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Extraction of wave characteristics from wavelet-based spectral finite element formulation

机译：基于小波的谱有限元公式提取波特征

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摘要

In this paper, a spectrally formulated wavelet finite element is developed and is used not only to study wave propagation in 1-D waveguides but also to extract the wave characteristics, namely the spectrum and dispersion relation for these waveguides. The use of compactly supported Daubechies wavelet basis circumvents several drawbacks of conventional FFT-based Spectral Finite Element Method (FSFEM) due to the required assumption of periodicity, particularly for time domain analysis. In this work, a study is done to use the formulated Wavelet-based Spectral Finite Element (WSFE) directly for such frequency domain analysis. This study shows that in WSFE formulation, a constraint on the time sampling rate is paced to avoid spurious dispersion being introduced in the analysis. Numerical experiments are performed to study frequency-dependent wave characteristics (dispersion and spectrum relations) in elementary rod, Euler-Bernoulli and Timoshenko beams. The effect of sampling rate on the accuracy of WSFE solution for both impulse and modulated sinusoidal loading with different frequency content is shown through different examples. In all above cases, comparison with FSFEM are provided to highlight the advantages and limitations of WSFE.
机译：本文开发了一种谱公式化的小波有限元，不仅可用于研究一维波导中的波传播，而且可用于提取波特性，即这些波导的频谱和色散关系。由于需要周期性的假设，特别是对于时域分析，使用紧密支持的Daubechies小波基规避了常规基于FFT的频谱有限元方法（FSFEM）的几个缺点。在这项工作中，进行了一项研究，将配制的基于小波的频谱有限元（WSFE）直接用于这种频域分析。这项研究表明，在WSFE公式中，对时间采样率施加了约束，以避免在分析中引入杂散。进行了数值实验，以研究基本杆，Euler-Bernoulli和Timoshenko梁中与频率有关的波特性（色散和频谱关系）。通过不同的示例显示了采样率对具有不同频率含量的脉冲和调制正弦负载的WSFE解决方案精度的影响。在以上所有情况下，均与FSFEM进行比较以突出WSFE的优点和局限性。

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