Autofilter method of class failed

Assuming you only need to autofilter the name field on a sheet and that field is in the same column on all sheets, try

    For Each sh In ActiveWorkbook.Sheets
        If sh.Name <> mainsh.Name Then
                With sh.UsedRange
                    .AutoFilter 4, "*" & search_val & "*"
                    .Offset(1, 1).Resize(, 11).Copy mainsh.Cells(Rows.Count, 2).End(xlUp)(2)
                    .AutoFilter
                End With
        End If
    Next