<p>This paper investigates the initial-boundary value problem for a biharmonic wave equation involving an <i>r</i>-Laplace damping and a superlinear source, given by <Equation ID="Equ45"> <EquationSource Format="TEX">\( u_{tt}+\Delta ^{2}u-\textrm{div}(|\nabla u_{t}|^{r-2}\nabla u_{t})-\Delta u_{t}=|u|^{p-2}u, \ (x,t)\in \Omega \times (0,T), \)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <msub> <mi>u</mi> <mrow> <mi mathvariant="italic">tt</mi> </mrow> </msub> <mo>+</mo> <msup> <mi mathvariant="normal">Δ</mi> <mn>2</mn> </msup> <mi>u</mi> <mo>-</mo> <mrow> <mtext>div</mtext> <mo stretchy="false">(</mo> <mo stretchy="false">|</mo> <mi mathvariant="normal">∇</mi> </mrow> <msub> <mi>u</mi> <mi>t</mi> </msub> <msup> <mrow> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>r</mi> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mi mathvariant="normal">∇</mi> <msub> <mi>u</mi> <mi>t</mi> </msub> <mrow> <mo stretchy="false">)</mo> <mo>-</mo> <mi mathvariant="normal">Δ</mi> </mrow> <msub> <mi>u</mi> <mi>t</mi> </msub> <mo>=</mo> <msup> <mrow> <mo stretchy="false">|</mo> <mi>u</mi> <mo stretchy="false">|</mo> </mrow> <mrow> <mi>p</mi> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mi>u</mi> <mo>,</mo> <mspace width="4pt" /> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>∈</mo> <mi mathvariant="normal">Ω</mi> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </Equation>with Navier boundary conditions. We establish the well-posedness of weak solutions using the Faedo-Galerkin method and the Banach contraction mapping principle. For critical and subcritical initial energy cases within the potential well framework, the global existence of solutions and energy decay estimates are obtained. Additionally, under certain conditions on <i>p</i> and <i>r</i>, the lower bound of the blow-up time is obtained.</p>