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Wavelet based spectral finite element for analysis of coupled wave propagation in higher order composite beams

机译：基于小波的谱有限元分析高阶复合光束中的耦合波传播

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In this paper, a spectrally formulated wavelet finite element is developed and is used to study coupled wave propagation in higher order composite beams. The beam element has four degrees of freedom at each node, namely axial and transverse displacements, shear and contraction. The formulation is used to perform both frequency and time domain analysis. The formulation is similar to conventional FFT based Spectral Finite Element (FSFE) except that, here Daubechies wavelet basis is used for approximation in time to reduce the governing PDE to a set of ODEs. The localized nature of the compactly supported Daubechies wavelet basis helps to circumvent several problems associated with FSFE due to the required assumption of periodicity, particularly for time domain analysis. However, in Wavelet based Spectral Finite Element (WSFE), a constraint on the time sampling rate has to be placed to avoid the introduction of spurious dispersion in the analysis. Numerical experiments are performed to study spectrum and dispersion relation. In addition, the wave propagation in finite length structures due to broad band impulse loading is studied to bring out the higher order effects. Simultaneous existence of various propagating modes are graphically captured using modulated sinusoidal pulse excitation. In all the cases comparison are provided with FSFE.
机译：本文开发了一种谱公式化的小波有限元，并用于研究高阶复合光束中的耦合波传播。梁单元在每个节点处具有四个自由度，即轴向和横向位移，剪切和收缩。该公式用于执行频域和时域分析。该公式类似于传统的基于FFT的频谱有限元（FSFE），不同之处在于，此处使用Daubechies小波基进行时间近似，以将控制PDE减少为一组ODE。紧密支持的Daubechies小波基的局部性质有助于规避与FSFE相关的一些问题，这是由于需要周期性的假设，特别是对于时域分析而言。但是，在基于小波的频谱有限元（WSFE）中，必须对时间采样率施加约束，以避免在分析中引入杂散。进行数值实验以研究光谱和色散关系。此外，研究了由于宽带脉冲负载而在有限长度结构中传播的波，以产生更高阶的效应。使用调制正弦脉冲激励以图形方式捕获各种传播模式的同时存在。在所有情况下，FSFE均提供了比较。

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