We investigate the multistability and bifurcation behavior in thermal vibrational convection through direct numerical simulations, focusing on the effects of varying initial conditions, vibrational Rayleigh number (${\text{Ra}}_{\mathrm{vib}}$), Strouhal number ($\text{St}$), and the aspect ratio ($\mathrm{\Gamma }$) at a fixed Prandtl number ($\text{Pr}=1$). In this study, the Nusselt and Reynolds numbers remain below the threshold for the fully turbulent regime, yet the system displays intricate nonlinear dynamics. By modulating the initial phase of external vibrations, we identify two distinct flow states: a periodic state with consistent large-scale circulation and periodic variations in the Nusselt number [$\text{Nu}\left(t\right)$] and the Reynolds number [$\text{Re}\left(t\right)$], and a chaotic state characterized by unstable flow structures and erratic $\text{Nu}\left(t\right)$ and $\text{Re}\left(t\right)$ fluctuations. The time-averaged Nusselt and Reynolds numbers are higher in the periodic state compared to the chaotic state. Fourier mode decomposition reveals that the periodic state is dominated by the single-roll ($M^{1,1}$) mode, while the chaotic state involves interplay among all modes. Initial velocity fields constructed from Fourier mode basis functions confirm that high-intensity $M^{1,1}$-dominated conditions yield the periodic state, while others produce the chaotic state. Parametric analysis highlights that bifurcations occur predominantly near $\text{St}=1$, where the vibration frequency matches the system's intrinsic timescale, fostering sensitivity to initial disturbances and multistability, and the bifurcation exhibits hysteresis across various ${\text{Ra}}_{\mathrm{vib}}$ and $\mathrm{\Gamma }$. This work elucidates the mechanisms driving flow state transitions in thermal vibrational convection, offering a novel framework for studying unsteady flow multistability with implications for heat transfer and flow control.

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• Bifurcations
• Thermal convection