Free vibration analysis of cracked plates using peridynamics

Abstract

In this study, free vibration analysis of cracked plates was performed by using peridynamics. Peridynamics is a new continuum mechanics formulation which is especially suitable for problems including discontinuities such as cracks. A peridynamic Mindlin plate formulation was used and the numerical implementation was done using commercial finite element software, ANSYS. First, the formulation was verified by considering intact and cracked plates and peridynamic solutions were compared against numerical, theoretical and experimental results available in the literature. Once the formulation was verified, the effect of plate thickness, crack size and crack orientation on the natural frequencies were investigated for a centrally cracked plate. It was found that natural frequency values increase as plate thickness increases. On the other hand, increase in crack length decreases the natural frequency values. Moreover, crack orientation also increases natural frequencies for larger cracks. Finally, linear variation of thickness inside the plate causes a tilt of the mode shapes towards the thin side of the plate.

Active Vibration Control and its application to a three-story building

“…Vibration analysis plays a crucial role in fault diagnosis and condition monitoring of machinery and structures. By studying the vibration patterns and trends, faults such as unbalance, misalignment, bearing defects, gear issues, or structural resonances can be detected and diagnosed early, allowing for timely maintenance or corrective actions [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Identificación mediante pruebas no destructivas de los cambios en el espectro de audiofrecuencias en discos de frenos automotrices fracturados

“…Por otro lado, se han analizado los comportamientos dinámicos transitorios no lineales de los sistemas de frenos tanto en el dominio del tiempo como de la frecuencia, investigando las propiedades de vibración de los componentes de los frenos en el proceso de evolución del ruido utilizando la transformada de Hilbert-Huang mejorada [18]. De igual forma, para el estudio de análisis de vibración libre en placas, se ha empleado una formulación peridinámica de placa de Mindlinm, como implementación numérica realizada mediante el software comercial de elementos finitos ANSYS [19]. También se han empleado sensores no auditivos, por ejemplo, una cámara infrarroja ha sido empleada para analizar parámetros mecánicos, como la correlación entre la tensión y la temperatura en compuestos de carbono/ carbono, la variación de temperatura en la pieza de prueba a lo largo del tiempo, la distribución del calor en la fractura y el punto mecánico de máxima tensión [20].…”

A nonperiodic Chebyshev spectral method avoiding penalization techniques for a class of nonlinear peridynamic models

“…The use of integro‐differential equations instead of the spatial differential equations allow the displacement and internal forces to develop singularities (see References 3‐8). Thus, such theory is suitable for modeling the dynamic of discontinuous phenomena, such as cracks and defects (see References 9‐14).…”