and acoustic waves (such as plane wave, random progressive wave, reverberant wave, turbulent boundary layer). Correlation of the loads can be considered. The loads can be defined as PSD function or time history curve. The pre-stress effect due to mechanical or thermal loading can be considered in the random vibration analysis.

Based on random vibration analysis results, random fatigue feature calculates accumulative damage ratio and expected life of the structures, according to material’s SN fatigue curve and the time of exposure. Furthermore, it provides assessment of the safety of the structure under given loading conditions. Random fatigue analysis can be performed by several methods: Steinberg’s three band method, Dirlik method, Narrow Band method, Wirsching method, Chaudhury & Dover method, Tunna method, and Hancock method. Each of the methods calculates the Probability Density Function (PDF) of each stress level based on different theory and assumption.

The random vibration and random fatigue features have wide application in auto, electronic, civil, mechanical, aerospace and spacecraft, and off-shore industries.

Response Spectrum Analysis

Response spectrum analysis feature calculates the possible peak response of structures under earthquake or other excitations. The response spectrum theory takes into account coupling of structural dynamic properties and the onsite earthquake spectrum. Since the earthquake inertial force is treated as static force, this method is a pseudo static analysis method. A couple of mode combination methods are provided in LS-DYNA (such as SRSS, CQC, NRC Grouping, Double Sum etc.). They consider the coupling of modes under different assumptions. The input spectrum can be given as single point excitation, or multi-point excitations.

The response spectrum analysis feature has important applications on aseismic design and safety evaluation of large scale structures such as bridges, high buildings, nuclear power plants, etc.

Boundary Element Method for Acoustics

A series of boundary element methods (BEM) and simplified boundary integral methods have been implemented to LS-DYNA to run acoustic computation. They include collocation BEM, variational indirect BEM, Rayleigh method, Kirchhoff method and a dual BEM based on Burton-Miller formulation. The boundary element methods in LS-DYNA employ a fast solver technique based on domain decomposition. It provides also the capabilities to run acoustic panel contribution analysis and acoustic transfer vector (ATV). It can be combined with structural time domain FEM analysis, or frequency domain FEM analysis, to study the vibro-acoustic problems. This method can also use user provided vibration data (e.g. nodal velocity) as boundary condition for acoustic computation. In case that the structural surface mesh and the acoustic domain surface mesh are not matching, an interpolation scheme is adopted to map the structural surface vibration data to the acoustic domain surface. By using a special half space fundamental solution, the acoustic BEM in LS-DYNA can consider reflection of acoustic waves on semi-infinite solid surface automatically.

In auto NVH, the BEM acoustic solver can be used to compute the radiated noise due to vehicle’s vibration.

Finite Element Method for Acoustics

The frequency domain FEM acoustic feature is based on the acoustic Helmholtz differential equation and the Galerkin method. It can be used to solve internal acoustic problems. User can choose Hexahedron, Tetrahedron, or Pentahedron elements or use their combinations to model complex acoustic domains such as auto compartment. The FEM acoustic solver can be combined with structural time domain or frequency domain FEM analysis, to solve the vibro-acoustic problems. This method can also use user-provided vibration data as boundary condition.

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