<p>This paper is devoted to the study of the initial value problem for a nonlinear plate equation in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10190_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^n\times (0,\infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>×</mo> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with initial data in modulation spaces, which includes the Bessel-potential <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10190_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^{s}_p\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>H</mi> <mi>p</mi> <mi>s</mi> </msubsup> </math></EquationSource> </InlineEquation> and Besov spaces <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11118_2025_10190_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(B^{s}_{p,q},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>B</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> <mi>s</mi> </msubsup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> for large regularity indexes <i>s</i>. We derive a set of time-decay estimates for the corresponding linear plate equation on the framework of modulation spaces, and then, we use these results to analyze the existence and asymptotic stability of global solutions of the nonlinear problem.</p>