Nonlinear thermo-piezoelectric waves in a cracked nano-beam with non-ideal support

This paper examines the free vibration of a cracked nano-beam with non-ideal support, considering thermo -piezoelectric effects through Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). A new approach models crack propagation in nano-beams using torsion springs within the NSGT framework, incorporating thermo-piezoelectric effects. The governing equations, incorporating non-ideal boundary conditions and related effects, are derived using Hamilton's method. The nano-beam is divided into two segments linked by a massless spring, accounting for additional strain energy and the deflection slope discontinuity induced by the crack. This study examines the effects of non-ideal supports, crack position, piezoelectricity, temperature variations, normal stress and strain, and the nonlocal parameter on the system's dynamic behavior. Comparisons with vibrational existing studies reveal strong agreement, emphasizing the significant impact of these parameters on characteristics.